64 IS16 Abstracts

86 Pages·2016·0.75 MB·English

64 IS16 Abstracts
IP1
Nonconformist Image Processing with the Graph
Thomas Strohmer
Laplacian Operator
Universityof California,Davis
Departmentof Mathematics
The key building blocks of modern image processing are
[email protected]
two-fold: a measure of affinity between pixels; and an op-
erator that turns these affinities into filters that can ac-
complishavarietyofusefultasks. Examplesoftheaffinity
IP4
measurearemany,includingbilateral, NLM,etc. Andthe
Semantic Scene Parsing by Entropy Pursuit
standard operator usedtoconstruct thefiltersis the(nor-
malized) weighted average of the affinities. But if we con-
The grand challenge of computer vision is to build a ma-
sider thepixels in an image as nodes in a weighted graph,
chinewhichproducesarichsemanticdescriptionofanun-
the Laplacian operator on this graph gives us a strikingly
derlyingscene based on image data. Mathematical frame-
versatiletoolforbuildingaverygeneralclassoffilterswith
works are advanced from time to time, but none clearly
a much larger range of applications. A little-appreciated
points the way to closing the performance gap with nat-
property of the (continuous) Laplacian operator is that it
ural vision. Entropy pursuit is a sequential Bayesian ap-
measures the nonconformity of a function to its surround-
proach to object detection and localization. The role of
ings. Thisremarkablepropertyanditsdiscreteapproxima-
the prior model is to apply contextual constraints in or-
tionsenable(1)progressiveimagedecompositionfromfine
der to determine, and coherently integrate, the evidence
to coarse scale, yielding a principled framework for image
acquiredat eachstep. Theevidenceisprovidedbyalarge
smoothing, sharpening and local tone manipulation; and
familyofpowerfulbutexpensivehigh-levelclassifiers(e.g.,
(2)aclearframework forbuildingimage-adaptedpriorsto
CNNs). Theorderofexecutionisdeterminedonline,andis
solvemoregeneralinverseproblemssuchasdeblurring. We
drivenbyremovingas muchuncertaintyaspossible about
have used this framework to develop many components of
theoverallsceneinterpretationgiventheevidencetodate.
a practical imaging pipeline for mobile and other applica-
Thegoal istomatch,orevenexceed, theperformance ob-
tions.
tainedwithalltheclassifiersbyimplementingonlyasmall
fraction.
Peyman Milanfar
Google
Donald Geman
[email protected]
Johns HopkinsUniversity
[email protected]
IP2
High Resolution Tactile Sensing for Robotics, IP5
Metrology, and Medicine
Recent Advances in Seismic Technology: From
Imaging to Inversion
Theinteractionoflightandmatteratasurfaceiscomplex.
A GelSight sensor overrides the native optics and isolates Theprimarygoalofseismicimagingistotransformseismic
3D shape. A clear elastomer slab with a reflective mem- time reflection data recorded at the earths surface into a
brane is pressed against the surface. An embedded cam- reflectivity or impedance image of the subsurface in order
era views the membrane; computer vision extracts shape. to locate hydrocarbon reserves. Historically this has been
Whileconceivedasarobottouchsensor,GelSightsmicron- accomplished in seismic processing through imaging algo-
scaleresolutionhasspawnedcommercialapplicationsin3D rithms that are based on the adjoint of acoustic forward
surfacemetrology(profilometry). Inrobotics,itshighreso- Born or Kirchhoff scattering. More recently, however, ad-
lution,combinedwithitsabilitytocaptureshape,texture, vancesinalgorithmdevelopmenthaveledtotheinitialuse
shear,andslip,providesuniquetactilecapabilities. Weare of nonlinear inversion as an alternative to standard imag-
also exploring medical measurements, ranging from blood ingalgorithms. InthistalkIwill brieflyreviewthehistor-
pressure to tissue pathology. ical development of seismic imaging, and then discuss the
status of nonlinear inversion in the seismic industry, in-
Edward Adelson
cluding the use of Full-Waveform Inversion for impedance
MIT
modelestimation,andmorerecenttomographicextensions
[email protected]
that attempt to promote inversion technology into a full-
bandwidth model-recovery solution. The various concepts
Ipresentwillbeillustratedwithseismicimagingandinver-
IP3
sion examples from a number of geologic settings around
Image Processing, Internet-of-Things, and In- theworld.
verse Problems: Blind Deconvolution Meets Blind
Demixing UweAlbertin
Chevron Energy Technology Company
Assume we need to correctly blindly deconvolve and sep- [email protected]
arate (demix) multiple signals at the same time from one
single received signal. This challenging problem appears
in numerous applications, and is also expected to arise in IP6
the future Internet-of-Things. We will prove that under Event-Based Silicon Retina Technology
reasonable assumptions, it is indeed possible to solve this
ill-posed inverseproblemandrecovermultipletransmitted This talk will be about the development of asynchronous
functions fi and the associated impulse responses gi ro- silicon retina vision sensors that offer a spike-event out-
bustly and efficiently from just one single received signal put like biological retinas. These neuromorphic sensors
via semidefinite programming. We will tip our toes into offer advantages for real-world vision problems in terms
the mathematical techniques behind our theory and dis- of latency, dynamic range, temporal resolution, and post-
cuss efficient numerical algorithms as well as applications. processing cost. These event-based sensors offer oppor-
IS16 Abstracts 65
tunities for theoretical and practical developments of new [email protected]
classes ofalgorithmsaimed atmanydynamicvision appli-
cations. The presentation will include a demonstration of
a recent-vintage sensor. URL:http://sensors.ini.uzh.ch CP1
Algorithm to Build A Parametrized Model for the
Tobi Delbruck Antenna Aperture Illumination for Radio Astro-
University of Zurich and ETH Zurich nomical Imaging Application
[email protected]
Theimagingperformanceofmodernarrayradiotelescopes
islimited bytheinstantaneousknowledgeofthetime,fre-
SP1 quencyandpolarizationpropertiesoftheantennaaperture
illuminationpattern(AIP).Whileimagingalgorithmsexist
SIAG/Imaging Science Early Career Prize Lecture that can correct for these effects, they requirean accurate
- Revisiting Classical Problems of Image Process- instantaneous model for the antenna AIP.We describe al-
ing: Looking for New Ways to Address Longstand- gorithm for a low-order parametrized model for the AIP
ing Problems and demonstrate that it captures the dominant time, fre-
quencyandpolarizationdependenceofthetrueAIP.Mod-
Digital images are generated by using physical acquisition ern interferometric radio telescopes consist of 100s of in-
devices, such as digital cameras, but also by simulating dependent antennas with wide-band receivers (bandwidth
light propagation through environmental models. In both 8GHz or more) which are together capable of imaging the
cases, physical or computational limitations in the image sky at imaging dynamic range well exceeding a part in a
formation process introduce artifacts such as image blur million. At such high sensitivities the antenna far-field
or noise. Thus, developing image processing techniques pattern varies with time, frequency, polarization. Cor-
becomes indispensable tohelp overcome these barriers. In recting for all these variables of the AIP during imag-
this talk, I present several image processing applications ing has so far been considered a hard problem, limiting
in which a change of perspective leads to new insight and theimaging performance of modern radio telescopes. The
simpler, yet powerful, algorithms. Examples are: intrinsic methoddescribedhereisanimportantstepforwardinsolv-
cameraPSFestimation,burstandvideodeblurring,Monte ing this major problem facing all current and future radio
Carlo renderingdenoising. telescopes for deep-imaging observations. We use a com-
putationally efficient ray-tracing code to predict the AIP
Mauricio Delbracio parametrized for the physicaland electromagnetic charac-
DukeUniversity teristicsoftheantenna. Weshowthatourmethodisopti-
Electrical & Computer Engineering malinbuildingan AIPmodelthat minimizesthedegrees-
[email protected] of-freedom and demonstrate that without such accurate
models, modern radio telescopes cannot achieve their ad-
vertised imaging performance.
SP2
Sanjay Bhatnagar
SIAG/Imaging Science Best Paper Prize Lecture -
National Radio Astronomy Observatory,Socorro, New
Scale Invariant Geometry for Nonrigid Shapes
Mexico
[email protected]
Animals of the same species frequently exhibit local vari-
ations in scale. Taking this into account we would like to
Preshanth Jagannathan, Walter Brisken
developmodelsandcomputationaltoolsthatanswerques-
National Radio Astronomy Observatory
tionsas: Howshouldwemeasurethediscrepancybetween
[email protected], [email protected]
a small dog with large ears and a large one with small
ears? Are there geometric structures common to both an
elephant and a giraffe? What is the morphometric simi-
CP1
larity between a blue whale and a dolphin? There have
Wide-field full-Stokes Radio Interferometric Imag-
been two schools of thoughts that quantified similarities
ing: The role of the antenna response function
between surfaces which are insensitive to deformations in
size. Namely, scale invariant local descriptors, and global
All modern radio interferometry now use wide bandwidth
normalization methods. Here, we propose a new tool for
receivescapableofenablinghighsensitivityimaging. How-
shape exploration. We introduce a scale invariant met-
ever such receivers and high sensitivities brings with it a
ric for surfaces that allows us to analyze nonrigid shapes,
number of instrumental and atmospheric effects that in-
generate locally invariant features, producescale invariant
hibithighfidelity,highdynamicrangecontinuumimaging.
geodesics, embed one surface into anotherdespite changes
The dominant instrumental direction dependent effect is
in local and global size, and assist in the computational
that of the antenna far field voltage pattern. Apart from
studyofintrinsicsymmetries wherethesizeof afeatureis
timeandfrequencydependence,theantennaapertureillu-
insignificant.
mination pattern (AIP– Fourier transform of thefar-field
voltage pattern) also introduces significant instrumental
Yonathan Aflalo
polarizationindirectionsawayfromthecenterinthefield-
Technion University
of-view. Tocorrect for theerrors dueto all theseeffects, I
johnafl[email protected]
presentageneralized imaging algorithm that enablesdeep
wide-bandimagingoftheradioskyinallStokes. Theradio
Ron Kimmel sky is inherently linearly polarized at only a few percent
Technion, Haifa, Israel level. The full-polarization antenna response to the signal
[email protected] in any one direction is given by theJones matrix. The di-
agonal termsof theJones matrix encodetheantennagain
Dan Raviv for thetwoincoming purepolarization products(linear or
MIT circular), while the off diagonal terms contains magnitude
66 IS16 Abstracts
of theleakage of onepolarization intootherduetoinstru- SBRAS Novosibirsk, Russia; (b) UniCIRP, Bergen,
mental imperfections. In practice these off-diagonal terms Norway
aremuchstrongerthanthesignalmakingprecisemeasure- [email protected]
ment of sky impossible. The existing A-Projection algo-
rithm accounts for only the diagonal terms. In this talk I Vladimir Tcheverda
will demonstrate the limitations that arise from ignoring Inst. of Petroleum Geology and Geophysics SB RAS
the off diagonal terms and theneed for thegeneralized A- Russia
Projection algorithm. I will then describe the Full-Jones [email protected]
A-Projection algorithm, and show that it will be required
forallcurrentandfuturetelescopestoachievetheiradver-
tised high fidelity,high dynamicrange imaging capability. CP1
CompressiveMid-InfraredSpectroscopicTomogra-
Preshanth Jagannathan
phy: Label Free and Chemically Specific 3D Imag-
National Radio Astronomy Observatory
ing.
[email protected]
We develop a mid-infrared optical imaging modality that
Sanjay Bhatnagar combines scattering microscopy and imaging spectroscopy
National Radio Astronomy Observatory,Socorro, New todeterminespatialmorphologyandchemicalcomposition
Mexico inthreespatialdimensionsfrominterferometricdata. The
[email protected] forwardimagingmodelincorporatestheconstraintthatthe
sample comprises few chemical species with known spec-
Urvashi Rau tra. Images are formed using an iterative reconstruction
National Radio Astronomy Observatory algorithm with sparsity-drivenregularization. Simulations
[email protected] illustrate imaging of layered media and sub-wavelength
point scatterers in the presence of noise.
Russ Taylor
LukePfister
University of Cape Town
Universityof Illinois at UrbanaChampaign
University of Western Cape
lpfi[email protected]
[email protected]
Yoram Bresler
CP1 Departmentof Electrical and Computer Engineering and
the
Effect of Micro-CT Scans Resolution and Scale on
Coordinated Science Laboratory, Universityof Illinois
the Prediction of Transport Properties of Digital
[email protected]
Rocks
Westudiedtheeffectsofimageresolutionontheprediction P.Scott Carney
of transportproperties ofdigital rocksamples. Having3D Universityof Illinois at UrbanaChampaign
micro-CT scans of Benthein sandstone acquired with dif- [email protected]
ferentresolutionsweestimatedstatisticalpropertiesofseg-
mentedimagesandperformedstatisticalimagereconstruc-
tion. Afterthattransportpropertiesandtopologicalstruc- CP1
ture of the original digital rocks and those reconstructed Sparse View Compton Scatter Tomography with
on the base of truncated Gaussian simulation were com- Energy Resolved Data
puted showing that transport properties stabilizes when
resolution goes below 3 micrometers. The useof energy selective detectors for Compton Scatter
Tomographyholdsthehopeofenhancingtheperformance
Vadim Lisitsa especially for problems with limited- view in presence of
Institute of Petropeum Geology & Geophysics of SBRAS highlyattenuatingmaterials. Wepresentabroken-rayfor-
Russia ward model mappingmass densityand photoelectrical co-
[email protected] efficients into observed scattered photons, an iterative re-
constructionmethodforimageformationandinitialresults
Nadezhda Arefeva for recovering spatial maps of these physical properties to
Novosibirsk State University characterizematerialinbaggagescreeningapplicationwith
Russia limited view, energy-resolved data.
[email protected]
Hamideh Rezaee
PhD Candidate, Electrical and Computer Engineering
Yaroslav Bazaikin
Department,Tufts University
Inst. of Mathematics of SB RAS
[email protected]
Russia
[email protected]
Brian Tracey, Eric Miller
TuftsUniversity
Tatyana Khachkova
[email protected], [email protected]
Inst. of Petroleum Geology and Geophysics SB RAS
Russia
[email protected] CP2
Matrix Decompositions Using Sub-Gaussian Ran-
Dmitriy Kolyukhin dom Matrices
(a) Trofimuk Instituteof Petroleum Geology and
Geophysics Matrix decompositions, and especially SVD, are very im-
IS16 Abstracts 67
portanttoolsindataanalysis. Whenbigdataisprocessed, [email protected]
thecomputationofmatrixdecompositionsbecomesexpen-
sive and impractical. In recent years, several algorithms, LotharReichel
which approximate matrix decomposition, have been de- KentState University
veloped. These algorithms are based on metric conserva- [email protected]
tion features for linear spaces of random projections. We
present a randomized method based on sparse matrix dis-
tributionthatachievesafastapproximationwithbounded
CP2
error for low rank matrix decomposition.
Parallel Douglas Rachford Algorithm for Restor-
Yariv Aizenbud
ing Images with Values in Symmetric Hadamard
Department of Applied Mathematics, School of
Manifolds
Mathematical
Sciences, Tel Aviv University.
[email protected] The talk addresses a generalization of the Douglas-
Rachfordalgorithm tosymmetricHadamardmanifolds. It
can be used to minimize an anisotropic TV functional for
Amir Averbuch
images having values on these manifolds. We derive an
School of Computer Sciences
parallelDRalgorithm,thatcanbeevaluatedfast. Conver-
Tel AvivUniversity.
genceofthealgorithmtoafixedpointisproofedforspaces
[email protected]
withconstantcurvature. Severalnumericalexamplesshow
its beneficial performance when compared with the cyclic
CP2 proximal point algorithm or half-quadratic minimization.
Iterated Tikhonov with General Penalty Term
Johannes Persch, RonnyBergmann, Gabriele Steidl
In many applications, such as astronomy and medicine, Universityof Kaiserslautern
arises the problem of image deblurring, this inverse prob- [email protected],
lem is ill-conditioned and the inevitable presence of noise [email protected],[email protected]
make a very difficult task obtaining a good reconstruction kl.de
ofthetrueimage. Thediscreteformulationofthisproblem
comes as a linear system
CP2
Ax=b,
A New Variable Metric Line-Search Proximal-
whereAisaverylargeandseverelyillconditionedmatrix
Gradient Method for Image Reconstruction
and b is corrupted by noise. In order to compute a fair
approximationoftheoriginalimagetheproblemhastobe
We present a variable metric line–search based proximal–
regularized. One of the most used regularization method
gradient method for the minimization of the sum of a
is Tikhonov regularization
smooth, possibly nonconvex function plus a convex, pos-
xα =argmin(cid:2)Ax−b(cid:2)2+α(cid:2)Lx(cid:2)2, α>0. sibly nonsmooth term. The strong convergence of the
x method can be proved if the objective function satisfies
theKurdyka–L(cid:4)ojasiewicz property at each point of its do-
The formulation above is called general from, since it in-
main. Numerical experience on some nonconvex image
cludes also the presence of a regularization operator L
reconstruction problems shows the proposed approach is
which weights the penalty term. This operator enhance
competitive with other state-of-the-art methods.
some features of the solution while penalizing others. In
the case L = I, in order to improve the quality of the re-
construction, a refinement techniquehas been introduced. SimoneRebegoldi
At each step the reconstruction error is approximated us- Universityof Modena and Reggio Emilia
ing the Tikhonov minimization on the error equation and [email protected]
isusedasacorrectionterm,sothisalgorithmisdenotedas
IteratedTikhonov. However,tothebestofourknowledge, Silvia Bonettini
the general theory about this iterative method has been Dipartimentodi Matematica e Informatica
developed only in the standard form, i.e., when L=I. In Universit{`a} di Ferrara
this talk we want to cover the theory behind the general [email protected]
iteratedTikhonov,whenoneconsidertheiteration related
to Tikhonov minimization in general form. We will form
Ignace Loris
the method, describe its characteristics and, in particular,
FNRSChercheurQualifi´e (ULB, Brussels)
weprovethattheproposediteration convergesandthatis
Mathematics
a regularization method. Moreover we will introduce the
[email protected]
non-stationaryiterationswhichwillshowtobemorerobust
in respect to thechoice of theregularization parameter α.
Federica Porta
Finally, we will show the effectiveness of this method on
Dipartimentodi Matematica e Informatica
image deblurring test data.
Universit{`a} di Ferrara
Alessandro Buccini [email protected]
Universit`a dell’Insubria
[email protected] Marco Prato
Dipartimentodi Scienze Fisiche, Informatiche e
Marco Donatelli Matematiche
University of Insubria Universit{`a} di Modena e Reggio Emilia
68 IS16 Abstracts
[email protected] Recoverywith Applications to Mri Reconstruction
A powerful new class of MRI reconstruction techniques
CP2 require solving a large-scale structured low-rank ma-
trix recovery problem. We present a novel, fast algo-
Modulus Iterative Methods for Nonnegative Con-
rithm for this class of problem that adapts an iteratively
strained Least Squares Problems Arising from Im-
reweightedleastsquaresapproachtoincorporatemulti-fold
age Restoration
Toeplitz/Hankelstructures. Theiteratescanbesolvedeffi-
cientlyintheoriginalproblemdomainwithfewFFTs. We
For the solution of large sparse nonnegative constrained
demonstrate the algorithm on undersampled MRI recon-
least squares (NNLS) problems with Tikhonov regulariza-
struction, which shows significant improvement over stan-
tionarisingfromimagerestoration,anewiterativemethod
dard compressed sensing techniques.
is proposed which usestheCGLS method for theinnerit-
erations and the modulus iterative method for the outer
Gregory Ongie
iterations to solve the linear complementarity problem
Universityof Iowa
resulted from the Karush-Kuhn-Tucker condition of the
Departmentof Mathematics
NNLS problem. Theoretical convergence analysis includ-
[email protected]
ingtheoptimalchoiceoftheparametermatrixispresented
for the proposed method. In addition, the method can be
Mathews Jacob
further enhanced by incorporating the active set strategy,
Electrical and Computer Engineering
which contains two stages where thefirst stage consists of
Universityof Iowa
modulusiterationstoidentifytheactiveset,whilethesec-
[email protected]
ond stage solves the reduced unconstrained least squares
problems only on the inactive variables. Numerical exper-
iments show the efficiency of the proposed methods com-
CP3
paredtoprojectiongradient-typemethodswithlessmatrix
Enhanced Sparse Low-Rank Matrix Estimation
vector multiplications and CPU time.
We propose to estimate sparse low-rank matrices by min-
Ning Zheng
imizing a convex objective function consisting of a data-
SOKENDAI(The Graduate Universityfor Advanced
fidelitytermandtwonon-convexregularizers. Theregular-
Studies)
izersinducesparsityofthesingularvaluesandtheelements
[email protected]
ofthematrix,moreeffectivelythanthenuclearandthe(cid:3)1
norm, respectively. We derive conditions on theregulariz-
Ken Hayami erstoensurestrictconvexityoftheobjectivefunction. An
National Instituteof Informatics ADMMbasedalgorithmisderivedandisappliedtoimage
[email protected] denoising.
Junfeng Yin AnkitParekh
Department of Mathematics, Tongji University,Shanghai Departmentof Mathematics, School of Engineering
[email protected] NewYork University
[email protected]
CP3 IvanSelesnick
Departmentof Electrical and Comp. Engg
Image Deblurring With An Imprecise Blur Kernel
NYUSchool of Engineering
Using a Group-Based Low-Rank Image Prior
[email protected]
Wepresentaregularizationmodelfortheimagedeblurring
problem with an imprecise blur kernel degraded by ran-
CP3
dom errors. Inthemodel, therestored imageand blurare
Image Regularization with Structure Tensors -
characterized by a group-based low-rank prior enforcing
Edge Detection, Filtering, Denoising
simultaneously the nonlocal self-similarity, local sparsity,
andmean-preservingproperties. Analternatingminimiza-
Edge detection, filtering, and denoising are fundamental
tion algorithm is developed to solve the proposed model.
topics in digital image and video processing area. Edge
Experimental results demonstrate the effectiveness of our
preserving regularization and diffusion based methods al-
model and theefficiency of ournumerical scheme.
though extensively studied and widely used for image
restoration,stillhavelimitationsinadaptingtolocalstruc-
Tian-Hui Ma, Ting-Zhu Huang, Xi-LeZhao
tures. We consider a class of filters based on multiscale
School of Mathematical Sciences
structure tensor based features. The spatially varying
University of Electronic Scienceand Technology of China
exponent model we develop leads to a novel restoration
[email protected], [email protected],
methodwhich retainsandenhancesedgestructuresacross
[email protected]
scales without generating artifacts. Promising extensions
to handle jpeg decompression, edge detection, and multi-
Yifei Lou, Yifei Lou
channelimageryareconsidered. Relatedprojectpagecon-
Department of Mathematical Sciences
tainsmoredetails: http://cell.missouri.edu/pages/MTTV.
University of Texas at Dallas
[email protected], [email protected] SuryaPrasath
Universityof Missouri-Columbia
[email protected]
CP3
AFastAlgorithmforStructuredLow-RankMatrix Dmitry A.Vorotnikov
IS16 Abstracts 69
Universidade deCoimbra [email protected]
[email protected]
CP4
Rengarajan Pelapur, ShaniJose
University of Missouri-Columbia, USA Sparse Approximation of Images by Adaptive
[email protected], [email protected] Thinning
Anisotropic triangulations provide efficient methods for
Kannappan Palaniappan
sparse image representations. We propose a locally adap-
University of Missouri-Columbia
tive algorithm for sparse image approximation, adaptive
[email protected]
thinning, which relies on linear splines on anisotropic tri-
angulations. Wediscuss both theoretical and practical as-
Guna Seetharaman
pects concerning image approximation by adaptive thin-
Navy Research Lab, USA
ning. This includes asymptotically optimal N-term ap-
[email protected]
proximations on relevant classes of target functions, such
as horizon functions across α H¨older smooth boundaries
andregularfunctionsofWα,p regularity,for α>2/p−1.
CP3
Armin Iske
Signal Classification Using Sparse Representation Universityof Hamburg
on Enhanced Training Dictionary Departmentof Mathematics
[email protected]
We propose a method to classify high-dimensional signals
basedonhowsparselyatestsignalcanberepresentedover Laurent Demaret
adictionarycontainingselectedtrainingsamplesandbasis Instituteof Biomathematics and Biometry
vectorsoftheapproximatedtangentplanesatthosetrain- Helmholtz ZentrumMu¨nchen, Germany
ingsamples,whicharecomputedusinglocalPCA.Ourex- [email protected]
periments on various datasets including the standard face
databasesdemonstratethatthismethodcanachievehigher
classification accuracy than other sparse representation- CP4
basedmethodswhentheclassmanifoldsarenonlinearand Joint Deconvolution and Blind Source Separation
sparsely-sampled. of Hyperspectral Data Using Sparsity
Thehyperspectralrestorationisverychallengingwhentak-
Naoki Saito
ing into account not only the spectral mixing, but also
Department of Mathematics
blurring effects. We propose a new Blind Source Separa-
University of California, Davis
tion method which addresses this problem by alternating
[email protected]
twominimizers, onesolvingahyperspectraldeconvolution
problem using sparsity, and leading to a generalization of
Chelsea Weaver
the FORWARD algorithm, and the second estimating the
University of California, Davis
mixing matrix by a least square inversion. A range of ex-
[email protected]
amples illustrates theresults.
Ming Jiang
CP3 CEA-Saclay
[email protected]
Low-Rank Approximation Pursuit for Matrix and
Tensor Completion Jean-LucStarck, J´erome Bobin
CEA Saclay
weintroduceanefficientgreedyalgorithm formatrixcom- [email protected], [email protected]
pletion, which is literally a generalization of orthogonal
rank-one matrix pursuit method (OR1MP) in the sense
that multiple s candidates are identified per iteration by CP4
low-rank matrix approximation. Owing to the selection Sparse Source Reconstruction for Nanomagnetic
of multiple s candidates, our approach is finished with Relaxometry
much smaller number of iterations when compared to the
OR1MP. Inaddition, we extendtheOR1MP algorithm to Source reconstruction for nanomagnetic relaxometry re-
deal with tensor completion. quiressolving themagnetic inverse problem. By discretiz-
ing the field of view, we can compute a lead field matrix
thatrelates thecontribution of each pixeltothesignal re-
An-Bao Xu
ceivedbythedetectors. Wethenapproximateaminimum
Hunan University
[email protected] l0-norm solution by iterating over the minimization prob-
lem:
min||xi||1 s.t. ||Ax−b||2 ≤(cid:4)
Dongxiu Xie x wi
School of science
Ourapproachforverificationandvalidationofouralgorith-
Beijing Information Science and Technology University
mic implementation in phantom studies will be presented.
[email protected]
Tin-Yau Tam Sara Loupot, Wolfgang Stefan, Reza Medankan,Kelsey
AuburnUniversity Mathieu, David Fuentes,John Hazle
70 IS16 Abstracts
University of Texas MD Anderson Cancer Center Model with Directional Forward Differences
[email protected], [email protected],
[email protected], [email protected], Focusedionbeamtomographyprovideshighresolutionvol-
[email protected], [email protected] umetric images on a micro scale. However, due to the
physical acquisition process the resulting images are often
corrupted by a so-called curtaining effect. In this talk, a
CP4 new convex variational model for removing such effects is
Convolutional Laplacian Sparse Coding proposed. More precisely, an infimal convolution model is
applied tosplit thecorrupted3D image intotheclean im-
We propose to extend the the standard convolutional age and two types of corruptions, namely a striped and a
sparse representation by combining it with a non-local laminar part.
graph Laplacian term. This additional term is chosen to
address some of the deficiencies of the (cid:3)1 norm in regular- Jan Henrik Fitschen
izing these representations, and is shown to have an ad- Universityof Kaiserslautern
vantageinbothdictionarylearningandanexampleimage fi[email protected]
reconstruction problem.
Jianwei Ma
Xiyang Luo
Departmentof Mathematics
University of California, Los Angeles
Harbin Instituteof Technology
[email protected]
[email protected]
Brendt Wohlberg
Sebastian Schuff
Los Alamos National Laboratory
Universityof Kaiserslautern
Theoretical Division
schuff@mv.uni-kl.de
[email protected]
CP5
CP4
NonLocal via Local–NonLinear via Linear: A New
Gap Safe Rules for Speeding-Up Sparse Regular-
Part-Coding Distance Field via Screened Poisson
ization
Equation
Highdimensionalregression/inverseproblemsmightben-
efit from sparsity promoting regularizations. Screening We propose a repeated use of Screened Poisson PDE to
rulesleveragethesparsityofthesolutionbyignoringsome compute a part coding field for perceptual tasks such as
variables in the optimization, hence speeding up solvers. shape decomposition. Despite efficient local and linear
When the procedure is proven not to discard features computations, thefield exhibitshighly nonlinear andnon-
wrongly, the rules are said to be ”safe”. We derive new local behavior. Our scheme is applicable to shapes in ar-
saferulesforgeneralizedlinearmodelsregularizedwithL1 bitrary dimensions, even to those implied by fragmented
or L1/L2 norms. The rules are based on duality gap com- partial contours. The local behavior is independent of the
putationsallowingtosafelydiscardmorevariables,inpar- image context in which theshape resides.
ticular for low regularization parameters. Our GAP Safe
rulecancopewithanyiterativesolverandweillustrateits Murat Genctav, Asli Genctav, Sibel Tari
performanceonLasso,multi-taskLasso,binaryandmulti- Middle East Technical University
nomial logistic regression, demonstrating significant speed [email protected], [email protected],
ups on all tested datasets with respect to previous safe [email protected]
rules. This is a joint work with E. Ndiaye, O. Fercoq and
A. Gramfort
CP5
Eugene Ndiaye Boundary Formulationof Finite Differences: Anal-
Telecom-ParisTech, CNRS LTCI ysis and Applications
Universit´e Paris-Saclay
[email protected]
Estimationofnumericalderivativesontheboundaryvalues
remainsanunresolveddilemmainmanyinverseproblems.
Olivier Fercoq Many formulations such as cyclic or Neumann conditions
Telecom-ParisTech, CNRS LTCI violate the derivative continuity and cause discrepancies.
Universit´e Paris-Saclay,75013, Paris, France This presentation provides a numerical solution to calcu-
[email protected] latederivativeson theboundarieswith highorderpolyno-
mialaccuracyinaunifiedconvolutionmatrix. Thenumer-
Alexandre Gramfort icalstabilityofthismatrixisanalyzedviathedistribution
Telecom-ParisTech, CNRS LTCI oftheeigenvaluesandperturbationanalysisandcompared
Universit´e Paris-Saclay tothe existing formulations in theliterature.
[email protected]
Mahdi S.Hosseini, Konstantinos N. Plataniotis
Joseph Salmon Universityof Toronto
Telecom-ParisTech, CNRS LTCI [email protected], [email protected]
[email protected]
CP5
CP5 Solving Variational Problems and Partial Differen-
Removal of Curtaining Effects by a Variational tial Equations That Map Between Manifolds Via
IS16 Abstracts 71
the Closest Point Method metryonatilemapsallregionsofonecolortotheregions
of another color. In this work, we propose a novel ap-
Maps from a manifold M to a manifold N appear in im- proach to extract the unit cells and fundamental domains
age processing, medical imaging, and many other areas. oftileswithvariouscolorsymmetries,bothconsideringand
Thistalkintroducesanumericalframeworkforvariational ignoring color permutations. We use multiple ideas from
problems and PDEs that map between manifolds. The variational and PDE based image processing methods.
problem of solving a constrained PDE between M and N
is reduced into two simpler problems: solving a PDE on VeneraAdanova
M and projecting onto N. Numerical examples of denois- Middle East Technical University
ing texture maps, diffusing random maps, and enhancing [email protected]
colour images are presented.
SibelTari
Nathan D.King
ComputerEngineering Department
Department of Mathematics
Middle East Technical University,Turkey
Simon Fraser University
[email protected]
[email protected]
Steven Ruuth CP6
Mathematics NewTechniquesforInversionofFull-WaveformIn-
Simon Fraser University duced Polarization Data
[email protected]
Induced polarization (IP) is a geophysical method that
measures electrical polarization of the subsurface. Stan-
CP5 dardmethodsforinversionofIPdatausesimplifiedmodels
Regularization Strategy for Inverse Problem for that neglect much of the information collected in modern
1+1 Dimensional Wave Equation surveys, limiting imaging resolution. We are developing
high performance multigrid based methods for modelling
Aninverseboundaryvalueproblem fora1+1dimensional full IP decay curves from large sources along with a cor-
wave equation with wave speed c(x) is considered. We responding inversion algorithm that combines voxel-based
give a regularisation strategy for inverting the map A : Tikhonovregularized inversion with aparametric-level set
c (cid:4)→ Λ, where Λ is the hyperbolic Neumann-to-Dirichlet approach.
map corresponding to the wave speed c. We consider the
casewhenwearegivenaperturbationoftheNeumann-to- Patrick T. Belliveau
Dirichlet map Λ˜ =Λ+E,and reconstruct anapproximate Universityof British Columbia
wave speed c˜. Our regularization strategy is based on a [email protected]
newformulatocomputecfromΛ. Moreoverwehavedone
numericalimplementationandexecuteditwithasimulated Eldad Haber
data. Departmentof Mathematics
TheUniversity of British Columbia
Jussi P. Korpela [email protected]
University of Helsinki
Department of Mathematics and Statistics
jussi.korpela@helsinki.fi CP6
Bidirectional Texture Function Bernoulli-Mixture
Compound Texture Model
CP5
Exploiting Sparsity in PDEs with Discontinuous This paper introduces a method for modeling texturesus-
Solutions ing a parametric BTF compound Markov random field
model. Thepurposeofourapproachistoreproduce,com-
Exploiting sparsity playsa centralrole in many recent de- press,and enlargea givenmeasured textureimage so that
velopments in imaging and other related fields. We use (cid:3)1 ideally both natural and synthetictexturewill be visually
regularization techniquesto promote sparsity in the edges indiscernible. ThemodelcanalsobeappliedtoBTFmate-
of PDEs with discontinuous solutions. This has led us to rialediting. ThecontrolfieldisgeneratedbytheBernoulli
thedevelopmentofnumericalalgorithms thatdonothave mixture model and the local textures are modeled using
the restrictive stability conditions on time stepping that the3DCAR.
normally occur. With these methods we increase the ac-
curacy of methods that do not account for sparsity in the Michal Haindl
solution. Instituteof Information Theory and Automation of the
CAS
Theresa A. Scarnati [email protected]
Arizona StateUniversity
School of Mathematical & Statistical Sciences
[email protected] CP6
Information Theoretic Approach for Accelerated
MagneticResonanceThermometryinthePresence
CP6 of Uncertainties
Extracting Plane Symmetry Group Information
from Tiles with Color Permutations Amodel-basedinformationtheoreticapproachispresented
toperform thetask of Magnetic Resonance (MR) thermal
Repeatingabasemotifcreatesatilewithdifferentsymme- image reconstruction from a limited number of observed
tries. A tile has color symmetry, if applying certain sym- samplesonk-space. Thekeyideaoftheproposedapproach
72 IS16 Abstracts
is to optimally detect samples of k-space that are infor- sity algorithm in order to improve theconvergence rate of
mation rich with respect to a model of the thermal data thesolution. Theexperimentalresultsondifferentdatasets
acquisition. These highly informative k-space samples are verify thevalidity of theproposed model.
thenusedtorefinethemathematicalmodelandefficiently
reconstruct the image. PushpendraKumar
Indian Instituteof Technology Roorkee
Reza Madankan, Wolfgang Stefan, Christopher [email protected]
MacLellan, Samuel Fahrenholtz, Drew Mitchell
University of Texas MD Anderson Cancer Center Sanjeev Kumar, Balasubramanian Raman
[email protected], [email protected], Indian Instituteof Technology Roorkee
[email protected], [email protected], [email protected]
[email protected],
[email protected]
CP7
R.J. Stafford Optical Flow on Evolving Sphere-Like Surfaces
MD Anderson Cancer Center
jstaff[email protected] Weconsideropticalflowonevolvingsurfaceswhichcanbe
parametrisedfromthe2-sphere. Ourmainmotivationisto
John Hazle estimate cell motion in time-lapse volumetric microscopy
University of Texas MD Anderson Cancer Center images depicting fluorescently labelled cells of a live ze-
[email protected] brafishembryo. Weexploitthefactthattherecordedcells
floatonthesurfaceoftheembryoandallowfortheextrac-
tion of an image sequence together with a sphere-like sur-
David Fuenstes
face. Wesolve the resulting variational problem by means
MD Anderson Cancer Center
ofaGalerkin method based onvectorspherical harmonics
[email protected]
and present numerical results.
LukasF. Lang
CP6
RICAM,Austrian Academyof Sciences
BLA: A Weak Form Attenuation Compensation
[email protected]
Model for Ultrasonic Imagery
OtmarScherzer
Thequalityofmedicalsonographyishinderedbytheshad-
Computational ScienceCenter
owingorenhancementartifactsduetoacousticwaveprop-
UniversityVienna
agation and attenuation across tissue layers. We present
[email protected]
a Backscatter-Levelset-Attenuation (BLA) joint estima-
tion model in the context of regional ultrasound attenua-
tioncompensation andstructuralsegmentation. TheBLA
CP7
model eliminates the need of solving PDEs over irregular
domains,andisformulatedusinglevelsets. Weprovidenu- Classification of Hyperspectral Data Using the
merical algorithms alongwith discretization schemes. The Besov Norm
mainadvantageoftheBLAmethodisitsremarkablecom-
putational efficiency. We demonstrate the results using Sparse representations have been extensively studied in
simulated, phantom and in vivoultrasound images. image processing, however not much has been done with
sparse-based classification problems. Inthisstudy,wedis-
Jue Wang cuss the use of wavelets in hyperspectral imaging. The
Union College analysis-based approach accounts for more aspects of the
[email protected] datathanthecoordinate-wiseeuclideandistanceapproach.
We estimate the local properties of the hyperspectral
stack using the Besov norm for a given choice of wavelet.
Yongjian Yu
Thereby, allowing for multiscale and multidirectional fea-
University of Virginia
tures.
[email protected]
Richard N.Lartey
Case Western ReserveUniversity
CP7
Departmentof Mathematics,Applied Mathematics and
A Fractional Order Variational Model for Optical
Statistics
Flow Estimation Based on Sparsity Algorithm
[email protected]
In this paper, a fractional order variational model is pro-
WeihongGuo
posed for estimating the optical flow. The proposed frac-
Departmentof Mathematics, Case Western Reserve
tionalordermodelisintroducedbygeneralizinganinteger
University
ordervariationalmodelformedwithaglobalmodelofHorn
[email protected]
and Schunck and the classical model of Nagel and Enkel-
mann. In particular, the proposed model generalizes the
existingvariationalmodelsfromintegertofractionalorder, Julia Dobrosotskaya
andthereforeamoresuitableinestimatingtheopticalflow. Case Western ReserveUniversity
However, it is difficult to solve this generalized model due [email protected]
to the complex fractional order partial differential equa-
tions. The Gru¨nwald-Letnikov derivative is used to dis-
cretize the fractional order derivative. The corresponding CP7
sparselinearsystemofequationsissolvedbyusingaspar- New Uncertainty Principles for Image Feature Ex-
IS16 Abstracts 73
traction oftheaffineparametersoftheregistration step,improving
themodel’sreliability. Wediscusshowthisapproachcom-
The motivation for this talk is window design for image parestosimilar methods,andpresentnumericalresultsto
feature extraction by a filter bank. There is a conven- demonstrate its performance.
tionalframework foranalyzinglocalization aspectsofwin-
dow functions. Weclaim that theconventionalframework Jack A.Spencer, KeChen
is flawed, and develop a new adequate theory. Our ap- Universityof Liverpool
proachleadstonewuncertaintyprinciplesandnewoptimal [email protected], [email protected]
window functions. Filter banks based on our new optimal
window functions havea certain notion of sparsity.
CP8
Ron Levie
Error Estimates and Convergence Rates for Fil-
School of Mathematical Sciences,
tered Back Projection
Tel AvivUniversity,Tel Aviv
[email protected] The filtered back projection (FBP) formula allows us to
reconstructbivariatefunctionsfrom givenRadonsamples.
Nir Sochen However,theFBPformulaisnumericallyunstableandlow-
Applied Mathematics Department passfiltersoffinitebandwidthareemployedtomakethere-
Tel AvivUniversity constructionlesssensitivetonoise. Inthistalkweanalyse
[email protected] the intrinsic reconstruction error incurred by the low-pass
filter. We prove L2-error estimates on Sobolev spaces of
fractional order along with asymptotic convergence rates,
CP7 where thebandwidth goes to infinity.
Hyperspectral Video Analysis Using Graph Clus-
tering Methods Matthias Beckmann
Universityof Hamburg
Perhapsthemostchallengingimagingmodalitytoanalyze [email protected]
in terms of thevast size of thedata are videos taken from
hyperspectral cameras. We consider an example involv-
Armin Iske
ingstandoffdetectionofagasplumeinvolvingLongWave
Universityof Hamburg
Infrared spectral data with 128 bands. Rather than using
Departmentof Mathematics
PCAorasimilardimensionreductionmethodwetreatthis
[email protected]
as a ”big data” classification problem and simultaneously
processallpixelsintheentirevideousingnovelnewgraph
clusteringtechniques. Computationoftheentiresimilarity CP8
graph is prohibitive for such data so we use the Nystrom
Density Compensation Factor Design for Non-
extension to randomly sample the graph and compute a
Uniform Fast Fourier Transforms
modest number of eigenfunctions of the graph Laplacian.
Averysmall partofthespectrumallows forspectralclus-
Inapplicationssuchasmagneticresonanceimaging(MRI),
tering of the data. However with a larger but still modest
radar imaging, and radio astronomy, data may be col-
number of eigenfunctions we can solve a graph-cut based
lected as a sequence of non-uniform Fourier samples. One
semisupervisedorunsupervisedmachinelearningproblem
common approach used to reconstruct images from non-
to sort the pixels into classes. We discuss challenges of
uniform Fourier data involves regridding the non-uniform
running such code on both desktopsand supercompers.
Fourier data to uniform points, and then applying the
FFT, a process often referred to as the non-uniform
Gloria Meng
FFT (NFFT). Intheregridding process, parameters often
UCLA
termed thedensity compensation factors (DCFs) are used
[email protected]
essentially as quadrature weights to construct the inverse
Fourier transform. The DCFs are typically chosen using
Ekaterina Merkurjev
heuristic arguments, and, depending on the sampling pat-
Department of Mathematics
tern,may not lead to a convergent approximation. Inthis
UCSD
talkweillustratetheimportanceofchoosingDCFsappro-
[email protected]
priately. We develop an algorithm to design DCFs based
on the given sampling scheme and demonstrate numerical
Alice Koniges convergence. We further apply our algorithm to recover
Lawrence Berekely Laboratory features (such as edges) of the underlying image, which is
[email protected] especiallyusefulintargetidentificationortissueclassifica-
tion.
Andrea L. Bertozzi
UCLA Department of Mathematics AnneGelb
[email protected] Arizona StateUniversity
[email protected]
CP7
CP8
Image Segmentation with a Shape Prior
The Factorization Method for Imaging Defects in
We study variational models for segmentation incorporat- Anisotropic Materials
ing ashapeprior, and ourmethod involvescomputingthe
global minimiser of a functional with fixed fitting terms. In this presentation we consider the inverse acoustic or
Wedefinethispriorimplicitlyinsuchawaythattheimage electromagnetic scattering problem of reconstructing pos-
intensityinformationisincorporatedintotheminimisation sibly multiple defective penetrable regions in a known