Results for "Elad Michael Schiller"

total 37800took 0.16s
Boosting of Image Denoising AlgorithmsFeb 22 2015Mar 12 2015In this paper we propose a generic recursive algorithm for improving image denoising methods. Given the initial denoised image, we suggest repeating the following "SOS" procedure: (i) (S)trengthen the signal by adding the previous denoised image to the ... More
Convolutional Neural Networks Analyzed via Convolutional Sparse CodingJul 27 2016Jul 30 2016Convolutional neural networks (CNN) have led to remarkable results in various fields. In this scheme, a signal is convolved with learned filters and a non-linear function is applied on the response map. The obtained result is then fed to another layer ... More
Practically-Self-Stabilizing Vector Clocks in the Absence of Execution FairnessDec 21 2017Vector clock algorithms are basic wait-free building blocks that facilitate causal ordering of events. As wait-free algorithms, they are guaranteed to complete their operations within a finite number of steps. Stabilizing algorithms allow the system to ... More
Self-Stabilizing Snapshot Objects for Asynchronous Fail-Prone Network SystemsJun 14 2019A snapshot object simulates the behavior of an array of single-writer/multi-reader shared registers that can be read atomically. Delporte-Gallet et al. proposed two fault-tolerant algorithms for snapshot objects in asynchronous crash-prone message-passing ... More
Membership-based Manoeuvre Negotiation in Autonomous and Safety-critical Vehicular SystemsJun 11 2019A fault-tolerant negotiation-based intersection crossing protocol is presented. Rigorous analytic proofs are used for demonstrating the correctness and fault-tolerance properties. Experimental results validate the correctness proof via detailed computer ... More
Practically-Self-Stabilizing Virtual SynchronyFeb 18 2015Apr 25 2018Virtual synchrony is an important abstraction that is proven to be extremely useful when implemented over asynchronous, typically large, message-passing distributed systems. Fault tolerant design is a key criterion for the success of such implementations. ... More
Practically Stabilizing Virtual SynchronyFeb 18 2015Jul 07 2016Virtual synchrony is an important abstraction that is proven to be extremely useful when implemented over asynchronous, typically large, message-passing distributed systems. Fault tolerant design is a key criterion for the success of such implementations. ... More
Self-Stabilizing TDMA Algorithms for Dynamic Wireless Ad-hoc NetworksOct 10 2012Jan 24 2013In dynamic wireless ad-hoc networks (DynWANs), autonomous computing devices set up a network for the communication needs of the moment. These networks require the implementation of a medium access control (MAC) layer. We consider MAC protocols for DynWANs ... More
Bismut-Elworthy-Li formulae for Bessel processesApr 14 2017In this article we are interested in the differentiability property of the Markovian semi-group corresponding to the Bessel processes of nonnegative dimension. More precisely, for all $\delta \geq 0$ and $T>0$, we compute the derivative of the function ... More
The Noise-Sensitivity Phase Transition in Spectral Group Synchronization Over Compact GroupsMar 08 2018May 21 2019In Group Synchronization, one attempts to find a collection of unknown group elements from noisy measurements of their pairwise differences. Several important problems in vision and data analysis reduce to group synchronization over various compact groups. ... More
Renaissance: Self-Stabilizing Distributed SDN Control PlaneDec 20 2017Feb 26 2019By introducing programmability, automated verification, and innovative debugging tools, Software-Defined Networks (SDNs) are poised to meet the increasingly stringent dependability requirements of today's communication networks. However, the design of ... More
Exterior square gamma factors for cuspidal representations of $\mathrm{GL}_n$: finite field analogs and level zero representationsJul 12 2018We follow Jacquet-Shalika, Matringe and Cogdell-Matringe to define exterior square gamma factors for irreducible cuspidal representations of $\mathrm{GL}_n(\mathbb{F}_q)$. These exterior square gamma factors are expressed in terms of Bessel functions, ... More
Split embedding problems over the open arithmetic discAug 05 2012Let Z{t} be the ring of arithmetic power series that converge on the complex open unit disc. A classical result of Harbater asserts that every finite group occurs as a Galois group over the quotient field of Z{t}. We strengthen this by showing that every ... More
Admissible groups over two dimensional complete local domainsOct 21 2009Let K be the quotient field of a complete local domain of dimension 2 with a separably closed residue field. Let G be a finite group of order not divisible by char(K). Then G is admissible over K if and only if its Sylow subgroups are abelian of rank ... More
Self-Stabilizing Byzantine Resilient Topology Discovery and Message DeliveryAug 28 2012Jan 30 2013Traditional Byzantine resilient algorithms use 2f+1 vertex disjoint paths to ensure message delivery in the presence of up to f Byzantine nodes. The question of how these paths are identified is related to the fundamental problem of topology discovery. ... More
Self-stabilizing TDMA Algorithms for Wireless Ad-hoc Networks without External ReferenceAug 29 2013Mar 25 2014Time division multiple access (TDMA) is a method for sharing communication media. In wireless communications, TDMA algorithms often divide the radio time into timeslots of uniform size, $\xi$, and then combine them into frames of uniform size, $\tau$. ... More
Aiding Autonomous Vehicles with Fault-tolerant V2V CommunicationSep 29 2017Vehicle-to-vehicle (V2V) communication is a key component of the future autonomous driving systems. V2V can provide an improved awareness of the surrounding environment, and the knowledge about the future actions of nearby vehicles. However, V2V communication ... More
Distributed Algorithm for Collision Avoidance at Road Intersections in the Presence of Communication FailuresJan 10 2017Vehicle-to-vehicle (V2V) communication is a crucial component of the future autonomous driving systems since it enables improved awareness of the surrounding environment, even without extensive processing of sensory information. However, V2V communication ... More
RIP-Based Near-Oracle Performance Guarantees for Subspace-Pursuit, CoSaMP, and Iterative Hard-ThresholdingMay 25 2010This paper presents an average case denoising performance analysis for the Subspace Pursuit (SP), the CoSaMP and the IHT algorithms. This analysis considers the recovery of a noisy signal, with the assumptions that (i) it is corrupted by an additive random ... More
Analysis of Basis Pursuit Via Capacity SetsApr 25 2010Finding the sparsest solution $\alpha$ for an under-determined linear system of equations $D\alpha=s$ is of interest in many applications. This problem is known to be NP-hard. Recent work studied conditions on the support size of $\alpha$ that allow its ... More
Power series over generalized Krull domainsOct 06 2008We resolve an open problem in commutative algebra and Field Arithmetic, posed by Jarden -- Let R be a generalized Krull domain. Is the ring R[[X]] of formal power series over R a generalized Krull domain? We show that the answer is negative.
Style-Transfer via Texture-SynthesisSep 10 2016Sep 20 2016Style-transfer is a process of migrating a style from a given image to the content of another, synthesizing a new image which is an artistic mixture of the two. Recent work on this problem adopting Convolutional Neural-networks (CNN) ignited a renewed ... More
Performance Guarantees of the Thresholding Algorithm for the Co-Sparse Analysis ModelMar 13 2012The co-sparse analysis model for signals assumes that the signal of interest can be multiplied by an analysis dictionary \Omega, leading to a sparse outcome. This model stands as an interesting alternative to the more classical synthesis based sparse ... More
Linearized Kernel Dictionary LearningSep 18 2015In this paper we present a new approach of incorporating kernels into dictionary learning. The kernel K-SVD algorithm (KKSVD), which has been introduced recently, shows an improvement in classification performance, with relation to its linear counterpart ... More
Sparsity Based Poisson Denoising with Dictionary LearningSep 17 2013Oct 14 2014The problem of Poisson denoising appears in various imaging applications, such as low-light photography, medical imaging and microscopy. In cases of high SNR, several transformations exist so as to convert the Poisson noise into an additive i.i.d. Gaussian ... More
Can we allow linear dependencies in the dictionary in the sparse synthesis framework?Mar 22 2013Signal recovery from a given set of linear measurements using a sparsity prior has been a major subject of research in recent years. In this model, the signal is assumed to have a sparse representation under a given dictionary. Most of the work dealing ... More
Structure-Aware Classification using Supervised Dictionary LearningSep 29 2016In this paper, we propose a supervised dictionary learning algorithm that aims to preserve the local geometry in both dimensions of the data. A graph-based regularization explicitly takes into account the local manifold structure of the data points. A ... More
Con-Patch: When a Patch Meets its ContextMar 22 2016Jun 09 2016Measuring the similarity between patches in images is a fundamental building block in various tasks. Naturally, the patch-size has a major impact on the matching quality, and on the consequent application performance. Under the assumption that our patch ... More
Finding GEMS: Multi-Scale Dictionaries for High-Dimensional Graph SignalsJun 14 2018Modern data introduces new challenges to classic signal processing approaches, leading to a growing interest in the field of graph signal processing. A powerful and well established model for real world signals in various domains is sparse representation ... More
Scaling Multidimensional Inference for Structured Gaussian ProcessesSep 18 2012Sep 21 2012Exact Gaussian Process (GP) regression has O(N^3) runtime for data size N, making it intractable for large N. Many algorithms for improving GP scaling approximate the covariance with lower rank matrices. Other work has exploited structure inherent in ... More
Predicting Counterfactuals from Large Historical Data and Small Randomized TrialsOct 24 2016When a new treatment is considered for use, whether a pharmaceutical drug or a search engine ranking algorithm, a typical question that arises is, will its performance exceed that of the current treatment? The conventional way to answer this counterfactual ... More
A unified operator splitting approach for multi-scale fluid-particle coupling in the lattice Boltzmann methodJun 09 2014A unified framework to derive discrete time-marching schemes for coupling of immersed solid and elastic objects to the lattice Boltzmann method is presented. Based on operator splitting for the discrete Boltzmann equation, second-order time-accurate schemes ... More
Self-stabilization Overhead: an Experimental Case Study on Coded Atomic StorageJul 20 2018Jul 26 2018Shared memory emulation can be used as a fault-tolerant and highly available distributed storage solution or as a low-level synchronization primitive. Attiya, Bar-Noy, and Dolev were the first to propose a single-writer, multi-reader linearizable register ... More
Cooperation with Disagreement Correction in the Presence of Communication FailuresAug 29 2014Feb 26 2015Vehicle-to-vehicle communication is a fundamental requirement in cooperative vehicular systems to achieve high performance while keeping high safety standards. Vehicles periodically exchange critical information with nearby vehicles to determine their ... More
Self-stabilizing ReconfigurationJun 01 2016Current reconfiguration techniques are based on starting the system in a consistent configuration, in which all participating entities are in their initial state. Starting from that state, the system must preserve consistency as long as a predefined churn ... More
Self-stabilizing ReconfigurationJun 01 2016Dec 06 2016Current reconfiguration techniques are based on starting the system in a consistent configuration, in which all participating entities are in their initial state. Starting from that state, the system must preserve consistency as long as a predefined churn ... More
Shared-object System Equilibria: Delay and Throughput AnalysisAug 07 2015Nov 03 2015We consider shared-object systems that require their threads to fulfill the system jobs by first acquiring sequentially the objects needed for the jobs and then holding on to them until the job completion. Such systems are in the core of a variety of ... More
Simple, Accurate, and Robust Nonparametric Blind Super-ResolutionMar 11 2015Mar 16 2015This paper proposes a simple, accurate, and robust approach to single image nonparametric blind Super-Resolution (SR). This task is formulated as a functional to be minimized with respect to both an intermediate super-resolved image and a nonparametric ... More
Spatially-Adaptive Reconstruction in Computed Tomography using Neural NetworksNov 28 2013We propose a supervised machine learning approach for boosting existing signal and image recovery methods and demonstrate its efficacy on example of image reconstruction in computed tomography. Our technique is based on a local nonlinear fusion of several ... More
Patch-Ordering as a Regularization for Inverse Problems in Image ProcessingFeb 26 2016Recent work in image processing suggests that operating on (overlapping) patches in an image may lead to state-of-the-art results. This has been demonstrated for a variety of problems including denoising, inpainting, deblurring, and super-resolution. ... More
Spatially-Adaptive Reconstruction in Computed Tomography Based on Statistical LearningApr 25 2010We propose a direct reconstruction algorithm for Computed Tomography, based on a local fusion of a few preliminary image estimates by means of a non-linear fusion rule. One such rule is based on a signal denoising technique which is spatially adaptive ... More
Compressed Learning: A Deep Neural Network ApproachOct 30 2016Compressed Learning (CL) is a joint signal processing and machine learning framework for inference from a signal, using a small number of measurements obtained by linear projections of the signal. In this paper we present an end-to-end deep learning approach ... More
Topological aspects of jetting to dripping transition in step emulsifiersDec 17 2018Fully three-dimensional, time-dependent, direct simulations of the non-ideal Navier-Stokes equations for a two-component fluid, shed light into the mechanism which inhibits droplet breakup in step emulsifiers below a critical threshold of the the width-to-height ... More
DeepRED: Deep Image Prior Powered by REDMar 25 2019Inverse problems in imaging are extensively studied, with a variety of strategies, tools, and theory that have been accumulated over the years. Recently, this field has been immensely influenced by the emergence of deep-learning techniques. One such contribution, ... More
Optimized Pre-Compensating CompressionNov 21 2017Jun 03 2018In imaging systems, following acquisition, an image/video is transmitted or stored and eventually presented to human observers using different and often imperfect display devices. While the resulting quality of the output image may severely be affected ... More
Restoration by CompressionNov 14 2017Jul 23 2018In this paper we study the topic of signal restoration using complexity regularization, quantifying the compression bit-cost of the signal estimate. While complexity-regularized restoration is an established concept, solid practical methods were suggested ... More
Working Locally Thinking Globally - Part II: Stability and Algorithms for Convolutional Sparse CodingJul 07 2016Jul 08 2016The convolutional sparse model has recently gained increasing attention in the signal and image processing communities, and several methods have been proposed for solving the pursuit problem emerging from it -- in particular its convex relaxation, Basis ... More
Working Locally Thinking Globally - Part I: Theoretical Guarantees for Convolutional Sparse CodingJul 07 2016The celebrated sparse representation model has led to remarkable results in various signal processing tasks in the last decade. However, despite its initial purpose of serving as a global prior for entire signals, it has been commonly used for modeling ... More
Acceleration of RED via Vector ExtrapolationMay 06 2018Models play an important role in inverse problems, serving as the prior for representing the original signal to be recovered. REgularization by Denoising (RED) is a recently introduced general framework for constructing such priors using state-of-the-art ... More
Phase transition in crowd synchrony of delay-coupled multilayer laser networksApr 17 2012An analogy between crowd synchrony and multi-layer neural network architectures is proposed. It indicates that many non-identical dynamical elements (oscillators) communicating indirectly via a few mediators (hubs) can synchronize when the number of delayed ... More
Acceleration of RED via Vector ExtrapolationMay 06 2018Apr 01 2019Models play an important role in inverse problems, serving as the prior for representing the original signal to be recovered. REgularization by Denoising (RED) is a recently introduced general framework for constructing such priors using state-of-the-art ... More
The Little Engine that Could: Regularization by Denoising (RED)Nov 09 2016Sep 03 2017Removal of noise from an image is an extensively studied problem in image processing. Indeed, the recent advent of sophisticated and highly effective denoising algorithms lead some to believe that existing methods are touching the ceiling in terms of ... More
Sublinear Optimization for Machine LearningOct 21 2010We give sublinear-time approximation algorithms for some optimization problems arising in machine learning, such as training linear classifiers and finding minimum enclosing balls. Our algorithms can be extended to some kernelized versions of these problems, ... More
The Projected GSURE for Automatic Parameter Tuning in Iterative Shrinkage MethodsMar 21 2010Linear inverse problems are very common in signal and image processing. Many algorithms that aim at solving such problems include unknown parameters that need tuning. In this work we focus on optimally selecting such parameters in iterative shrinkage ... More
Unsupervised Single Image Dehazing Using Dark Channel Prior LossDec 06 2018Single image dehazing is a critical stage in many modern-day autonomous vision applications. Early prior-based methods often involved a time-consuming minimization of a hand-crafted energy function. Recent learning-based approaches utilize the representational ... More
Modeling influenza-like illnesses through composite compartmental modelsJun 07 2017Epidemiological models for the spread of pathogens in a population are usually only able to describe a single pathogen. This makes their application unrealistic in cases where multiple pathogens with similar symptoms are spreading concurrently within ... More
Convolutional Neural Networks Analyzed via Convolutional Sparse CodingJul 27 2016Oct 10 2016Convolutional neural networks (CNN) have led to many state-of-the-art results spanning through various fields. However, a clear and profound theoretical understanding of the forward pass, the core algorithm of CNN, is still lacking. In parallel, within ... More
Exploiting Statistical Dependencies in Sparse Representations for Signal RecoveryOct 27 2010Mar 15 2012Signal modeling lies at the core of numerous signal and image processing applications. A recent approach that has drawn considerable attention is sparse representation modeling, in which the signal is assumed to be generated as a combination of a few ... More
The Little Engine that Could: Regularization by Denoising (RED)Nov 09 2016Removal of noise from an image is an extensively studied problem in image processing. Indeed, the recent advent of sophisticated and highly effective denoising algorithms lead some to believe that existing methods are touching the ceiling in terms of ... More
Compression for Multiple ReconstructionsFeb 12 2018In this work we propose a method for optimizing the lossy compression for a network of diverse reconstruction systems. We focus on adapting a standard image compression method to a set of candidate displays, presenting the decompressed signals to viewers. ... More
Image Processing using Smooth Ordering of its PatchesOct 14 2012We propose an image processing scheme based on reordering of its patches. For a given corrupted image, we extract all patches with overlaps, refer to these as coordinates in high-dimensional space, and order them such that they are chained in the "shortest ... More
Unified Single-Image and Video Super-Resolution via Denoising AlgorithmsOct 03 2018Single Image Super-Resolution (SISR) aims to recover a high-resolution image from a given low-resolution version of it. Video Super Resolution (VSR) targets series of given images, aiming to fuse them to create a higher resolution outcome. Although SISR ... More
On the Global-Local Dichotomy in Sparsity ModelingFeb 11 2017The traditional sparse modeling approach, when applied to inverse problems with large data such as images, essentially assumes a sparse model for small overlapping data patches. While producing state-of-the-art results, this methodology is suboptimal, ... More
Interactive Proofs For Quantum ComputationsOct 30 2008Nov 18 2008The widely held belief that BQP strictly contains BPP raises fundamental questions: Upcoming generations of quantum computers might already be too large to be simulated classically. Is it possible to experimentally test that these systems perform as they ... More
System-Aware CompressionJan 15 2018May 11 2018Many information systems employ lossy compression as a crucial intermediate stage among other processing components. While the important distortion is defined by the system's input and output signals, the compression usually ignores the system structure, ... More
Variations on the CSC modelOct 02 2018Over the past decade, the celebrated sparse representation model has achieved impressive results in various signal and image processing tasks. A convolutional version of this model, termed convolutional sparse coding (CSC), has been recently reintroduced ... More
DeepRED: Deep Image Prior Powered by REDMar 25 2019May 06 2019Inverse problems in imaging are extensively studied, with a variety of strategies, tools, and theory that have been accumulated over the years. Recently, this field has been immensely influenced by the emergence of deep-learning techniques. One such contribution, ... More
Redundant Wavelets on Graphs and High Dimensional Data CloudsNov 20 2011In this paper, we propose a new redundant wavelet transform applicable to scalar functions defined on high dimensional coordinates, weighted graphs and networks. The proposed transform utilizes the distances between the given data points. We modify the ... More
Generalized Tree-Based Wavelet TransformNov 20 2010Feb 28 2011In this paper we propose a new wavelet transform applicable to functions defined on graphs, high dimensional data and networks. The proposed method generalizes the Haar-like transform proposed in [1], and it is defined via a hierarchical tree, which is ... More
Example-Based Image Synthesis via Randomized Patch-MatchingSep 23 2016Image and texture synthesis is a challenging task that has long been drawing attention in the fields of image processing, graphics, and machine learning. This problem consists of modelling the desired type of images, either through training examples or ... More
Sparsity Based Methods for Overparameterized Variational ProblemsMay 20 2014Aug 14 2015Two complementary approaches have been extensively used in signal and image processing leading to novel results, the sparse representation methodology and the variational strategy. Recently, a new sparsity based model has been proposed, the cosparse analysis ... More
Poisson Inverse Problems by the Plug-and-Play schemeNov 08 2015The Anscombe transform offers an approximate conversion of a Poisson random variable into a Gaussian one. This transform is important and appealing, as it is easy to compute, and becomes handy in various inverse problems with Poisson noise contamination. ... More
Decoherence in Disordered Conductors at Low Temperatures, the effect of Soft Local ExcitationsDec 04 2003The conduction electrons' dephasing rate, $\tau_{\phi}^{-1}$, is expected to vanish with the temperature. A very intriguing apparent saturation of this dephasing rate in several systems was recently reported at very low temperatures. The suggestion that ... More
Optical mode characterization of single photons prepared via conditional measurements on a biphoton stateJul 16 2001A detailed theoretical analysis of the spatiotemporal mode of a single photon prepared via conditional measurements on a photon pair generated in the process of parametric down-conversion is presented. The maximum efficiency of coupling the photon into ... More
Toward a systematic 1/d expansion: Two particle propertiesFeb 04 2000We present a procedure to calculate 1/d corrections to the two-particle properties around the infinite dimensional dynamical mean field limit. Our method is based on a modified version of the scheme of Ref. onlinecite{SchillerIngersent}}. To test our ... More
Decay time integrals in neutral meson mixing and their efficient evaluationJul 03 2014In neutral meson mixing, a certain class of convolution integrals is required whose solution involves the error function $\mathrm{erf}(z)$ of a complex argument $z$. We show the the general shape of the analytic solution of these integrals, and give expressions ... More
Trainlets: Dictionary Learning in High DimensionsJan 31 2016May 12 2016Sparse representations has shown to be a very powerful model for real world signals, and has enabled the development of applications with notable performance. Combined with the ability to learn a dictionary from signal examples, sparsity-inspired algorithms ... More
A Deep Learning Approach to Block-based Compressed Sensing of ImagesJun 05 2016Compressed sensing (CS) is a signal processing framework for efficiently reconstructing a signal from a small number of measurements, obtained by linear projections of the signal. Block-based CS is a lightweight CS approach that is mostly suitable for ... More
Spin glass models for a network of real neuronsDec 30 2009Ising models with pairwise interactions are the least structured, or maximum-entropy, probability distributions that exactly reproduce measured pairwise correlations between spins. Here we use this equivalence to construct Ising models that describe the ... More
Postprocessing of Compressed Images via Sequential DenoisingOct 30 2015Mar 18 2016In this work we propose a novel postprocessing technique for compression-artifact reduction. Our approach is based on posing this task as an inverse problem, with a regularization that leverages on existing state-of-the-art image denoising algorithms. ... More
Bi-l0-l2-Norm Regularization for Blind Motion DeblurringAug 20 2014Jan 22 2015In blind motion deblurring, leading methods today tend towards highly non-convex approximations of the l0-norm, especially in the image regularization term. In this paper, we propose a simple, effective and fast approach for the estimation of the motion ... More
Doped Biomolecules in miniaturized electric junctionsDec 12 2011Control over molecular scale electrical properties within nano junctions is demonstrated, utilizing site-directed C60 targeting into protein macromolecules as a doping means. The protein molecules, self-assembled in a miniaturized transistor device, yield ... More
SEBOOST - Boosting Stochastic Learning Using Subspace Optimization TechniquesSep 02 2016We present SEBOOST, a technique for boosting the performance of existing stochastic optimization methods. SEBOOST applies a secondary optimization process in the subspace spanned by the last steps and descent directions. The method was inspired by the ... More
Adversarial Noise Attacks of Deep Learning Architectures -- Stability Analysis via Sparse Modeled SignalsMay 29 2018Aug 05 2019Despite their impressive performance, deep convolutional neural networks (CNNs) have been shown to be sensitive to small adversarial perturbations. These nuisances, which one can barely notice, are powerful enough to fool sophisticated and well performing ... More
Ising models for networks of real neuronsNov 22 2006Ising models with pairwise interactions are the least structured, or maximum-entropy, probability distributions that exactly reproduce measured pairwise correlations between spins. Here we use this equivalence to construct Ising models that describe the ... More
Adversarial Noise Attacks of Deep Learning Architectures - Stability Analysis via Sparse Modeled SignalsMay 29 2018Nov 22 2018Despite their impressive performance, deep convolutional neural networks (CNNs) have been shown to be sensitive to small adversarial perturbations. These nuisances, which one can barely notice, are powerful enough to fool sophisticated and well performing ... More
On MMSE and MAP Denoising Under Sparse Representation Modeling Over a Unitary DictionaryMar 21 2010Among the many ways to model signals, a recent approach that draws considerable attention is sparse representation modeling. In this model, the signal is assumed to be generated as a random linear combination of a few atoms from a pre-specified dictionary. ... More
Convolutional Dictionary Learning via Local ProcessingMay 09 2017Convolutional Sparse Coding (CSC) is an increasingly popular model in the signal and image processing communities, tackling some of the limitations of traditional patch-based sparse representations. Although several works have addressed the dictionary ... More
Coherence-Based Performance Guarantees for Estimating a Sparse Vector Under Random NoiseMar 26 2009Dec 02 2009We consider the problem of estimating a deterministic sparse vector x from underdetermined measurements Ax+w, where w represents white Gaussian noise and A is a given deterministic dictionary. We analyze the performance of three sparse estimation algorithms: ... More
An information theoretic approach to the functional classification of neuronsDec 31 2002A population of neurons typically exhibits a broad diversity of responses to sensory inputs. The intuitive notion of functional classification is that cells can be clustered so that most of the diversity is captured in the identity of the clusters rather ... More
Weak pairwise correlations imply strongly correlated network states in a neural populationDec 06 2005Biological networks have so many possible states that exhaustive sampling is impossible. Successful analysis thus depends on simplifying hypotheses, but experiments on many systems hint that complicated, higher order interactions among large groups of ... More
On Multi-Layer Basis Pursuit, Efficient Algorithms and Convolutional Neural NetworksJun 02 2018Nov 21 2018Parsimonious representations are ubiquitous in modeling and processing information. Motivated by the recent Multi-Layer Convolutional Sparse Coding (ML-CSC) model, we herein generalize the traditional Basis Pursuit problem to a multi-layer setting, introducing ... More
The Cosparse Analysis Model and AlgorithmsJun 24 2011After a decade of extensive study of the sparse representation synthesis model, we can safely say that this is a mature and stable field, with clear theoretical foundations, and appealing applications. Alongside this approach, there is an analysis counterpart ... More
Network information and connected correlationsJul 15 2003Entropy and information provide natural measures of correlation among elements in a network. We construct here the information theoretic analog of connected correlation functions: irreducible $N$--point correlation is measured by a decrease in entropy ... More
Multi-Layer Convolutional Sparse Modeling: Pursuit and Dictionary LearningAug 29 2017Jun 30 2018The recently proposed Multi-Layer Convolutional Sparse Coding (ML-CSC) model, consisting of a cascade of convolutional sparse layers, provides a new interpretation of Convolutional Neural Networks (CNNs). Under this framework, the computation of the forward ... More
Sorting and Selection in PosetsJul 10 2007Classical problems of sorting and searching assume an underlying linear ordering of the objects being compared. In this paper, we study a more general setting, in which some pairs of objects are incomparable. This generalization is relevant in applications ... More
Finding Approximate Local Minima for Nonconvex Optimization in Linear TimeNov 03 2016Nov 04 2016We design a non-convex second-order optimization algorithm that is guaranteed to return an approximate local minimum in time which is linear in the input representation. The time complexity of our algorithm to find an approximate local minimum is even ... More
Inverting Singlet and Triplet Excited States using Strong Light-Matter CouplingMar 21 2019In organic microcavities, hybrid light-matter states can form with energies that differ from the bare molecular excitation energies by nearly 1 eV. A timely question, given recent advances in the development of thermally activated delayed fluorescence ... More
Synchronization of complex human networksJun 07 2019The synchronization of human networks is essential for our civilization, and understanding the motivations, behavior, and basic parameters that govern the dynamics of human networks is important in many aspects of our lives. Human ensembles have been ... More
The Optimality of Correlated SamplingDec 04 2016In the "correlated sampling" problem, two players, say Alice and Bob, are given two distributions, say $P$ and $Q$ respectively, over the same universe and access to shared randomness. The two players are required to output two elements, without any interaction, ... More