arXiv subjects

Michael Elad

Publications and source records attributed to Michael Elad.

At least 73 records · Page 4Linked to original sources

arXiv2020

Learned Greedy Method (LGM): A Novel Neural Architecture for Sparse Coding and Beyond

The fields of signal and image processing have been deeply influenced by the introduction of deep neural networks. These are successfully deployed in a wide range of real-world applications, obtaining state of the art results and surpassing well-known and well-established classical methods. Despite their impressive success, the architectures used in many of these neural networks come with no clear justification. As such, these are usually treated as "black box" machines that lack any kind of interpretability. A constructive remedy to this drawback is a systematic design of such networks by unfolding well-understood iterative algorithms. A popular representative of this approach is the Iterative Shrinkage-Thresholding Algorithm (ISTA) and its learned version -- LISTA, aiming for the sparse representations of the processed signals. In this paper we revisit this sparse coding task and propose an unfolded version of a greedy pursuit algorithm for the same goal. More specifically, we concentrate on the well-known Orthogonal-Matching-Pursuit (OMP) algorithm, and introduce its unfolded and learned version. Key features of our Learned Greedy Method (LGM) are the ability to accommodate a dynamic number of unfolded layers, and a stopping mechanism based on representation error, both adapted to the input. We develop several variants of the proposed LGM architecture and test some of them in various experiments, demonstrating their flexibility and efficiency.

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arXiv2020

The Rate-Distortion-Accuracy Tradeoff: JPEG Case Study

Handling digital images is almost always accompanied by a lossy compression in order to facilitate efficient transmission and storage. This introduces an unavoidable tension between the allocated bit-budget (rate) and the faithfulness of the resulting image to the original one (distortion). An additional complicating consideration is the effect of the compression on recognition performance by given classifiers (accuracy). This work aims to explore this rate-distortion-accuracy tradeoff. As a case study, we focus on the design of the quantization tables in the JPEG compression standard. We offer a novel optimal tuning of these tables via continuous optimization, leveraging a differential implementation of both the JPEG encoder-decoder and an entropy estimator. This enables us to offer a unified framework that considers the interplay between rate, distortion and classification accuracy. In all these fronts, we report a substantial boost in performance by a simple and easily implemented modification of these tables.

eess.IV↗

arXiv2020

When and How Can Deep Generative Models be Inverted?

Deep generative models (e.g. GANs and VAEs) have been developed quite extensively in recent years. Lately, there has been an increased interest in the inversion of such a model, i.e. given a (possibly corrupted) signal, we wish to recover the latent vector that generated it. Building upon sparse representation theory, we define conditions that are applicable to any inversion algorithm (gradient descent, deep encoder, etc.), under which such generative models are invertible with a unique solution. Importantly, the proposed analysis is applicable to any trained model, and does not depend on Gaussian i.i.d. weights. Furthermore, we introduce two layer-wise inversion pursuit algorithms for trained generative networks of arbitrary depth, and accompany these with recovery guarantees. Finally, we validate our theoretical results numerically and show that our method outperforms gradient descent when inverting such generators, both for clean and corrupted signals.

cs.LG↗

arXiv2020

LIDIA: Lightweight Learned Image Denoising with Instance Adaptation

Image denoising is a well studied problem with an extensive activity that has spread over several decades. Despite the many available denoising algorithms, the quest for simple, powerful and fast denoisers is still an active and vibrant topic of research. Leading classical denoising methods are typically designed to exploit the inner structure in images by modeling local overlapping patches, while operating in an unsupervised fashion. In contrast, recent newcomers to this arena are supervised and universal neural-network-based methods that bypass this modeling altogether, targeting the inference goal directly and globally, while tending to be very deep and parameter heavy. This work proposes a novel lightweight learnable architecture for image denoising, and presents a combination of supervised and unsupervised training of it, the first aiming for a universal denoiser and the second for adapting it to the incoming image. Our architecture embeds in it several of the main concepts taken from classical methods, relying on patch processing, leveraging non-local self-similarity, exploiting representation sparsity and providing a multiscale treatment. Our proposed universal denoiser achieves near state-of-the-art results, while using a small fraction of the typical number of parameters. In addition, we introduce and demonstrate two highly effective ways for further boosting the denoising performance, by adapting this universal network to the input image.

eess.IV↗

arXiv2020

Ada-LISTA: Learned Solvers Adaptive to Varying Models

Neural networks that are based on unfolding of an iterative solver, such as LISTA (learned iterative soft threshold algorithm), are widely used due to their accelerated performance. Nevertheless, as opposed to non-learned solvers, these networks are trained on a certain dictionary, and therefore they are inapplicable for varying model scenarios. This work introduces an adaptive learned solver, termed Ada-LISTA, which receives pairs of signals and their corresponding dictionaries as inputs, and learns a universal architecture to serve them all. We prove that this scheme is guaranteed to solve sparse coding in linear rate for varying models, including dictionary perturbations and permutations. We also provide an extensive numerical study demonstrating its practical adaptation capabilities. Finally, we deploy Ada-LISTA to natural image inpainting, where the patch-masks vary spatially, thus requiring such an adaptation.

cs.LG↗

arXiv2019

DeepRED: Deep Image Prior Powered by RED

Inverse 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, which is the focus of this paper, is the Deep Image Prior (DIP) work by Ulyanov, Vedaldi, and Lempitsky (2018). DIP offers a new approach towards the regularization of inverse problems, obtained by forcing the recovered image to be synthesized from a given deep architecture. While DIP has been shown to be quite an effective unsupervised approach, its results still fall short when compared to state-of-the-art alternatives. In this work, we aim to boost DIP by adding an explicit prior, which enriches the overall regularization effect in order to lead to better-recovered images. More specifically, we propose to bring-in the concept of Regularization by Denoising (RED), which leverages existing denoisers for regularizing inverse problems. Our work shows how the two (DIP and RED) can be merged into a highly effective unsupervised recovery process while avoiding the need to differentiate the chosen denoiser, and leading to very effective results, demonstrated for several tested problems.

cs.CV↗

arXiv2019

Rethinking the CSC Model for Natural Images

Sparse representation with respect to an overcomplete dictionary is often used when regularizing inverse problems in signal and image processing. In recent years, the Convolutional Sparse Coding (CSC) model, in which the dictionary consists of shift-invariant filters, has gained renewed interest. While this model has been successfully used in some image processing problems, it still falls behind traditional patch-based methods on simple tasks such as denoising. In this work we provide new insights regarding the CSC model and its capability to represent natural images, and suggest a Bayesian connection between this model and its patch-based ancestor. Armed with these observations, we suggest a novel feed-forward network that follows an MMSE approximation process to the CSC model, using strided convolutions. The performance of this supervised architecture is shown to be on par with state of the art methods while using much fewer parameters.

eess.IV↗

arXiv2019

Deep-Energy: Unsupervised Training of Deep Neural Networks

The success of deep learning has been due, in no small part, to the availability of large annotated datasets. Thus, a major bottleneck in current learning pipelines is the time-consuming human annotation of data. In scenarios where such input-output pairs cannot be collected, simulation is often used instead, leading to a domain-shift between synthesized and real-world data. This work offers an unsupervised alternative that relies on the availability of task-specific energy functions, replacing the generic supervised loss. Such energy functions are assumed to lead to the desired label as their minimizer given the input. The proposed approach, termed "Deep Energy", trains a Deep Neural Network (DNN) to approximate this minimization for any chosen input. Once trained, a simple and fast feed-forward computation provides the inferred label. This approach allows us to perform unsupervised training of DNNs with real-world inputs only, and without the need for manually-annotated labels, nor synthetically created data. "Deep Energy" is demonstrated in this paper on three different tasks -- seeded segmentation, image matting and single image dehazing -- exposing its generality and wide applicability. Our experiments show that the solution provided by the network is often much better in quality than the one obtained by a direct minimization of the energy function, suggesting an added regularization property in our scheme.

cs.LG↗

arXiv2019

Unsupervised Single Image Dehazing Using Dark Channel Prior Loss

Single 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 power of deep neural networks (DNNs) to learn the underlying transformation between hazy and clear images. Due to inherent limitations in collecting matching clear and hazy images, these methods resort to training on synthetic data; constructed from indoor images and corresponding depth information. This may result in a possible domain shift when treating outdoor scenes. We propose a completely unsupervised method of training via minimization of the well-known, Dark Channel Prior (DCP) energy function. Instead of feeding the network with synthetic data, we solely use real-world outdoor images and tune the network's parameters by directly minimizing the DCP. Although our "Deep DCP" technique can be regarded as a fast approximator of DCP, it actually improves its results significantly. This suggests an additional regularization obtained via the network and learning process. Experiments show that our method performs on par with large-scale supervised methods.

cs.CV↗

arXiv2019

Adversarial Noise Attacks of Deep Learning Architectures -- Stability Analysis via Sparse Modeled Signals

Despite 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 classifiers, leading to ridiculous misclassification results. In this paper we analyze the stability of state-of-the-art deep-learning classification machines to adversarial perturbations, where we assume that the signals belong to the (possibly multi-layer) sparse representation model. We start with convolutional sparsity and then proceed to its multi-layered version, which is tightly connected to CNNs. Our analysis links between the stability of the classification to noise and the underlying structure of the signal, quantified by the sparsity of its representation under a fixed dictionary. In addition, we offer similar stability theorems for two practical pursuit algorithms, which are posed as two different deep-learning architectures - the layered Thresholding and the layered Basis Pursuit. Our analysis establishes the better robustness of the later to adversarial attacks. We corroborate these theoretical results by numerical experiments on three datasets: MNIST, CIFAR-10 and CIFAR-100.

stat.ML↗

arXiv2019

MMSE Approximation For Sparse Coding Algorithms Using Stochastic Resonance

Sparse coding refers to the pursuit of the sparsest representation of a signal in a typically overcomplete dictionary. From a Bayesian perspective, sparse coding provides a Maximum a Posteriori (MAP) estimate of the unknown vector under a sparse prior. In this work, we suggest enhancing the performance of sparse coding algorithms by a deliberate and controlled contamination of the input with random noise, a phenomenon known as stochastic resonance. The proposed method adds controlled noise to the input and estimates a sparse representation from the perturbed signal. A set of such solutions is then obtained by projecting the original input signal onto the recovered set of supports. We present two variants of the described method, which differ in their final step. The first is a provably convergent approximation to the Minimum Mean Square Error (MMSE) estimator, relying on the generative model and applying a weighted average over the recovered solutions. The second is a relaxed variant of the former that simply applies an empirical mean. We show that both methods provide a computationally efficient approximation to the MMSE estimator, which is typically intractable to compute. We demonstrate our findings empirically and provide a theoretical analysis of our method under several different cases.

eess.SP↗

arXiv2019

Acceleration of RED via Vector Extrapolation

Models 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 denoising algorithms. Using RED, solving inverse problems is shown to amount to an iterated denoising process. However, as the complexity of denoising algorithms is generally high, this might lead to an overall slow algorithm. In this paper, we suggest an accelerated technique based on vector extrapolation (VE) to speed-up existing RED solvers. Numerical experiments validate the obtained gain by VE, leading to a substantial savings in computations compared with the original fixed-point method.

cs.CV↗

arXiv2018

On Multi-Layer Basis Pursuit, Efficient Algorithms and Convolutional Neural Networks

Parsimonious 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 similar sparse enforcing penalties at different representation layers in a symbiotic relation between synthesis and analysis sparse priors. We explore different iterative methods to solve this new problem in practice, and we propose a new Multi-Layer Iterative Soft Thresholding Algorithm (ML-ISTA), as well as a fast version (ML-FISTA). We show that these nested first order algorithms converge, in the sense that the function value of near-fixed points can get arbitrarily close to the solution of the original problem. We further show how these algorithms effectively implement particular recurrent convolutional neural networks (CNNs) that generalize feed-forward ones without introducing any parameters. We present and analyze different architectures resulting unfolding the iterations of the proposed pursuit algorithms, including a new Learned ML-ISTA, providing a principled way to construct deep recurrent CNNs. Unlike other similar constructions, these architectures unfold a global pursuit holistically for the entire network. We demonstrate the emerging constructions in a supervised learning setting, consistently improving the performance of classical CNNs while maintaining the number of parameters constant.

cs.LG↗

arXiv2018

A Local Block Coordinate Descent Algorithm for the Convolutional Sparse Coding Model

The Convolutional Sparse Coding (CSC) model has recently gained considerable traction in the signal and image processing communities. By providing a global, yet tractable, model that operates on the whole image, the CSC was shown to overcome several limitations of the patch-based sparse model while achieving superior performance in various applications. Contemporary methods for pursuit and learning the CSC dictionary often rely on the Alternating Direction Method of Multipliers (ADMM) in the Fourier domain for the computational convenience of convolutions, while ignoring the local characterizations of the image. A recent work by Papyan et al. suggested the SBDL algorithm for the CSC, while operating locally on image patches. SBDL demonstrates better performance compared to the Fourier-based methods, albeit still relying on the ADMM. In this work we maintain the localized strategy of the SBDL, while proposing a new and much simpler approach based on the Block Coordinate Descent algorithm - this method is termed Local Block Coordinate Descent (LoBCoD). Furthermore, we introduce a novel stochastic gradient descent version of LoBCoD for training the convolutional filters. The Stochastic-LoBCoD leverages the benefits of online learning, while being applicable to a single training image. We demonstrate the advantages of the proposed algorithms for image inpainting and multi-focus image fusion, achieving state-of-the-art results.

cs.CV↗

arXiv2018

Unified Single-Image and Video Super-Resolution via Denoising Algorithms

Single 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 and VSR seem to have a lot in common, most SISR algorithms do not have a simple and direct extension to VSR. VSR is considered a more challenging inverse problem, mainly due to its reliance on a sub-pixel accurate motion-estimation, which has no parallel in SISR. Another complication is the dynamics of the video, often addressed by simply generating a single frame instead of a complete output sequence. In this work we suggest a simple and robust super-resolution framework that can be applied to single images and easily extended to video. Our work relies on the observation that denoising of images and videos is well-managed and very effectively treated by a variety of methods. We exploit the Plug-and-Play-Prior framework and the Regularization-by-Denoising (RED) approach that extends it, and show how to use such denoisers in order to handle the SISR and the VSR problems using a unified formulation and framework. This way, we benefit from the effectiveness and efficiency of existing image/video denoising algorithms, while solving much more challenging problems. More specifically, harnessing the VBM3D video denoiser, we obtain a strongly competitive motion-estimation free VSR algorithm, showing tendency to a high-quality output and fast processing.

eess.IV↗

arXiv2018

Variations on the CSC model

Over 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 and extensively studied. CSC brings a natural remedy to the limitation of typical sparse enforcing approaches of handling global and high-dimensional signals by local, patch-based, processing. While the classic field of sparse representations has been able to cater for the diverse challenges of different signal processing tasks by considering a wide range of problem formulations, almost all available algorithms that deploy the CSC model consider the same $\ell_1 - \ell_2$ problem form. As we argue in this paper, this CSC pursuit formulation is also too restrictive as it fails to explicitly exploit some local characteristics of the signal. This work expands the range of formulations for the CSC model by proposing two convex alternatives that merge global norms with local penalties and constraints. The main contribution of this work is the derivation of efficient and provably converging algorithms to solve these new sparse coding formulations.

eess.SP↗

arXiv2018

Multi-Layer Sparse Coding: The Holistic Way

The recently proposed multi-layer sparse model has raised insightful connections between sparse representations and convolutional neural networks (CNN). In its original conception, this model was restricted to a cascade of convolutional synthesis representations. In this paper, we start by addressing a more general model, revealing interesting ties to fully connected networks. We then show that this multi-layer construction admits a brand new interpretation in a unique symbiosis between synthesis and analysis models: while the deepest layer indeed provides a synthesis representation, the mid-layers decompositions provide an analysis counterpart. This new perspective exposes the suboptimality of previously proposed pursuit approaches, as they do not fully leverage all the information comprised in the model constraints. Armed with this understanding, we address fundamental theoretical issues, revisiting previous analysis and expanding it. Motivated by the limitations of previous algorithms, we then propose an integrated - holistic - alternative that estimates all representations in the model simultaneously, and analyze all these different schemes under stochastic noise assumptions. Inspired by the synthesis-analysis duality, we further present a Holistic Pursuit algorithm, which alternates between synthesis and analysis sparse coding steps, eventually solving for the entire model as a whole, with provable improved performance. Finally, we present numerical results that demonstrate the practical advantages of our approach.

eess.IV↗

arXiv2018

Restoration by Compression

In 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 only for the Gaussian denoising task, leaving more complicated restoration problems without a generally constructive approach. Here we present practical methods for complexity-regularized restoration of signals, accommodating degradations caused by a known linear operator of an arbitrary form. Our iterative procedure, obtained using the alternating direction method of multipliers (ADMM) approach, addresses the restoration task as a sequence of simpler problems involving L2-regularized estimations and rate-distortion optimizations (considering the squared-error criterion). Further, we replace the rate-distortion optimizations with an arbitrary standardized compression technique and thereby restore the signal by leveraging underlying models designed for compression. Additionally, we propose a shift-invariant complexity regularizer, measuring the bit-cost of all the shifted forms of the estimate, extending our method to use averaging of decompressed outputs gathered from compression of shifted signals. On the theoretical side, we present an analysis of complexity-regularized restoration of a cyclo-stationary Gaussian signal from deterioration by a linear shift-invariant operator and an additive white Gaussian noise. The theory shows that optimal complexity-regularized restoration relies on an elementary restoration filter and compression spreading reconstruction quality unevenly based on the energy distribution of the degradation filter. Nicely, these ideas are realized also in the proposed practical methods. The presented experiments show good results for image deblurring and inpainting using the JPEG2000 and HEVC compression standards.

cs.IT↗