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A dictionary is a database of standard vectors, so that other vectors / signals are expressed as linear combinations of dictionary vectors, and the task of learning a dictionary for a given data is to find a good dictionary so that the…
Stochastic gradient descent type methods are ubiquitous in machine learning, but they are only applicable to the optimization of differentiable functions. Proximal algorithms are more general and applicable to nonsmooth functions. We…
Compressed sensing provided a data-acquisition paradigm for sparse signals. Remarkably, it has been shown that practical algorithms provide robust recovery from noisy linear measurements acquired at a near optimal sampling rate. In many…
The problem of population recovery refers to estimating a distribution based on incomplete or corrupted samples. Consider a random poll of sample size $n$ conducted on a population of individuals, where each pollee is asked to answer $d$…
Blind inverse problems arise in many experimental settings where both the signal of interest and the forward operator are (partially) unknown. In this context, methods developed for the non-blind case cannot be adapted in a straightforward…
We study the Dictionary Learning (aka Sparse Coding) problem of obtaining a sparse representation of data points, by learning \emph{dictionary vectors} upon which the data points can be written as sparse linear combinations. We view this…
For noisy compressive sensing systems, the asymptotic distortion with respect to an arbitrary distortion function is determined when a general class of least-square based reconstruction schemes is employed. The sampling matrix is considered…
Neural retrievers based on dense representations combined with Approximate Nearest Neighbors search have recently received a lot of attention, owing their success to distillation and/or better sampling of examples for training -- while…
Signal 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…
State-of-the-art learned reconstruction methods often rely on black-box modules that, despite their strong performance, raise questions about their interpretability and robustness. Here, we build on a recently proposed image reconstruction…
The theory of Compressed Sensing, the emerging sampling paradigm 'that goes against the common wisdom', asserts that 'one can recover signals in Rn from far fewer samples or measurements, if the signal has a sparse representation in some…
The Inexact Restoration approach has proved to be an adequate tool for handling the problem of minimizing an expensive function within an arbitrary feasible set by using different degrees of precision in the objective function. The Inexact…
We present a sparse estimation and dictionary learning framework for compressed fiber sensing based on a probabilistic hierarchical sparse model. To handle severe dictionary coherence, selective shrinkage is achieved using a Weibull prior,…
Model selection and sparse recovery are two important problems for which many regularization methods have been proposed. We study the properties of regularization methods in both problems under the unified framework of regularized least…
Phase retrieval aims at reconstructing unknown signals from magnitude measurements of linear mixtures. In this paper, we consider the phase retrieval with dictionary learning problem, which includes an additional prior information that the…
We obtain new sampling discretization results in Orlicz norms on finite dimensional spaces. As applications, we study sampling recovery problems, where the error of the recovery process is calculated with respect to different Orlicz norms.…
In this work, we study the problem of learning a nonlinear dynamical system by parameterizing its dynamics using basis functions. We assume that disturbances occur at each time step with an arbitrary probability $p$, which models the…
In this work, we propose an adaptive sparse learning algorithm that can be applied to learn the physical processes and obtain a sparse representation of the solution given a large snapshot space. Assume that there is a rich class of…
This paper proposes a robust adaptive algorithm for smooth graph signal recovery which is based on generalized correntropy. A proper cost function is defined for this purpose. The proposed algorithm is derived and a kernel width…
Convolutional sparse representations are a form of sparse representation with a dictionary that has a structure that is equivalent to convolution with a set of linear filters. While effective algorithms have recently been developed for the…