Related papers: Dictionary Identification - Sparse Matrix-Factoris…
Nonnegative matrix factorization (NMF) with group sparsity constraints is formulated as a probabilistic graphical model and, assuming some observed data have been generated by the model, a feasible variational Bayesian algorithm is derived…
This work investigates the problem of signal recovery from undersampled noisy sub-Gaussian measurements under the assumption of a synthesis-based sparsity model. Solving the $\ell^1$-synthesis basis pursuit allows for a simultaneous…
We consider the problem of recovering a partially sparse solution of an underdetermined system of linear equations by minimizing the $\ell_1$-norm of the part of the solution vector which is known to be sparse. Such a problem is closely…
Linear system identification and sparse dictionary learning can both be seen as structured matrix factorization problems. However, these two problems have historically been studied in isolation by the systems theory and machine learning…
In sparse signal representation, the choice of a dictionary often involves a tradeoff between two desirable properties -- the ability to adapt to specific signal data and a fast implementation of the dictionary. To sparsely represent…
Over the past decade, learning a dictionary from input images for sparse modeling has been one of the topics which receive most research attention in image processing and compressed sensing. Most existing dictionary learning methods…
One way to understand time-series data is to identify the underlying dynamical system which generates it. This task can be done by selecting an appropriate model and a set of parameters which best fits the dynamics while providing the…
We propose an iterative algorithm for the minimization of a $\ell_1$-norm penalized least squares functional, under additional linear constraints. The algorithm is fully explicit: it uses only matrix multiplications with the three matrices…
In this paper, we introduce a sparse approximation property of order $s$ for a measurement matrix ${\bf A}$: $$\|{\bf x}_s\|_2\le D \|{\bf A}{\bf x}\|_2+ \beta \frac{\sigma_s({\bf x})}{\sqrt{s}} \quad {\rm for\ all} \ {\bf x},$$ where ${\bf…
This paper investigates the problem of signal estimation from undersampled noisy sub-Gaussian measurements under the assumption of a cosparse model. Based on generalized notions of sparsity, we derive novel recovery guarantees for the…
We consider the problem of learning overcomplete dictionaries in the context of sparse coding, where each sample selects a sparse subset of dictionary elements. Our main result is a strategy to approximately recover the unknown dictionary…
We investigate the problem of factorizing a matrix into several sparse matrices and propose an algorithm for this under randomness and sparsity assumptions. This problem can be viewed as a simplification of the deep learning problem where…
Sparsity-based models and techniques have been exploited in many signal processing and imaging applications. Data-driven methods based on dictionary and sparsifying transform learning enable learning rich image features from data, and can…
This article presents new results concerning the recovery of a signal from magnitude only measurements where the signal is not sparse in an orthonormal basis but in a redundant dictionary. To solve this phaseless problem, we analyze the $…
Convolutional 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…
Recently, the problem of blind image separation has been widely investigated, especially the medical image denoise which is the main step in medical diag-nosis. Removing the noise without affecting relevant features of the image is the main…
We consider the problem of learning a low-dimensional signal model from a collection of training samples. The mainstream approach would be to learn an overcomplete dictionary to provide good approximations of the training samples using…
This technical note considers the identification of nonlinear discrete-time systems with additive process noise but without measurement noise. In particular, we propose a method and its associated algorithm to identify the system nonlinear…
The power of sparse signal coding with learned dictionaries has been demonstrated in a variety of applications and fields, from signal processing to statistical inference and machine learning. However, the statistical properties of these…
This work presents an approach for image reconstruction in clinical low-dose tomography that combines principles from sparse signal processing with ideas from deep learning. First, we describe sparse signal representation in terms of…