Related papers: A null space analysis of the L1 synthesis method i…
A popular approach within the signal processing and machine learning communities consists in modelling signals as sparse linear combinations of atoms selected from a learned dictionary. While this paradigm has led to numerous empirical…
We propose a novel method for compressed sensing recovery using untrained deep generative models. Our method is based on the recently proposed Deep Image Prior (DIP), wherein the convolutional weights of the network are optimized to match…
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…
Compressive sensing (CS) has recently emerged as a powerful framework for acquiring sparse signals. The bulk of the CS literature has focused on the case where the acquired signal has a sparse or compressible representation in an…
The aim of this paper is to study the stability of the $\ell_1$ minimization for the compressive phase retrieval and to extend the instance-optimality in compressed sensing to the real phase retrieval setting. We first show that the…
This paper studies the problem of reconstructing sparse or compressible signals from compressed sensing measurements that have undergone nonuniform quantization. Previous approaches to this Quantized Compressed Sensing (QCS) problem based…
We study a class of real robust phase retrieval problems under a Gaussian assumption on the coding matrix when the received signal is sparsely corrupted by noise. The goal is to establish conditions on the sparsity under which the input…
High signal to noise ratio (SNR) consistency of model selection criteria in linear regression models has attracted a lot of attention recently. However, most of the existing literature on high SNR consistency deals with model order…
In this study, we investigated the stability of dynamic mode decomposition (DMD) algorithms to noisy data. To achieve a stable DMD algorithm, we applied the truncated total least squares (T-TLS) regression and optimal truncation level…
Signal reconstruction in compressive sensing involves finding a sparse solution that satisfies a set of linear constraints. Several approaches to this problem have been considered in existing reconstruction algorithms. They each provide a…
We consider the compressed sensing problem, where the object $x_0 \in \bR^N$ is to be recovered from incomplete measurements $y = Ax_0 + z$; here the sensing matrix $A$ is an $n \times N$ random matrix with iid Gaussian entries and $n < N$.…
This letter proposes a dictionary learning algorithm for blind one bit compressed sensing. In the blind one bit compressed sensing framework, the original signal to be reconstructed from one bit linear random measurements is sparse in an…
In the first part of the series papers, we set out to answer the following question: given specific restrictions on a set of samplers, what kind of signal can be uniquely represented by the corresponding samples attained, as the foundation…
Sparse modeling has been widely and successfully used in many applications such as computer vision, machine learning, and pattern recognition. Accompanied with those applications, significant research has studied the theoretical limits and…
In this paper, a fully compressed pattern matching problem is studied. The compression is represented by straight-line programs (SLPs), i.e. a context-free grammars generating exactly one string; the term fully means that both the pattern…
Many signal and image processing applications have benefited remarkably from the fact that the underlying signals reside in a low dimensional subspace. One of the main models for such a low dimensionality is the sparsity one. Within this…
Speaker adaptation methods aim to create fair quality synthesis speech voice font for target speakers while only limited resources available. Recently, as deep neural networks based statistical parametric speech synthesis (SPSS) methods…
In this paper, we study the problem of compressed sensing using binary measurement matrices and $\ell_1$-norm minimization (basis pursuit) as the recovery algorithm. We derive new upper and lower bounds on the number of measurements to…
Pretrained diffusion models have demonstrated strong capabilities in zero-shot inverse problem solving by incorporating observation information into the generation process of the diffusion models. However, this presents an inherent dilemma:…
Sparse coding, which refers to modeling a signal as sparse linear combinations of the elements of a learned dictionary, has proven to be a successful (and interpretable) approach in applications such as signal processing, computer vision,…