Related papers: Sparse Recovery over Graph Incidence Matrices
We study the recovery of sparse signals from underdetermined linear measurements when a potentially erroneous support estimate is available. Our results are twofold. First, we derive necessary and sufficient conditions for signal recovery…
In signal processing and data recovery, reconstructing a signal from quadratic measurements poses a significant challenge, particularly in high-dimensional settings where measurements $m$ is far less than the signal dimension $n$ (i.e., $m…
Graph inference plays an essential role in machine learning, pattern recognition, and classification. Signal processing based approaches in literature generally assume some variational property of the observed data on the graph. We make a…
The problem of estimating a sparse signal from low dimensional noisy observations arises in many applications, including super resolution, signal deconvolution, and radar imaging. In this paper, we consider a sparse signal model with…
The phase retrieval problem asks to recover a natural signal $y_0 \in \mathbb{R}^n$ from $m$ quadratic observations, where $m$ is to be minimized. As is common in many imaging problems, natural signals are considered sparse with respect to…
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…
The effectiveness of using model sparsity as a priori information when solving linear inverse problems is studied. We investigate the reconstruction quality of such a method in the non-idealized case and compute some typical recovery errors…
The paper discusses the recovery of signals in the case that signals are nearly sparse with respect to a tight frame $D$ by means of the $l_1$-analysis approach. We establish several new sufficient conditions regarding the $D$-restricted…
Sparse phase retrieval with redundant dictionary is to reconstruct the signals of interest that are (nearly) sparse in a redundant dictionary or frame from the phaseless measurements via the optimization models. Gao [7] presented conditions…
This paper considers efficient sampling of simultaneously sparse and correlated (S$\&$C) signals. Such signals arise in various applications in array processing. We propose an implementable sampling architecture for the acquisition of…
We describe a probabilistic, {\it sublinear} runtime, measurement-optimal system for model-based sparse recovery problems through dimensionality reducing, {\em dense} random matrices. Specifically, we obtain a linear sketch $u\in \R^M$ of a…
The sampling of graph signals has recently drawn much attention due to the wide applications of graph signal processing. While a lot of efficient methods and interesting results have been reported to the sampling of band-limited or smooth…
Parsimony in signal representation is a topic of active research. Sparse signal processing and representation is the outcome of this line of research which has many applications in information processing and has shown significant…
We consider a specific graph learning task: reconstructing a symmetric matrix that represents an underlying graph using linear measurements. We present a sparsity characterization for distributions of random graphs (that are allowed to…
This article treats the problem of learning a dictionary providing sparse representations for a given signal class, via $\ell_1$-minimisation. The problem can also be seen as factorising a $\ddim \times \nsig$ matrix $Y=(y_1 >... y_\nsig),…
Lower dimensional signal representation schemes frequently assume that the signal of interest lies in a single vector space. In the context of the recently developed theory of compressive sensing (CS), it is often assumed that the signal of…
Compressed Sensing aims to capture attributes of a sparse signal using very few measurements. Cand\`{e}s and Tao showed that sparse reconstruction is possible if the sensing matrix acts as a near isometry on all $\boldsymbol{k}$-sparse…
We formulate a unified framework for the separation of signals that are sparse in "morphologically" different redundant dictionaries. This formulation incorporates the so-called "analysis" and "synthesis" approaches as special cases and…
In this paper, we consider the recovery of block sparse signals, whose nonzero entries appear in blocks (or clusters) rather than spread arbitrarily throughout the signal, from incomplete linear measurement. A high order sufficient…
Sparse matrices are favorable objects in machine learning and optimization. When such matrices are used, in place of dense ones, the overall complexity requirements in optimization can be significantly reduced in practice, both in terms of…