Related papers: Critical point theory for sparse recovery
Motivated by recent results in the statistical physics of spin glasses, we study the recovery of a sparse vector $\mathbf{x}_0\in \mathbb{S}^{n-1}$, $\|\mathbf{x}_0\|_{\ell_0} = k<n$, from $m$ quadratic measurements of the form $…
We propose a new algorithm for recovery of sparse signals from their compressively sensed samples. The proposed algorithm benefits from the strategy of gradual movement to estimate the positions of non-zero samples of sparse signal. We…
Data assimilation algorithms combine information from observations and prior model information to obtain the most likely state of a dynamical system. The linearised weak-constraint four-dimensional variational assimilation problem can be…
For mathematical programs with complementarity constraints (MPCC), we study the stability properties of their Scholtes regularization. Our goal is to relate nondegenerate C-stationary points of MPCC with nondegenerate Karush-Kuhn-Tucker…
This paper develops a novel Continuous-time Accelerated Proximal Point Algorithm (CAPPA) for $\ell_1$-minimization problems with provable fixed-time convergence guarantees. The problem of $\ell_1$-minimization appears in several contexts,…
Deep learning researchers commonly suggest that converged models are stuck in local minima. More recently, some researchers observed that under reasonable assumptions, the vast majority of critical points are saddle points, not true minima.…
Given an overcomplete dictionary $A$ and a signal $b = Ac^*$ for some sparse vector $c^*$ whose nonzero entries correspond to linearly independent columns of $A$, classical sparse signal recovery theory considers the problem of whether…
Control contraction metrics (CCMs) are a new approach to nonlinear control design based on contraction theory. The resulting design problems are expressed as pointwise linear matrix inequalities and are and well-suited to solution via…
This manuscript goes through the fundamental connections between statistical mechanics and estimation theory by focusing on the particular problem of compressive sensing. We first show that the asymptotic analysis of a sparse recovery…
Decentralized sparsity learning has attracted a significant amount of attention recently due to its rapidly growing applications. To obtain the robust and sparse estimators, a natural idea is to adopt the non-smooth median loss combined…
A noisy underdetermined system of linear equations is considered in which a sparse vector (a vector with a few nonzero elements) is subject to measurement. The measurement matrix elements are drawn from a Gaussian distribution. We study the…
In this paper, we study the support recovery guarantees of underdetermined sparse regression using the $\ell_1$-norm as a regularizer and a non-smooth loss function for data fidelity. More precisely, we focus in detail on the cases of…
The fundamental principle underlying compressed sensing is that a signal, which is sparse under some basis representation, can be recovered from a small number of linear measurements. However, prior knowledge of the sparsity basis is…
This paper considers the problem of recovering either a low rank matrix or a sparse vector from observations of linear combinations of the vector or matrix elements. Recent methods replace the non-convex regularization with $\ell_1$ or…
Recent advances in quantized compressed sensing and high-dimensional estimation have shown that signal recovery is even feasible under strong non-linear distortions in the observation process. An important characteristic of associated…
The sparse spike estimation problem consists in estimating a number of off-the-grid impulsive sources from under-determined linear measurements. Information theoretic results ensure that the minimization of a non-convex functional is able…
Compressive sensing relies on the sparse prior imposed on the signal of interest to solve the ill-posed recovery problem in an under-determined linear system. The objective function used to enforce the sparse prior information should be…
In centralized settings, it is well known that stochastic gradient descent (SGD) avoids saddle points and converges to local minima in nonconvex problems. However, similar guarantees are lacking for distributed first-order algorithms. The…
Sequential Compressive Sensing, which may be widely used in sensing devices, is a popular topic of recent research. This paper proposes an online recovery algorithm for sparse approximation of sequential compressive sensing. Several…
Compared with digital methods, sparse recovery based on spiking neural networks has great advantages like high computational efficiency and low power-consumption. However, current spiking algorithms cannot guarantee more accurate estimates…