Related papers: Robust Sparse Analysis Regularization
Regularization is a common tool in variational inverse problems to impose assumptions on the parameters of the problem. One such assumption is sparsity, which is commonly promoted using lasso and total variation-like regularization.…
In the problem of learning mixtures of linear regressions, the goal is to learn a collection of signal vectors from a sequence of (possibly noisy) linear measurements, where each measurement is evaluated on an unknown signal drawn uniformly…
We propose a unified fractional regularization framework for sparse signal recovery based on the $\ell_1/\ell_p^q$ model. This model generalizes several widely used sparsity-promoting regularizers and provides additional flexibility through…
A recent technique of randomized smoothing has shown that the worst-case (adversarial) $\ell_2$-robustness can be transformed into the average-case Gaussian-robustness by "smoothing" a classifier, i.e., by considering the averaged…
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…
We consider the problem of exact support recovery of sparse signals via noisy measurements. The main focus is the sufficient and necessary conditions on the number of measurements for support recovery to be reliable. By drawing an analogy…
This paper considers the use of total variation regularization in the recovery of approximately gradient sparse signals from their noisy discrete Fourier samples in the context of compressed sensing. It has been observed over the last…
The notion of developing statistical methods in machine learning which are robust to adversarial perturbations in the underlying data has been the subject of increasing interest in recent years. A common feature of this work is that the…
In this paper, we are concerned with regularized regression problems where the prior regularizer is a proper lower semicontinuous and convex function which is also partly smooth relative to a Riemannian submanifold. This encompasses as…
In this paper we study the recovery conditions of weighted $l_{1}$ minimization for signal reconstruction from incomplete linear measurements when partial prior support information is available. We obtain that a high order RIP condition can…
The Lasso is a popular regression method for high-dimensional problems in which the number of parameters $\theta_1,\dots,\theta_N$, is larger than the number $n$ of samples: $N>n$. A useful heuristics relates the statistical properties of…
We investigate the stabilization of unstable multidimensional partially observed single-sensor and multi-sensor linear systems driven by unbounded noise and controlled over discrete noiseless channels under fixed-rate information…
In high-dimensional statistical inference, sparsity regularizations have shown advantages in consistency and convergence rates for coefficient estimation. We consider a generalized version of Sparse-Group Lasso which captures both…
Compressed sensing deals with the reconstruction of sparse signals using a small number of linear measurements. One of the main challenges in compressed sensing is to find the support of a sparse signal. In the literature, several bounds on…
Sparse recovery is one of the most fundamental and well-studied inverse problems. Standard statistical formulations of the problem are provably solved by general convex programming techniques and more practical, fast (nearly-linear time)…
Phase-only compressed sensing (PO-CS) concerns the recovery of sparse signals from the phases of complex measurements. Recent results show that sparse signals in the standard sphere $\mathbb{S}^{n-1}$ can be exactly recovered from complex…
We study sparse signal recovery from noisy linear observations using nonconvex log-sum regularization. The log-sum penalty reduces the shrinkage bias of $\ell_1$ regularization and more closely approximates the $\ell_0$ regularization, but…
We study the complexity of the entire regularization path for least squares regression with 1-norm penalty, known as the Lasso. Every regression parameter in the Lasso changes linearly as a function of the regularization value. The number…
In-network distributed estimation of sparse parameter vectors via diffusion LMS strategies has been studied and investigated in recent years. In all the existing works, some convex regularization approach has been used at each node of the…
The least squares problem with L1-regularized regressors, called Lasso, is a widely used approach in optimization problems where sparsity of the regressors is desired. This formulation is fundamental for many applications in signal…