Related papers: Sparse Time-Frequency decomposition by dictionary …

In this paper, we discuss application of iterative Stochastic Optimization routines to the problem of sparse signal recovery from noisy observation. Using Stochastic Mirror Descent algorithm as a building block, we develop a multistage…

Using a Bayesian approach, we consider the problem of recovering sparse signals under additive sparse and dense noise. Typically, sparse noise models outliers, impulse bursts or data loss. To handle sparse noise, existing methods…

In this paper, we denoise a given noisy image by minimizing a smoothness promoting function over a set of local similarity measures which compare the mean of the given image and some candidate image on a large collection of subboxes. The…

In this paper, we studied the problem of beam alignment for millimeter wave (mmWave) communications, in which we assume a hybrid analog and digital beamforming structure is employed at the transmitter (i.e. base station), and an…

Large language models (LLMs) augmented with retrieval exhibit robust performance and extensive versatility by incorporating external contexts. However, the input length grows linearly in the number of retrieved documents, causing a dramatic…

The augmented Lagrangian (AL) method that solves convex optimization problems with linear constraints has drawn more attention recently in imaging applications due to its decomposable structure for composite cost functions and empirical…

Audio-LLM introduces audio modality into a large language model (LLM) to enable a powerful LLM to recognize, understand, and generate audio. However, during speech recognition in noisy environments, we observed the presence of illusions and…

In this paper, we propose a new method to reconstruct a signal corrupted by noise where both signal and noise are sparse but in different domains. The problem investigated in this paper arises in different applications such as impulsive…

We propose a new fast algorithm for solving one of the standard formulations of image restoration and reconstruction which consists of an unconstrained optimization problem where the objective includes an $\ell_2$ data-fidelity term and a…

Convolutional sparse coding improves on the standard sparse approximation by incorporating a global shift-invariant model. The most efficient convolutional sparse coding methods are based on the alternating direction method of multipliers…

The augmented Lagrangian method (ALM) is a classical optimization tool that solves a given "difficult" (constrained) problem via finding solutions of a sequence of "easier"(often unconstrained) sub-problems with respect to the original…

We propose a new fast algorithm for solving one of the standard approaches to ill-posed linear inverse problems (IPLIP), where a (possibly non-smooth) regularizer is minimized under the constraint that the solution explains the observations…

Multiscale phenomena that evolve on multiple distinct timescales are prevalent throughout the sciences. It is often the case that the governing equations of the persistent and approximately periodic fast scales are prescribed, while the…

As technology grows, higher frequency signals are required to be processed in various applications. In order to digitize such signals, conventional analog to digital convertors are facing implementation challenges due to the higher sampling…

Spike and Slab priors have been of much recent interest in signal processing as a means of inducing sparsity in Bayesian inference. Applications domains that benefit from the use of these priors include sparse recovery, regression and…

A new algorithm for solving large-scale convex optimization problems with a separable objective function is proposed. The basic idea is to combine three techniques: Lagrangian dual decomposition, excessive gap and smoothing. The main…

First-order methods have been studied for nonlinear constrained optimization within the framework of the augmented Lagrangian method (ALM) or penalty method. We propose an improved inexact ALM (iALM) and conduct a unified analysis for…

Audio events are quite often overlapping in nature, and more prone to noise than visual signals. There has been increasing evidence for the superior performance of representations learned using sparse dictionaries for applications like…

We study the properties of the Frank-Wolfe algorithm to solve the m-EXACT-SPARSE reconstruction problem, where a signal y must be expressed as a sparse linear combination of a predefined set of atoms, called dictionary. We prove that when…

In this paper, adaptive non-uniform compressive sampling (ANCS) of time-varying signals, which are sparse in a proper basis, is introduced. ANCS employs the measurements of previous time steps to distribute the sensing energy among…