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We have developed an approximate signal recovery algorithm with low computational cost for compressed sensing on the basis of randomly constructed sparse measurement matrices. The law of large numbers and the central limit theorem suggest…

The goal of compressed sensing is to reconstruct a sparse signal under a few linear measurements far less than the dimension of the ambient space of the signal. However, many real-life applications in physics and biomedical sciences carry…

Non-stationary blind super-resolution is an extension of the traditional super-resolution problem, which deals with the problem of recovering fine details from coarse measurements. The non-stationary blind super-resolution problem appears…

Motivated by recent work on atomic norms in inverse problems, we propose a new approach to line spectral estimation that provides theoretical guarantees for the mean-squared-error (MSE) performance in the presence of noise and without…

In this paper we present a fast and efficient method for the reconstruction of Magnetic Resonance Images (MRI) from severely under-sampled data. From the Compressed Sensing theory we have mathematically modeled the problem as a constrained…

Compressed sensing allows perfect recovery of sparse signals (or signals sparse in some basis) using only a small number of random measurements. Existing results in compressed sensing literature have focused on characterizing the achievable…

Phase retrieval (PR) is a popular research topic in signal processing and machine learning. However, its performance degrades significantly when the measurements are corrupted by noise or outliers. To address this limitation, we propose a…

Sharpness-Aware Minimization (SAM) improves generalization by minimizing the worst-case loss within a fixed parameter-space radius neighborhood. SAM and its variants mainly rely on a first-order linearized surrogate, while flat minima are…

Sparsity is one of the key concepts that allows the recovery of signals that are subsampled at a rate significantly lower than required by the Nyquist-Shannon sampling theorem. Our proposed framework uses arbitrary multiscale transforms,…

Sparse neural networks are a key factor in developing resource-efficient machine learning applications. We propose the novel and powerful sparse learning method Adaptive Regularized Training (ART) to compress dense into sparse networks.…

In the area of sparse recovery, numerous researches hint that non-convex penalties might induce better sparsity than convex ones, but up until now those corresponding non-convex algorithms lack convergence guarantees from the initial…

Sharpness-Aware Minimization (SAM) optimizer enhances the generalization ability of the machine learning model by exploring the flat minima landscape through weight perturbations. Despite its empirical success, SAM introduces an additional…

This work examines the problem of exact data interpolation via sparse (neuron count), infinitely wide, single hidden layer neural networks with leaky rectified linear unit activations. Using the atomic norm framework of [Chandrasekaran et…

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)…

This paper considers the problem of estimating the sparse millimeter wave (mmWave) massive multiple-input multiple-output (MIMO) OFDM channel from 1-bit quantized measurements. Unlike previous quantized on-grid approaches to compressive…

In today's heavily overparameterized models, the value of the training loss provides few guarantees on model generalization ability. Indeed, optimizing only the training loss value, as is commonly done, can easily lead to suboptimal model…

The robust low-rank tensor completion problem addresses the challenge of recovering corrupted high-dimensional tensor data with missing entries, outliers, and sparse noise commonly found in real-world applications. Existing methodologies…

Natural signals and images are well-known to be approximately sparse in transform domains such as Wavelets and DCT. This property has been heavily exploited in various applications in image processing and medical imaging. Compressed sensing…

In the area of near-field millimeter-wave imaging, the generalized sparse array synthesis (SAS) method is in great demand. The traditional methods usually employ the greedy algorithms, which may have the convergence problem. This paper…

We develop a multidimensional version of Gradient-MUSIC for estimating the frequencies of a nonharmonic signal from noisy samples. The guiding principle is that frequency recovery should be based only on the signal subspace determined by…