Related papers: Orthogonal subspace based fast iterative threshold…
A well-known analysis of Tropp and Gilbert shows that orthogonal matching pursuit (OMP) can recover a k-sparse n-dimensional real vector from 4 k log(n) noise-free linear measurements obtained through a random Gaussian measurement matrix…
The resolution of many large-scale inverse problems using MCMC methods requires a step of drawing samples from a high dimensional Gaussian distribution. While direct Gaussian sampling techniques, such as those based on Cholesky…
We address the non-convex optimisation problem of finding a sparse matrix on the Stiefel manifold (matrices with mutually orthogonal columns of unit length) that maximises (or minimises) a quadratic objective function. Optimisation problems…
Compressive Sensing (CS) is a new paradigm for the efficient acquisition of signals that have sparse representation in a certain domain. Traditionally, CS has provided numerous methods for signal recovery over an orthonormal basis. However,…
Motivated by recent work on stochastic gradient descent methods, we develop two stochastic variants of greedy algorithms for possibly non-convex optimization problems with sparsity constraints. We prove linear convergence in expectation to…
In many practical applications such as direction-of-arrival (DOA) estimation and line spectral estimation, the sparsifying dictionary is usually characterized by a set of unknown parameters in a continuous domain. To apply the conventional…
Gradient-based learning imposes (deep) neural networks to be differentiable at all steps. This includes model-based architectures constructed by unrolling iterations of an iterative algorithm onto layers of a neural network, known as…
Sparse signals can be recovered from a reduced set of samples by using compressive sensing algorithms. In common methods the signal is recovered in the sparse domain. A method for the reconstruction of sparse signal which reconstructs the…
Motivated by the needs of selecting important features for massive neuroimaging data, we propose a spatially varying coefficient model (SVCMs) with sparsity and piecewise smoothness imposed on the coefficient functions. A new class of…
We consider the estimation of the transition matrix in the high-dimensional time-varying vector autoregression (TV-VAR) models. Our model builds on a general class of locally stationary VAR processes that evolve smoothly in time. We propose…
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…
We study the square root bottleneck in the recovery of sparse vectors from quadratic equations. It is acknowledged that a sparse vector $ \mathbf x_0\in \mathbb{R}^n$, $\| \mathbf x_0\|_0 = k$ can in theory be recovered from as few as…
Compressive sensing is a methodology for the reconstruction of sparse or compressible signals using far fewer samples than required by the Nyquist criterion. However, many of the results in compressive sensing concern random sampling…
Sparse coding is a class of unsupervised methods for learning a sparse representation of the input data in the form of a linear combination of a dictionary and a sparse code. This learning framework has led to state-of-the-art results in…
Sparse signal recovery is one of the most fundamental problems in various applications, including medical imaging and remote sensing. Many greedy algorithms based on the family of hard thresholding operators have been developed to solve the…
Orthogonal Matching Pursuit (OMP) plays an important role in data science and its applications such as sparse subspace clustering and image processing. However, the existing OMP-based approaches lack of data adaptiveness so that the data…
Scalable algorithms to solve optimization and regression tasks even approximately, are needed to work with large datasets. In this paper we study efficient techniques from matrix sketching to solve a variety of convex constrained regression…
We address the problem of estimating time and frequency shifts of a known waveform in the presence of multiple measurement vectors (MMVs). This problem naturally arises in radar imaging and wireless communications. Specifically, a signal…
High-throughput characterization often requires estimating parameters and model dimension from experimental data of limited quantity and quality. Such data may result in an ill-posed inverse problem, where multiple sets of parameters and…
Recovery of arbitrarily positioned samples that are missing in sparse signals recently attracted significant research interest. Sparse signals with heavily corrupted arbitrary positioned samples could be analyzed in the same way as…