Related papers: Reconstructing Sparse Signals via Greedy Monte-Car…
The main focus of this article is to provide a mathematical study of the algorithm proposed in \cite{boyaval2010variance} where the authors proposed a variance reduction technique for the computation of parameter-dependent expectations…
The recovery of sparsest overcomplete representation has recently attracted intensive research activities owe to its important potential in the many applied fields such as signal processing, medical imaging, communication, and so on. This…
The reversible jump Markov chain Monte Carlo (RJMCMC) method offers an across-model simulation approach for Bayesian estimation and model comparison, by exploring the sampling space that consists of several models of possibly varying…
In the last two decades, the linear model of coregionalization (LMC) has been widely used to model multivariate spatial processes. However, it can be a challenging task to conduct likelihood-based inference for such models because of the…
It is now well understood that (1) it is possible to reconstruct sparse signals exactly from what appear to be highly incomplete sets of linear measurements and (2) that this can be done by constrained L1 minimization. In this paper, we…
Low-cost message passing (MP) algorithm has been recognized as a promising technique for sparse vector recovery. However, the existing MP algorithms either focus on mean square error (MSE) of the value recovery while ignoring the sparsity…
Cooperative Greedy Pursuit Strategies are considered for approximating a signal partition subjected to a global constraint on sparsity. The approach aims at producing a high quality sparse approximation of the whole signal, using highly…
We consider the problem of sparse signal recovery from noisy measurements. Many of frequently used recovery methods rely on some sort of tuning depending on either noise or signal parameters. If no estimates for either of them are…
Spectrum sensing is an important process in cognitive radio. A number of sensing techniques that have been proposed suffer from high processing time, hardware cost and computational complexity. To address these problems, compressive sensing…
We propose a method to reconstruct and cluster incomplete high-dimensional data lying in a union of low-dimensional subspaces. Exploring the sparse representation model, we jointly estimate the missing data while imposing the intrinsic…
Recently, Stochastic Gradient Markov Chain Monte Carlo (SG-MCMC) methods have been proposed for scaling up Monte Carlo computations to large data problems. Whilst these approaches have proven useful in many applications, vanilla SG-MCMC…
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 consider the problem of phase retrieval, namely, recovery of a signal from the magnitude of its Fourier transform, or of any other linear transform. Due to the loss of the Fourier phase information, this problem is ill-posed. Therefore,…
In the area of magnetic resonance imaging (MRI), an extensive range of non-linear reconstruction algorithms have been proposed that can be used with general Fourier subsampling patterns. However, the design of these subsampling patterns has…
Monte Carlo simulations of neutronic systems are computationally intensive and demand significant memory resources for high-fidelity modeling. Compressed sensing enables accurate reconstruction of signals from significantly fewer samples…
We derive a method to reconstruct Gaussian signals from linear measurements with Gaussian noise. This new algorithm is intended for applications in astrophysics and other sciences. The starting point of our considerations is the principle…
We propose a Monte Carlo sampler from the reverse diffusion process. Unlike the practice of diffusion models, where the intermediary updates -- the score functions -- are learned with a neural network, we transform the score matching…
Many problems in signal processing and machine learning can be formalized as weak submodular optimization tasks. For such problems, a simple greedy algorithm (\textsc{Greedy}) is guaranteed to find a solution achieving the objective with a…
This work addresses the robust reconstruction problem of a sparse signal from compressed measurements. We propose a robust formulation for sparse reconstruction which employs the $\ell_1$-norm as the loss function for the residual error and…
Compressed sensing aims to undersample certain high-dimensional signals, yet accurately reconstruct them by exploiting signal characteristics. Accurate reconstruction is possible when the object to be recovered is sufficiently sparse in a…