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Information processing techniques based on sparseness have been actively studied in several disciplines. Among them, a mathematical framework to approximately express a given dataset by a combination of a small number of basis vectors of an…
We propose a unified modeling and algorithmic framework for audio restoration problem. It encompasses analysis sparse priors as well as more classical synthesis sparse priors, and regular sparsity as well as various forms of structured…
Sparse and convolutional constraints form a natural prior for many optimization problems that arise from physical processes. Detecting motifs in speech and musical passages, super-resolving images, compressing videos, and reconstructing…
We know that compressive sensing can establish stable sparse recovery results from highly undersampled data under a restricted isometry property condition. In reality, however, numerous problems are coherent, and vast majority conventional…
Electronic transport is at the heart of many phenomena in condensed matter physics and material science. Magnetic imaging is a non-invasive tool for detecting electric current in materials and devices. A two-dimensional current density can…
We present a method for supervised learning of sparsity-promoting regularizers for denoising signals and images. Sparsity-promoting regularization is a key ingredient in solving modern signal reconstruction problems; however, the operators…
We present significant improvements to our previous work on noise reduction in {\sl Herschel} observation maps by defining sparse filtering tools capable of handling, in a unified formalism, a significantly improved noise reduction as well…
We consider a separation problem where the observation consists of the sum of a high amplitude smooth signal and a low amplitude transient signal. We propose a method for decomposition that relies on solving instances of a `constrained…
We propose a new fast algorithm for solving one of the standard formulations of frame-based image deconvolution: an unconstrained optimization problem, involving an $\ell_2$ data-fidelity term and a non-smooth regularizer. Our approach is…
Synthetic Aperture Radar (SAR) images are widely used in remote sensing due to their all-weather, all-day imaging capabilities. However, SAR images are highly susceptible to noise, particularly speckle noise, caused by the coherent imaging…
Denoising images contaminated by the mixture of additive white Gaussian noise (AWGN) and impulse noise (IN) is an essential but challenging problem. The presence of impulsive disturbances inevitably affects the distribution of noises and…
We propose a novel sparse spectrum approximation of Gaussian process (GP) tailored for Bayesian optimization. Whilst the current sparse spectrum methods provide desired approximations for regression problems, it is observed that this…
While variational methods have been among the most powerful tools for solving linear inverse problems in imaging, deep (convolutional) neural networks have recently taken the lead in many challenging benchmarks. A remaining drawback of deep…
Salt and pepper noise removal is a common inverse problem in image processing. Traditional denoising methods have two limitations. First, noise characteristics are often not described accurately. For example, the noise location information…
We are motivated by problems that arise in a number of applications such as Online Marketing and Explosives detection, where the observations are usually modeled using Poisson statistics. We model each observation as a Poisson random…
Multi-channel sparse blind deconvolution, or convolutional sparse coding, refers to the problem of learning an unknown filter by observing its circulant convolutions with multiple input signals that are sparse. This problem finds numerous…
We present a parametric deterministic formulation of Bayesian inverse problems with input parameter from infinite dimensional, separable Banach spaces. In this formulation, the forward problems are parametric, deterministic elliptic partial…
In this work, we address the problem of estimating sparse communication channels in OFDM systems in the presence of carrier frequency offset (CFO) and unknown noise variance. To this end, we consider a convex optimization problem, including…
This note considers the spectral estimation problems of sparse spectral measures under unknown noise levels. The main technical tool is the eigenmatrix method for solving unstructured sparse recovery problems. When the noise level is…
Recently, the problem of blind image separation has been widely investigated, especially the medical image denoise which is the main step in medical diag-nosis. Removing the noise without affecting relevant features of the image is the main…