Related papers: Blind free deconvolution over one-parameter sparse…

The increased sensitivity of future radio telescopes will result in requirements for higher dynamic range within the image as well as better resolution and immunity to interference. In this paper we propose a new matrix formulation of the…

Recently, a class of algorithms combining classical fixed point iterations with repeated random sparsification of approximate solution vectors has been successfully applied to eigenproblems with matrices as large as $10^{108} \times…

Retinal implants aim to restore functional vision despite photoreceptor degeneration, yet are fundamentally constrained by low resolution electrode arrays and patient-specific perceptual distortions. Most deployed encoders rely on…

The nonlinear inverse problem of exponential data fitting is separable since the fitting function is a linear combination of parameterized exponential functions, thus allowing to solve for the linear coefficients separately from the…

Recovering jointly sparse signals in the multiple measurement vectors (MMV) setting is a fundamental problem in machine learning, but traditional methods often require careful parameter tuning or prior knowledge of the sparsity of the…

Blind deconvolution is a classical yet challenging low-level vision problem with many real-world applications. Traditional maximum a posterior (MAP) based methods rely heavily on fixed and handcrafted priors that certainly are insufficient…

We propose a new solver for the sparse spikes deconvolution problem over the space of Radon measures. A common approach to off-the-grid deconvolution considers semidefinite (SDP) relaxations of the total variation (the total mass of the…

We propose a simple, interpretable framework for solving a wide range of image reconstruction problems such as denoising and deconvolution. Given a corrupted input image, the model synthesizes a spatially varying linear filter which, when…

In this study, the problem of computing a sparse representation of multi-dimensional visual data is considered. In general, such data e.g., hyperspectral images, color images or video data consists of signals that exhibit strong local…

An inverse problem in spectroscopy is considered. The objective is to restore the discrete spectrum from observed spectrum data, taking into account the spectrometer's line spread function. The problem is reduced to solution of a system of…

In this paper we propose a new iterative method to hierarchically compute a relatively large number of leftmost eigenpairs of a sparse symmetric positive matrix under the multiresolution operator compression framework. We exploit the…

In this paper, we develop a nonconvex approach to the problem of low-rank and sparse matrix decomposition. In our nonconvex method, we replace the rank function and the $l_{0}$-norm of a given matrix with a non-convex fraction function on…

The ability to resolve detail in the object that is being imaged, named by resolution, is the core parameter of an imaging system. Super-resolution is a class of techniques that can enhance the resolution of an imaging system and even…

We consider a linear inverse problem whose solution is expressed as a sum of two components: one smooth and the other sparse. This problem is addressed by minimizing an objective function with a least squares data-fidelity term and a…

Dictionary learning is the task of determining a data-dependent transform that yields a sparse representation of some observed data. The dictionary learning problem is non-convex, and usually solved via computationally complex iterative…

Faraday tomography (or rotation measure synthesis) is a procedure to convert linear polarization spectra into the Faraday dispersion function, which provides us with unique information of magneto-ionic media along the line of sight.…

Dynamic density-matrix renormalization provides valuable numerical information on dynamic correlations by computing convolutions of the corresponding spectral densities. Here we discuss and illustrate how and to which extent such data can…

Recovery of support of a sparse vector from simple measurements is a widely-studied problem, considered under the frameworks of compressed sensing, 1-bit compressed sensing, and more general single index models. We consider generalizations…

Deconvolution with a box (square wave) is a key operation for super-resolution with pixel-shift cameras. In general convolution with a box is not invertible. However, we can obtain perfect reconstructions of sparse signals using convex…

Sparse blind deconvolution is the problem of estimating the blur kernel and sparse excitation, both of which are unknown. Considering a linear convolution model, as opposed to the standard circular convolution model, we derive a sufficient…