相关论文: Demixing Sines and Spikes Using Multiple Measureme…

Spectral measures arise in numerous applications such as quantum mechanics, signal processing, resonances, and fluid stability. Similarly, spectral decompositions (pure point, absolutely continuous and singular continuous) often…

This paper presents a fast spectral unmixing algorithm based on Dykstra's alternating projection. The proposed algorithm formulates the fully constrained least squares optimization problem associated with the spectral unmixing task as an…

Sparse signals (i.e., vectors with a small number of non-zero entries) build the foundation of most kernel (or nullspace) results, uncertainty relations, and recovery guarantees in the sparse signal processing and compressive sensing…

Frequency recovery/estimation from discrete samples of superimposed sinusoidal signals is a classic yet important problem in statistical signal processing. Its research has recently been advanced by atomic norm techniques which exploit…

In this work, we consider the problem of estimating the parameters of polynomially damped sinusoidal signals, commonly encountered in, for instance, spectroscopy. Generally, finding the parameter values of such signals constitutes a…

In this work, we investigate the problem of simultaneous blind demixing and super-resolution. Leveraging the subspace assumption regarding unknown point spread functions, this problem can be reformulated as a low-rank matrix demixing…

We revisit the source image estimation problem from blind source separation (BSS). We generalize the traditional minimum distortion principle to maximum likelihood estimation with a model for the residual spectrograms. Because residual…

Separating signals from an additive mixture may be an unnecessarily hard problem when one is only interested in specific properties of a given signal. In this work, we tackle simpler "statistical component separation" problems that focus on…

We consider simultaneous blind deconvolution of r source signals from their noisy superposition, a problem also referred to blind demixing and deconvolution. This signal processing problem occurs in the context of the Internet of Things…

Currently, the engineering of miniature spectrometers mainly faces three problems: the mismatch between the number of filters at the front end of the detector and the spectral reconstruction accuracy; the lack of a stable spectral…

This paper studies the problem of accurately recovering a structured signal from a small number of corrupted sub-Gaussian measurements. We consider three different procedures to reconstruct signal and corruption when different kinds of…

We consider an important class of signal processing problems where the signal of interest is known to be sparse, and can be recovered from data given auxiliary information about how the data was generated. For example, a sparse Green's…

This paper investigates the phase retrieval problem, which aims to recover a signal from the magnitudes of its linear measurements. We develop statistically and computationally efficient algorithms for the situation when the measurements…

In linear inverse problems, the goal is to recover a target signal from undersampled, incomplete or noisy linear measurements. Typically, the recovery relies on complex numerical optimization methods; recent approaches perform an unfolding…

We consider the line spectral estimation problem which aims to recover a mixture of complex sinusoids from a small number of randomly observed time domain samples. Compressed sensing methods formulates line spectral estimation as a sparse…

This paper investigates the problem of recovering missing samples using methods based on sparse representation adapted especially for image signals. Instead of $l_2$-norm or Mean Square Error (MSE), a new perceptual quality measure is used…

We study the reconstruction of discrete-valued sparse signals from underdetermined systems of linear equations. On the one hand, classical compressed sensing (CS) is designed to deal with real-valued sparse signals. On the other hand,…

Multiplicative noise, also known as speckle or pepper noise, commonly affects images produced by synthetic aperture radar (SAR), lasers, or optical lenses. Unlike additive noise, which typically arises from thermal processes or external…

Linear spectral unmixing under nonnegativity and sum-to-one constraints is a convex optimization problem for which many algorithms were proposed. In practice, especially for supervised unmixing (i.e., with a large dictionary), solutions…

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…