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Signal recovery is one of the key techniques of Compressive sensing (CS). It reconstructs the original signal from the linear sub-Nyquist measurements. Classical methods exploit the sparsity in one domain to formulate the L0 norm…
Existing convex relaxation-based approaches to reconstruction in compressed sensing assume that noise in the measurements is independent of the signal of interest. We consider the case of noise being linearly correlated with the signal and…
In the last decade, the study of cosmic microwave background (CMB) data has become one of the most powerful tools to study and understand the Universe. More precisely, measuring the CMB power spectrum leads to the estimation of most…
Music source separation aims to separate polyphonic music into different types of sources. Most existing methods focus on enhancing the quality of separated results by using a larger model structure, rendering them unsuitable for deployment…
Blind methods often separate or identify signals or signal subspaces up to an unknown scaling factor. Sometimes it is necessary to cope with the scaling ambiguity, which can be done through reconstructing signals as they are received by…
Decomposing surface electromyography (EMG) into the spike trains of individual motor neurons is a long-standing inverse problem and a key step toward motor-neuron-driven neural interfaces such as prosthetics and exoskeletons. The standard…
This paper considers the problem of sampling and reconstruction of a continuous-time sparse signal without assuming the knowledge of the sampling instants or the sampling rate. This topic has its roots in the problem of recovering multiple…
Increasing the imaging speed is a central aim in photoacoustic tomography. This issue is especially important in the case of sequential scanning approaches as applied for most existing optical detection schemes. In this work we address this…
Fourier PCA is Principal Component Analysis of a matrix obtained from higher order derivatives of the logarithm of the Fourier transform of a distribution.We make this method algorithmic by developing a tensor decomposition method for a…
Understanding the dynamics of the land-atmosphere exchange of CO$_2$ is key to advance our predictive capacities of the coupled climate-carbon feedback system. In essence, the net vegetation flux is the difference of the uptake of CO$_2$…
The extraction of a desired speech signal from a noisy environment has become a challenging issue. In the recent years, the scientific community has particularly focused on multichannel techniques which are dealt with in this review. In…
In this work the numerical solution of acoustic tomography problem based on the iterative and functional-analytical algorithms is considered. The mathematical properties of these algorithms were previously described in works of R.G.Novikov…
Consider a time series of signal measurements $x(t)$, having components $x_k \mbox{ for } k = 1,2, \ldots ,N$. This paper shows how to determine if these signals are equal to linear or nonlinear mixtures of the state variables of two or…
Passive acoustic mapping (PAM) is a key imaging technique for characterizing cavitation activity in therapeutic ultrasound applications. Recent model-based beamforming algorithms offer high reconstruction quality and strong physical…
This paper is devoted to a novel quantitative imaging scheme of identifying impenetrable obstacles in time-harmonic acoustic scattering from the associated far-field data. The proposed method consists of two phases. In the first phase, we…
The signal demixing problem seeks to separate a superposition of multiple signals into its constituent components. This paper studies a two-stage approach that first decompresses and subsequently deconvolves the noisy and undersampled…
We introduce a noise-aware extension to the parametric maximum-likelihood framework for component separation by modeling correlated $1/f^\alpha$ noise as a harmonic-space power law. This approach addresses a key limitation of existing…
Stochastic sampling techniques are ubiquitous in real-time rendering, where performance constraints force the use of low sample counts, leading to noisy intermediate results. To remove this noise, the post-processing step of temporal and…
Timbre allows us to distinguish between sounds even when they share the same pitch and loudness, playing an important role in music, instrument recognition, and speech. Traditional approaches, such as frequency analysis or machine learning,…
Recently there has been many works on adaptive subspace filtering in the signal processing literature. Most of them are concerned with tracking the signal subspace spanned by the eigenvectors corresponding to the eigenvalues of the…