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We analyze a practical algorithm for sparse PCA on incomplete and noisy data under a general non-random sampling scheme. The algorithm is based on a semidefinite relaxation of the $\ell_1$-regularized PCA problem. We provide theoretical…
In many practical applications such as direction-of-arrival (DOA) estimation and line spectral estimation, the sparsifying dictionary is usually characterized by a set of unknown parameters in a continuous domain. To apply the conventional…
Audio source separation is often achieved by estimating the magnitude spectrogram of each source, and then applying a phase recovery (or spectrogram inversion) algorithm to retrieve time-domain signals. Typically, spectrogram inversion is…
The problem of source localization with ad hoc microphone networks in noisy and reverberant enclosures, given a training set of prerecorded measurements, is addressed in this paper. The training set is assumed to consist of a limited number…
This paper considers the problem of recovery of a low-rank matrix in the situation when most of its entries are not observed and a fraction of observed entries are corrupted. The observations are noisy realizations of the sum of a low rank…
Sparse coding and dictionary learning are popular techniques for linear inverse problems such as denoising or inpainting. However in many cases, the measurement process is nonlinear, for example for clipped, quantized or 1-bit measurements.…
Sparse signal reconstruction algorithms have attracted research attention due to their wide applications in various fields. In this paper, we present a simple Bayesian approach that utilizes the sparsity constraint and a priori statistical…
Signals sparse in a transformation domain can be recovered from a reduced set of randomly positioned samples by using compressive sensing algorithms. Simple re- construction algorithms are presented in the first part of the paper. The…
Inverse problems and regularization theory is a central theme in contemporary signal processing, where the goal is to reconstruct an unknown signal from partial indirect, and possibly noisy, measurements of it. A now standard method for…
Source conditions are a key tool in regularisation theory that are needed to derive error estimates and convergence rates for ill-posed inverse problems. In this paper, we provide a recipe to practically compute source condition elements as…
Recent advances in audio declipping have substantially improved the state of the art.% in certain saturation regimes. Yet, practitioners need guidelines to choose a method, and while existing benchmarks have been instrumental in advancing…
Performing a large number of spatial measurements enables high-resolution photoacoustic imaging without specific prior information. However, the acquisition of spatial measurements is time-consuming, costly, and technically challenging. By…
Reconstructing continuous signals from a small number of discrete samples is a fundamental problem across science and engineering. In practice, we are often interested in signals with 'simple' Fourier structure, such as bandlimited,…
The sparse signal recovery in the standard compressed sensing (CS) problem requires that the sensing matrix be known a priori. Such an ideal assumption may not be met in practical applications where various errors and fluctuations exist in…
We study the problem of recovering an incomplete $m\times n$ matrix of rank $r$ with columns arriving online over time. This is known as the problem of life-long matrix completion, and is widely applied to recommendation system, computer…
Sparse recovery is one of the most fundamental and well-studied inverse problems. Standard statistical formulations of the problem are provably solved by general convex programming techniques and more practical, fast (nearly-linear time)…
In this paper we present a linear programming solution for sign pattern recovery of a sparse signal from noisy random projections of the signal. We consider two types of noise models, input noise, where noise enters before the random…
Line spectral estimation theory aims to estimate the off-the-grid spectral components of a time signal with optimal precision. Recent results have shown that it is possible to recover signals having sparse line spectra from few temporal…
This paper presents a method to reconstruct the 3D structure of generic convex rooms from sound signals. Differently from most of the previous approaches, the method is fully uncalibrated in the sense that no knowledge about the microphones…
We tackle the multi-party speech recovery problem through modeling the acoustic of the reverberant chambers. Our approach exploits structured sparsity models to perform room modeling and speech recovery. We propose a scheme for…