Related papers: Phase Unmixing : Multichannel Source Separation wi…
In this paper, a novel approach for single channel source separation (SCSS) using a deep neural network (DNN) architecture is introduced. Unlike previous studies in which DNN and other classifiers were used for classifying time-frequency…
We consider the problem of recovering a signal consisting of a superposition of point sources from low-resolution data with a cut-off frequency f. If the distance between the sources is under 1/f, this problem is not well posed in the sense…
We demonstrate the utility of machine learning in the separation of superimposed chaotic signals using a technique called Reservoir Computing. We assume no knowledge of the dynamical equations that produce the signals, and require only…
Correspondence problems are often modelled as quadratic optimization problems over permutations. Common scalable methods for approximating solutions of these NP-hard problems are the spectral relaxation for non-convex energies and the…
Multicriterion optimization and Pareto optimality are fundamental tools in economics. In this paper we propose a new relaxation method for solving multiple objective quadratic programming problems. Exploiting the technique of the linear…
In this paper we consider a system of quadratic equations |<z_j, x>|^2 = b_j, j = 1, ..., m, where x in R^n is unknown while normal random vectors z_j in R_n and quadratic measurements b_j in R are known. The system is assumed to be…
Atomic norm methods have recently been proposed for spectral super-resolution with flexibility in dealing with missing data and miscellaneous noises. A notorious drawback of these convex optimization methods however is their lower…
In the undersampled phase retrieval problem, the goal is to recover an $N$-dimensional complex signal $\mathbf{x}$ from only $M<N$ noisy intensity measurements without phase information. This problem has drawn a lot of attention to reduce…
A waveform channel is considered where the transmitted signal is corrupted by Wiener phase noise and additive white Gaussian noise. A discrete-time channel model that takes into account the effect of filtering on the phase noise is…
Hyperspectral remote sensing is a prominent research topic in data processing. Most of the spectral unmixing algorithms are developed by adopting the linear mixing models. Nonnegative matrix factorization (NMF) and its developments are used…
In this paper, we show that the popular K-means clustering problem can equivalently be reformulated as a conic program of polynomial size. The arising convex optimization problem is NP-hard, but amenable to a tractable semidefinite…
In this article we consider the filtering problem associated to partially observed diffusions, with observations following a marked point process. In the model, the data form a point process with observation times that have its intensity…
Source separation involves the ill-posed problem of retrieving a set of source signals that have been observed through a mixing operator. Solving this problem requires prior knowledge, which is commonly incorporated by imposing regularity…
Existing nonconvex statistical optimization theory and methods crucially rely on the correct specification of the underlying "true" statistical models. To address this issue, we take a first step towards taming model misspecification by…
High-dimensional matrix regression has been studied in various aspects, such as statistical properties, computational efficiency and application to specific instances including multivariate regression, system identification and matrix…
The problem of phase-noise compensation for correlated phase noise in coded multichannel optical transmission is investigated. To that end, a simple multichannel phase-noise model is considered and the maximum a posteriori detector for this…
Hyperspectral image unmixing has proven to be a useful technique to interpret hyperspectral data, and is a prolific research topic in the community. Most of the approaches used to perform linear unmixing are based on convex geometry…
The 2-D phase unwrapping problem aims at retrieving a "phase" image from its modulo $2\pi$ observations. Many applications, such as interferometry or synthetic aperture radar imaging, are concerned by this problem since they proceed by…
Blind source separation (BSS) is addressed, using a novel data-driven approach, based on a well-established probabilistic model. The proposed method is specifically designed for separation of multichannel audio mixtures. The algorithm…
This work deals with an inverse source problem for the biharmonic wave equation. A two-stage numerical method is proposed to identify the unknown source from the multi-frequency phaseless data. In the first stage, we introduce some…