Related papers: Unearthing InSights into Mars: Unsupervised Source…
Unsupervised source separation involves unraveling an unknown set of source signals recorded through a mixing operator, with limited prior knowledge about the sources, and only access to a dataset of signal mixtures. This problem is…
Blind source separation (BSS) algorithms are unsupervised methods, which are the cornerstone of hyperspectral data analysis by allowing for physically meaningful data decompositions. BSS problems being ill-posed, the resolution requires…
This paper is concerned with uniqueness, phase retrieval and shape reconstruction methods for solving inverse electromagnetic source scattering problems with multi-frequency sparse phased or phaseless far field data. With the phased data,…
We consider an inverse problem for the linear one-dimensional wave equation with variable coefficients consisting in determining an unknown source term from a boundary observation. A method to obtain approximations of this inverse problem…
Similar to the obstacle or medium scattering problems, an important property of the phaseless far field patterns for source scattering problems is the translation invariance. Thus it is impossible to reconstruct the location of the…
Supervised deep learning approaches to underdetermined audio source separation achieve state-of-the-art performance but require a dataset of mixtures along with their corresponding isolated source signals. Such datasets can be extremely…
Starting with far field data of time-harmonic acoustic or electromagnetic waves radiated by a collection of compactly supported sources in two-dimensional free space, we develop criteria and algorithms for the recovery of the far field…
This paper deals with a source separation strategy based on second-order statistics, namely, on data covariance matrices estimated at several lags. In general, ``blind'' approaches to source separation do not assume any knowledge on the…
Scattering obscures information carried by wave by producing a speckle pattern, posing a common challenge across various fields, including microscopy and astronomy. Traditional methods for extracting information from speckles often rely on…
With the progress of Mars exploration, numerous Mars image data are collected and need to be analyzed. However, due to the imbalance and distortion of Martian data, the performance of existing computer vision models is unsatisfactory. In…
In recent years, rapid progress has been made on the problem of single-channel sound separation using supervised training of deep neural networks. In such supervised approaches, a model is trained to predict the component sources from…
A common challenge in the natural sciences is to disentangle distinct, unknown sources from observations. Examples of this source separation task include deblending galaxies in a crowded field, distinguishing the activity of individual…
Single-channel audio separation aims to separate individual sources from a single-channel mixture. Most existing methods rely on supervised learning with synthetically generated paired data. However, obtaining high-quality paired data in…
Microwave imaging is commonly based on the solution of linearized inverse scattering problems by matched filtering algorithms, i.e., by applying the adjoint of the forward scattering operator to the observation data. A more rigorous…
The task of blind source separation (BSS) involves separating sources from a mixture without prior knowledge of the sources or the mixing system. Single-channel mixtures and non-linear mixtures are a particularly challenging problem in BSS.…
Supervised neural network training has led to significant progress on single-channel sound separation. This approach relies on ground truth isolated sources, which precludes scaling to widely available mixture data and limits progress on…
We consider the problem of single-channel audio source separation with the goal of reconstructing $K$ sources from their mixture. We address this ill-posed problem with FLOSS (FLOw matching for Source Separation), a constrained generation…
Given a time series of multicomponent measurements x(t), the usual objective of nonlinear blind source separation (BSS) is to find a "source" time series s(t), comprised of statistically independent combinations of the measured components.…
Source separation problems are ubiquitous in the physical sciences; any situation where signals are superimposed calls for source separation to estimate the original signals. In this tutorial I will discuss the Bayesian approach to the…
This work addresses image restoration tasks through the lens of inverse problems using unpaired datasets. In contrast to traditional approaches -- which typically assume full knowledge of the forward model or access to paired degraded and…