Related papers: Polar Deconvolution of Mixed Signals
We analyze the statistical problem of recovering an atomic signal, modeled as a discrete uniform distribution $\mu$, from a binned Poisson convolution model. This question is motivated, among others, by super-resolution laser microscopy…
Deconvolution of the telescope Point Spread Function (PSF) is necessary for even moderate dynamic range imaging with interferometric telescopes. The process of deconvolution can be treated as a search for a model image such that the…
In this paper, we are interested in the classical problem of restoring data degraded by a convolution and the addition of a white Gaussian noise. The originality of the proposed approach is two-fold. Firstly, we formulate the restoration…
Structured optimization uses a prescribed set of atoms to assemble a solution that fits a model to data. Polarity, which extends the familiar notion of orthogonality from linear sets to general convex sets, plays a special role in a simple…
We consider a linear inverse problem whose solution is expressed as a sum of two components: one smooth and the other sparse. This problem is addressed by minimizing an objective function with a least squares data-fidelity term and a…
We consider the problem of sampling from the posterior distribution of a $d$-dimensional coefficient vector $\boldsymbol{\theta}$, given linear observations $\boldsymbol{y} = \boldsymbol{X}\boldsymbol{\theta}+\boldsymbol{\varepsilon}$. In…
The typical approach for recovery of spatially correlated signals is regularized least squares with a coupled regularization term. In the Bayesian framework, this algorithm is seen as a maximum-a-posterior estimator whose postulated prior…
Sparse signal recovery from a small number of random measurements is a well known NP-hard to solve combinatorial optimization problem, with important applications in signal and image processing. The standard approach to the sparse signal…
Suppose that we have $r$ sensors and each one intends to send a function $\boldsymbol{g}_i$ (e.g.\ a signal or an image) to a receiver common to all $r$ sensors. During transmission, each $\boldsymbol{g}_i$ gets convolved with a function…
Noise suppression is an essential step in any seismic processing workflow. A portion of this noise, particularly in land datasets, presents itself as random noise. In recent years, neural networks have been successfully used to denoise…
Low-rank matrix recovery from structured measurements has been a topic of intense study in the last decade and many important problems like matrix completion and blind deconvolution have been formulated in this framework. An important…
Spatial mode demultiplexing was proved to be a successful tool for estimation of the separation between incoherent sources, allowing for sensitivity much below the Rayleigh limit. However, with the presence of measurement's noise,…
This paper proposes the design of polar and convolutional coset codes for the unequal message protection (UMP) in the short blocklength regime, to overcome the rate loss introduced by preamble-based solutions. After providing conditions to…
Bilevel optimisation is used in inverse imaging problems for hyperparameter learning/identification and experimental design, for instance, to find optimal regularisation parameters and forward operators. However, computationally, the…
Audio source separation is a difficult machine learning problem and performance is measured by comparing extracted signals with the component source signals. However, if separation is motivated by the ultimate goal of re-mixing then…
Real-valued Phase retrieval is a non-convex continuous inference problem, where a high-dimensional signal is to be reconstructed from a dataset of signless linear measurements. Focusing on the noiseless case, we aim to disentangle the two…
In imaging modalities recording diffraction data, the original image can be reconstructed assuming known phases. When phases are unknown, oversampling and a constraint on the support region in the original object can be used to solve a…
We study an auto-calibration problem in which a transform-sparse signal is acquired via compressive sensing by multiple sensors in parallel, but with unknown calibration parameters of the sensors. This inverse problem has an important…
High resolution ultrasound image reconstruction from a reduced number of measurements is of great interest in ultrasound imaging, since it could enhance both the frame rate and image resolution. Compressive deconvolution, combining…
We consider the inverse problem of recovering a continuous-domain function from a finite number of noisy linear measurements. The unknown signal is modeled as the sum of a slowly varying trend and a periodic or quasi-periodic seasonal…