Related papers: Polar Deconvolution of Mixed Signals
Additive or multiplicative stationary noise recently became an important issue in applied fields such as microscopy or satellite imaging. Relatively few works address the design of dedicated denoising methods compared to the usual white…
Polar codes are a family of capacity-achieving codes that have explicit and low-complexity construction, encoding, and decoding algorithms. Decoding of polar codes is based on the successive-cancellation decoder, which decodes in a bit-…
Variational regularization of ill-posed inverse problems is based on minimizing the sum of a data fidelity term and a regularization term. The balance between them is tuned using a positive regularization parameter, whose automatic choice…
We study the question of reconstructing two signals $f$ and $g$ from their convolution $y = f\ast g$. This problem, known as {\em blind deconvolution}, pervades many areas of science and technology, including astronomy, medical imaging,…
Despeckling is a crucial noise reduction task in improving the quality of synthetic aperture radar (SAR) images. Directly obtaining noise-free SAR images is a challenging task that has hindered the development of accurate despeckling…
The recovery of signals with finite-valued components from few linear measurements is a problem with widespread applications and interesting mathematical characteristics. In the compressed sensing framework, tailored methods have been…
Hyperspectral (HS) unmixing is the process of decomposing an HS image into material-specific spectra (endmembers) and their spatial distributions (abundance maps). Existing unmixing methods have two limitations with respect to noise…
We describe a new multi-scale deconvolution algorithm that can also be used in multi-frequency mode. The algorithm only affects the minor clean loop. In single-frequency mode, the minor loop of our improved multi-scale algorithm is over an…
We study a blind deconvolution problem on graphs, which arises in the context of localizing a few sources that diffuse over networks. While the observations are bilinear functions of the unknown graph filter coefficients and sparse input…
We revisit the Blind Deconvolution problem with a focus on understanding its robustness and convergence properties. Provable robustness to noise and other perturbations is receiving recent interest in vision, from obtaining immunity to…
In this paper, a fresh procedure to handle image mixtures by means of blind signal separation relying on a combination of second order and higher order statistics techniques are introduced. The problem of blind signal separation is…
Convex optimization with sparsity-promoting convex regularization is a standard approach for estimating sparse signals in noise. In order to promote sparsity more strongly than convex regularization, it is also standard practice to employ…
A new algorithm for solving large-scale convex optimization problems with a separable objective function is proposed. The basic idea is to combine three techniques: Lagrangian dual decomposition, excessive gap and smoothing. The main…
Recovering a signal from auto-correlations or, equivalently, retrieving the phase linked to a given Fourier modulus, is a wide-spread problem in imaging. This problem has been tackled in a number of experimental situations, from optical…
This study provides a computationally effective deconvolution algorithm capable to reconstruct piled-up events in scintillating detector systems with high count rate where fully digitized waveforms are available. A fixed-point iteration…
In this paper, we introduce a new coding and decoding structure for enhancing the reliability and performance of polar codes, specifically at low error rates. We achieve this by concatenating two polar codes in series to create robust…
We consider the problems of compressed sensing and optimal denoising for signals $\mathbf{x_0}\in\mathbb{R}^N$ that are monotone, i.e., $\mathbf{x_0}(i+1) \geq \mathbf{x_0}(i)$, and sparsely varying, i.e., $\mathbf{x_0}(i+1) >…
In this paper an extension of the sparse decomposition problem is considered and an algorithm for solving it is presented. In this extension, it is known that one of the shifted versions of a signal s (not necessarily the original signal…
We discuss a general approach to handling "multiple hypotheses" testing in the case when a particular hypothesis states that the vector of parameters identifying the distribution of observations belongs to a convex compact set associated…
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…