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This note considers the spectral estimation problems of sparse spectral measures under unknown noise levels. The main technical tool is the eigenmatrix method for solving unstructured sparse recovery problems. When the noise level is…
Reproducing an all-in-focus image from an image with defocus regions is of practical value in many applications, eg, digital photography, and robotics. Using the output of some existing defocus map estimator, existing approaches first…
Linear encoding of sparse vectors is widely popular, but is commonly data-independent -- missing any possible extra (but a priori unknown) structure beyond sparsity. In this paper we present a new method to learn linear encoders that adapt…
This paper focuses on solving a challenging problem of blind deconvolution demixing involving modulated inputs. Specifically, multiple input signals $s_n(t)$, each bandlimited to $B$ Hz, are modulated with known random sequences $r_n(t)$…
Blind image deconvolution is the problem of recovering the latent image from the only observed blurry image when the blur kernel is unknown. In this paper, we propose an edge-based blur kernel estimation method for blind motion…
In this paper, we discuss application of iterative Stochastic Optimization routines to the problem of sparse signal recovery from noisy observation. Using Stochastic Mirror Descent algorithm as a building block, we develop a multistage…
A fruitful approach for solving signal deconvolution problems consists of resorting to a frame-based convex variational formulation. In this context, parallel proximal algorithms and related alternating direction methods of multipliers have…
We consider simultaneous blind deconvolution of r source signals from their noisy superposition, a problem also referred to blind demixing and deconvolution. This signal processing problem occurs in the context of the Internet of Things…
This paper considers the problem of solving systems of quadratic equations, namely, recovering an object of interest $\mathbf{x}^{\natural}\in\mathbb{R}^{n}$ from $m$ quadratic equations/samples…
Non-blind image deblurring is typically formulated as a linear least-squares problem regularized by natural priors on the corresponding sharp picture's gradients, which can be solved, for example, using a half-quadratic splitting method…
We address the problem of simultaneously recovering a sequence of point source signals from observations limited to the low-frequency end of the spectrum of their summed convolution, where the point spread functions (PSFs) are unknown. By…
In this paper, we propose a new unsupervised feature learning framework, namely Deep Sparse Coding (DeepSC), that extends sparse coding to a multi-layer architecture for visual object recognition tasks. The main innovation of the framework…
We propose a new solver for the sparse spikes deconvolution problem over the space of Radon measures. A common approach to off-the-grid deconvolution considers semidefinite (SDP) relaxations of the total variation (the total mass of the…
Recent years have seen a flurry of activities in designing provably efficient nonconvex procedures for solving statistical estimation problems. Due to the highly nonconvex nature of the empirical loss, state-of-the-art procedures often…
Natural signals and images are well-known to be approximately sparse in transform domains such as Wavelets and DCT. This property has been heavily exploited in various applications in image processing and medical imaging. Compressed sensing…
In this paper, we present an algorithm for identifying a parametrically described destructive unknown system based on a non-gaussianity measure. It is known that under certain conditions the output of a linear system is more gaussian than…
This work is focussed on the inversion task of inferring the distribution over parameters of interest leading to multiple sets of observations. The potential to solve such distributional inversion problems is driven by increasing…
Observations from ground based telescopes are affected by the presence of the Earth atmosphere, which severely perturbs them. The use of adaptive optics techniques has allowed us to partly beat this limitation. However, image selection or…
This paper considers the deconvolution problem in the case where the target signal is multidimensional and no information is known about the noise distribution. More precisely, no assumption is made on the noise distribution and no samples…
This work considers the multi-channel blind deconvolution problem under the assumption that the channels are short. First, we investigate the ill-posedness issues inherent to blind deconvolution problems and sufficient and necessary…