Related papers: Identifiability in Blind Deconvolution with Subspa…
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 present a new Bayesian methodology to learn the unknown material density of a given sample by inverting its two-dimensional images that are taken with a Scanning Electron Microscope. An image results from a sequence of projections of the…
This study addresses the blind deconvolution problem with modulated inputs, focusing on a measurement model where an unknown blurring kernel $\boldsymbol{h}$ is convolved with multiple random modulations…
Benders' decomposition (BD) is a framework for solving optimization problems by removing some variables and modeling their contribution to the original problem via so-called Benders cuts. While many advanced optimization techniques can be…
Multi-channel sparse blind deconvolution, or convolutional sparse coding, refers to the problem of learning an unknown filter by observing its circulant convolutions with multiple input signals that are sparse. This problem finds numerous…
Compressed sensing is a powerful tool in applications such as magnetic resonance imaging (MRI). It enables accurate recovery of images from highly undersampled measurements by exploiting the sparsity of the images or image patches in a…
Blind deconvolution has made significant progress in the past decade. Most successful algorithms are classified either as Variational or Maximum a-Posteriori ($MAP$). In spite of the superior theoretical justification of variational…
We derive multiscale statistics for deconvolution in order to detect qualitative features of the unknown density. An important example covered within this framework is to test for local monotonicity on all scales simultaneously. We…
This paper considers recovering $L$-dimensional vectors $\boldsymbol{w}$, and $\boldsymbol{x}_1,\boldsymbol{x}_2, \ldots, \boldsymbol{x}_N$ from their circular convolutions $\boldsymbol{y}_n = \boldsymbol{w}*\boldsymbol{x}_n, \ n = 1,2,3,…
Single image blind deblurring is highly ill-posed as neither the latent sharp image nor the blur kernel is known. Even though considerable progress has been made, several major difficulties remain for blind deblurring, including the…
Low-density parity-check (LDPC) convolutional codes have been shown to exhibit excellent performance under low-complexity belief-propagation decoding [1], [2]. This phenomenon is now termed threshold saturation via spatial coupling. The…
Blind Source Separation (BSS) is a challenging matrix factorization problem that plays a central role in multichannel imaging science. In a large number of applications, such as astrophysics, current unmixing methods are limited since…
Using total variation based energy minimisation we address the recovery of a blurred (convoluted) one dimensional (1D) barcode. We consider functionals defined over all possible barcodes with fidelity to a convoluted signal of a barcode,…
Blind Compressed Sensing (BCS) is an extension of Compressed Sensing (CS) where the optimal sparsifying dictionary is assumed to be unknown and subject to estimation (in addition to the CS sparse coefficients). Since the emergence of BCS,…
Real-world datasets often combine data collected under different experimental conditions. This yields larger datasets, but also introduces spurious correlations that make it difficult to model the phenomena of interest. We address this by…
In this work we characterize all ambiguities of the linear (aperiodic) one-dimensional convolution on two fixed finite-dimensional complex vector spaces. It will be shown that the convolution ambiguities can be mapped one-to-one to…
Matrix Joint Diagonalization (MJD) is a powerful approach for solving the Blind Source Separation (BSS) problem. It relies on the construction of matrices which are diagonalized by the unknown demixing matrix. Their joint diagonalizer…
We propose a blind deconvolution method for signals on graphs, with the exact sparseness constraint for the original signal. Graph blind deconvolution is an algorithm for estimating the original signal on a graph from a set of blurred and…
We consider the problem of multivariate density deconvolution when the interest lies in estimating the distribution of a vector-valued random variable but precise measurements of the variable of interest are not available, observations…
We propose a low complexity complex valued Sphere Decoding (CV-SD) algorithm, referred to as Circular Sphere Decoding (CSD) which is applicable to multiple-input multiple-output (MIMO) systems with arbitrary two dimensional (2D)…