Related papers: Blind Deconvolution Meets Blind Demixing: Algorith…
This paper presents an innovative set of tools to support a methodology for the multichannel interpolation (MCI) of a discrete signal. It is shown that a bandlimited signal $f$ can be exactly reconstructed from finite samples of $g_k$…
The lack of interpretability in current deep learning models causes serious concerns as they are extensively used for various life-critical applications. Hence, it is of paramount importance to develop interpretable deep learning models. In…
Recovery of signals with elements defined on the nodes of a graph, from compressive measurements is an important problem, which can arise in various domains such as sensor networks, image reconstruction and group testing. In some scenarios,…
Blind image deblurring, i.e., deblurring without knowledge of the blur kernel, is a highly ill-posed problem. The problem can be solved in two parts: i) estimate a blur kernel from the blurry image, and ii) given estimated blur kernel,…
Blind gain and phase calibration (BGPC) is a structured bilinear inverse problem, which arises in many applications, including inverse rendering in computational relighting (albedo estimation with unknown lighting), blind phase and gain…
Over the last decade, a number of Computational Imaging (CI) systems have been proposed for tasks such as motion deblurring, defocus deblurring and multispectral imaging. These techniques increase the amount of light reaching the sensor via…
Multispectral imaging is an important task of image processing and computer vision, which is especially relevant to applications such as dehazing or object detection. With the development of the RGBT (RGB & Thermal) sensor, the problem of…
We extend deconvolution in a periodic setting to deal with functional data. The resulting functional deconvolution model can be viewed as a generalization of a multitude of inverse problems in mathematical physics where one needs to recover…
Objects moving at high speed appear significantly blurred when captured with cameras. The blurry appearance is especially ambiguous when the object has complex shape or texture. In such cases, classical methods, or even humans, are unable…
Machine learning, and more specifically deep learning, have shown remarkable performance in sensing, communications, and inference. In this paper, we consider the application of the deep unfolding technique in the problem of signal…
In many experimental contexts, it is necessary to statistically remove the impact of instrumental effects in order to physically interpret measurements. This task has been extensively studied in particle physics, where the deconvolution…
We consider a standard distributed optimisation setting where $N$ machines, each holding a $d$-dimensional function $f_i$, aim to jointly minimise the sum of the functions $\sum_{i = 1}^N f_i (x)$. This problem arises naturally in…
In a large class of statistical inverse problems it is necessary to suppose that the transformation that is inverted is known. Although, in many applications, it is unrealistic to make this assumption, the problem is often insoluble without…
The main focus of this work is the reconstruction of the signals $f$ and $g_{i}$, $i=1,...,N$, from the knowledge of their sums $h_{i}=f+g_{i}$, under the assumption that $f$ and the $g_{i}$'s can be sparsely represented with respect to two…
Barcodes are ubiquitous and have been used in most of critical daily activities for decades. However, most of traditional decoders require well-founded barcode under a relatively standard condition. While wilder conditioned barcodes such as…
The increasingly crowded spectrum has spurred the design of joint radar-communications systems that share hardware resources and efficiently use the radio frequency spectrum. We study a general spectral coexistence scenario, wherein the…
In this paper, we study the problem of recovering two unknown signals from their convolution, which is commonly referred to as blind deconvolution. Reformulation of blind deconvolution as a low-rank recovery problem has led to multiple…
Modern reconstruction methods for magnetic resonance imaging (MRI) exploit the spatially varying sensitivity profiles of receive-coil arrays as additional source of information. This allows to reduce the number of time-consuming…
Phase retrieval consists in the recovery of an unknown signal from phaseless measurements of its usually complex-valued Fourier transform. Without further assumptions, this problem is notorious to be severe ill posed such that the recovery…
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…