Related papers: Fundamental Limits of Blind Deconvolution Part I: …
Signal models formed as linear combinations of few atoms from an over-complete dictionary or few frame vectors from a redundant frame have become central to many applications in high dimensional signal processing and data analysis. A core…
Assume that an unknown integral operator living in some known subspace is observed indirectly, by evaluating its action on a few Dirac masses at unknown locations. Is this information enough to recover the operator and the impulse responses…
Bilinear inverse problems (BIPs), the resolution of two vectors given their image under a bilinear mapping, arise in many applications. Without further constraints, BIPs are usually ill-posed. In practice, properties of natural signals are…
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,…
We discuss a technique that allows blind recovery of signals or blind identification of mixtures in instances where such recovery or identification were previously thought to be impossible: (i) closely located or highly correlated sources…
This paper proposes a verification-based decoding approach for reconstruction of a sparse signal with incremental sparse measurements. In its first step, the verification-based decoding algorithm is employed to reconstruct the signal with a…
Blind inverse problems in imaging arise from uncertainties in the system used to collect (noisy) measurements of images. Recovering clean images from these measurements typically requires identifying the imaging system, either implicitly or…
The support recovery problem consists of determining a sparse subset of a set of variables that is relevant in generating a set of observations, and arises in a diverse range of settings such as compressive sensing, and subset selection in…
Inverse problems in image reconstruction are fundamentally complicated by unknown noise properties. Classical iterative deconvolution approaches amplify noise and require careful parameter selection for an optimal trade-off between…
We present a novel approach for recovering a sparse signal from cross-correlated data. Cross-correlations naturally arise in many fields of imaging, such as optics, holography and seismic interferometry. Compared to the sparse signal…
Recent advances have demonstrated the possibility of solving the deconvolution problem without prior knowledge of the noise distribution. In this paper, we study the repeated measurements model, where information is derived from multiple…
Blind image deblurring remains a challenging problem for modern artificial neural networks. Unlike other image restoration problems, deblurring networks fail behind the performance of existing deblurring algorithms in case of uniform and 3D…
Denoising, the process of reducing random fluctuations in a signal to emphasize essential patterns, has been a fundamental problem of interest since the dawn of modern scientific inquiry. Recent denoising techniques, particularly in…
Despite strong empirical performance for image classification, deep neural networks are often regarded as ``black boxes'' and they are difficult to interpret. On the other hand, sparse convolutional models, which assume that a signal can be…
Blind Image deblurring tries to estimate blurriness and a latent image out of a blurred image. This estimation, as being an ill-posed problem, requires imposing restrictions on the latent image or a blur kernel that represents blurriness.…
The implementation of computational sensing strategies often faces calibration problems typically solved by means of multiple, accurately chosen training signals, an approach that can be resource-consuming and cumbersome. Conversely, blind…
The celebrated sparse representation model has led to remarkable results in various signal processing tasks in the last decade. However, despite its initial purpose of serving as a global prior for entire signals, it has been commonly used…
We propose a learned-structured unfolding neural network for the problem of compressive sparse multichannel blind-deconvolution. In this problem, each channel's measurements are given as convolution of a common source signal and sparse…
In this work we explore the previously proposed approach of direct blind deconvolution and denoising with convolutional neural networks in a situation where the blur kernels are partially constrained. We focus on blurred images from a…
Image blur and image noise are imaging artifacts intrinsically arising in image acquisition. In this paper, we consider multi-frame blind deconvolution (MFBD), where image blur is described by the convolution of an unobservable,…