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In image deconvolution problems, the diagonalization of the underlying operators by means of the FFT usually yields very large speedups. When there are incomplete observations (e.g., in the case of unknown boundaries), standard…
Blind deconvolution is a ubiquitous problem of recovering two unknown signals from their convolution. Unfortunately, this is an ill-posed problem in general. This paper focuses on the {\em short and sparse} blind deconvolution problem,…
Non-blind deconvolution aims to restore a sharp image from its blurred counterpart given an obtained kernel. Existing deep neural architectures are often built based on large datasets of sharp ground truth images and trained with…
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…
Blind pansharpening addresses the problem of generating a high spatial-resolution multi-spectral (HRMS) image given a low spatial-resolution multi-spectral (LRMS) image with the guidance of its associated spatially misaligned high…
Given the superposition of a low-rank matrix plus the product of a known fat compression matrix times a sparse matrix, the goal of this paper is to establish deterministic conditions under which exact recovery of the low-rank and sparse…
In the blind deconvolution problem, we observe the convolution of an unknown filter and unknown signal and attempt to reconstruct the filter and signal. The problem seems impossible in general, since there are seemingly many more unknowns…
We propose a novel method to accurately reconstruct a set of images representing a single scene from few linear multi-view measurements. Each observed image is modeled as the sum of a background image and a foreground one. The background…
Lensless microscopy with coherent or partially coherent light sources is a well known imaging technique, commonly referred as digital in-line holographic microscopy. In the established methods, both the spatial and temporal coherence of…
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…
Learned image compression research has achieved state-of-the-art compression performance with auto-encoder based neural network architectures, where the image is mapped via convolutional neural networks (CNN) into a latent representation…
An optical imaging system forms an object image by recollecting light scattered by the object. However, intact optical information of the object delivered through the imaging system is deteriorated by imperfect optical elements and unwanted…
The image deblurring problem consists of reconstructing images from blur and noise contaminated available data. In this AMS Notices article, we provide an overview of some well known numerical linear algebra techniques that are use for…
Image deblurring aims to restore the latent sharp images from the corresponding blurred ones. In this paper, we present an unsupervised method for domain-specific single-image deblurring based on disentangled representations. The…
Face recognition system is one of the esteemed research areas in pattern recognition and computer vision as long as its major challenges. A few challenges in recognizing faces are blur, illumination, and varied expressions. Blur is natural…
In this paper, we propose to reformulate the blind image deblurring task to directly learn an inverse of the degradation model represented by a deep linear network. We introduce Deep Identity Learning (DIL), a novel learning strategy that…
The miniaturization of optics through the use of two-dimensional metalenses has enabled novel applications in imaging. To date, single-lens imaging remains the most common configuration, in part due to the limited focusing efficiency of…
Deep learning-based blind image deblurring plays an essential role in solving image blur since all existing kernels are limited in modeling the real world blur. Thus far, researchers focus on powerful models to handle the deblurring problem…
When capturing and storing images, devices inevitably introduce noise. Reducing this noise is a critical task called image denoising. Deep learning has become the de facto method for image denoising, especially with the emergence of…
Computational sensing strategies often suffer from calibration errors in the physical implementation of their ideal sensing models. Such uncertainties are typically addressed by using multiple, accurately chosen training signals to recover…