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An adjustable algorithm of exclusion of conditional equations with excessive residuals is proposed. The criteria applied in the algorithm use variable exclusion limits which decrease as the number of equations goes down. The algorithm is…

Recently deep neutral networks have achieved promising performance for filling large missing regions in image inpainting tasks. They usually adopted the standard convolutional architecture over the corrupted image, leading to meaningless…

With the wide deployment of digital image capturing equipment, the need of denoising to produce a crystal clear image from noisy capture environment has become indispensable. This work presents a novel image denoising method that can tackle…

Automatic colorization of images without human intervention has been a subject of interest in the machine learning community for a brief period of time. Assigning color to an image is a highly ill-posed problem because of its innate nature…

This paper studies the achievable rates of Gaussian interference channels with additive white Gaussian noise (AWGN), when improper or circularly asymmetric complex Gaussian signaling is applied. For the Gaussian multiple-input…

We present a novel approach to nonlinear constrained Tikhonov regularization from the viewpoint of optimization theory. A second-order sufficient optimality condition is suggested as a nonlinearity condition to handle the nonlinearity of…

Image deconvolution is still to be a challenging ill-posed problem for recovering a clear image from a given blurry image, when the point spread function is known. Although competitive deconvolution methods are numerically impressive and…

$\ell_1$ regularization is used to preserve edges or enforce sparsity in a solution to an inverse problem. We investigate the Split Bregman and the Majorization-Minimization iterative methods that turn this non-smooth minimization problem…

Many current state-of-the-art methods for anomaly localization in medical images rely on calculating a residual image between a potentially anomalous input image and its "healthy" reconstruction. As the reconstruction of the unseen…

Image-to-image translation is an ill-posed problem as unique one-to-one mapping may not exist between the source and target images. Learning-based methods proposed in this context often evaluate the performance on test data that is similar…

We propose a new optimization framework for aleatoric uncertainty estimation in regression problems. Existing methods can quantify the error in the target estimation, but they tend to underestimate it. To obtain the predictive uncertainty…

Decreased visibility, intensive noise, and biased color are the common problems existing in low-light images. These visual disturbances further reduce the performance of high-level vision tasks, such as object detection, and tracking. To…

We propose a globally convergent alternating minimization (AM) algorithm for image reconstruction in transmission tomography, which extends automatic relevance determination (ARD) to Poisson noise models with Beer's law. The algorithm…

Electron ptychography provides new opportunities to resolve atomic structures with deep sub-angstrom spatial resolution and studying electron-beam sensitive materials with high dose efficiency. In practice, obtaining accurate ptychography…

We consider choice of the regularization parameter in Tikhonov method in the case of the unknown noise level of the data. From known heuristic parameter choice rules often the best results were obtained in the quasi-optimality criterion…

We study empirical and hierarchical Bayes approaches to the problem of estimating an infinite-dimensional parameter in mildly ill-posed inverse problems. We consider a class of prior distributions indexed by a hyperparameter that quantifies…

We propose maximum likelihood estimation for learning Gaussian graphical models with a Gaussian (ell_2^2) prior on the parameters. This is in contrast to the commonly used Laplace (ell_1) prior for encouraging sparseness. We show that our…

A simple, yet general, formalism for the optimized linear combination of astrophysical images is constructed and demonstrated. The formalism allows the user to combine multiple undersampled images to provide oversampled output at high…

Denoising is omnipresent in image processing. It is usually addressed with algorithms relying on a set of hyperparameters that control the quality of the recovered image. Manual tuning of those parameters can be a daunting task, which calls…

We consider the problem of modulating the value of a parameter onto a band-limited signal to be transmitted over a continuous-time, additive white Gaussian noise (AWGN) channel, and estimating this parameter at the receiver. The performance…