Related papers: Blind Deconvolution by a Steepest Descent Algorith…
Submodular function minimization is a fundamental optimization problem that arises in several applications in machine learning and computer vision. The problem is known to be solvable in polynomial time, but general purpose algorithms have…
Low-rank optimization problems with sparse simplex constraints involve variables that must satisfy nonnegativity, sparsity, and sum-to-1 conditions, making their optimization particularly challenging due to the interplay between low-rank…
We address the problem of recovering a sparse signal from clipped or quantized measurements. We show how these two problems can be formulated as minimizing the distance to a convex feasibility set, which provides a convex and differentiable…
In this paper, we present modifications of the iterative hard thresholding (IHT) method for recovery of jointly row-sparse and low-rank matrices. In particular a Riemannian version of IHT is considered which significantly reduces…
We present steepest descent (SD) implementation of multimodulus algorithm (MMA2-2) for blind signal retrieval in digital communication systems. In comparison to stochastic approximate (gradient descent) realization, the proposed SD…
Solving a bilevel optimization problem is at the core of several machine learning problems such as hyperparameter tuning, data denoising, meta- and few-shot learning, and training-data poisoning. Different from simultaneous or…
Projected gradient descent and its Riemannian variant belong to a typical class of methods for low-rank matrix estimation. This paper proposes a new Nesterov's Accelerated Riemannian Gradient algorithm by efficient orthographic retraction…
We propose a stochastic variance-reduced cubic regularized Newton algorithm to optimize the finite-sum problem over a Riemannian submanifold of the Euclidean space. The proposed algorithm requires a full gradient and Hessian update at the…
We present a novel optimization-based decoding algorithm for LDPC codes that is suitable for hardware architectures specialized to feed-forward neural networks. The algorithm is based on the projected gradient descent algorithm with a…
Previous methods decompose blind super resolution (SR) problem into two sequential steps: \textit{i}) estimating blur kernel from given low-resolution (LR) image and \textit{ii}) restoring SR image based on estimated kernel. This two-step…
This paper demonstrates a practical method that can correct spatial varying blur from a set of images of the same object. The algorithm jointly estimates the object and local point spread functions~(PSF). The method prioritizes sections…
Reproducing an all-in-focus image from an image with defocus regions is of practical value in many applications, eg, digital photography, and robotics. Using the output of some existing defocus map estimator, existing approaches first…
Rotating synthetic aperture (RSA) imaging system captures images of the target scene at different rotation angles by rotating a rectangular aperture. Deblurring acquired RSA images plays a critical role in reconstructing a latent sharp…
We present a new method for blind motion deblurring that uses a neural network trained to compute estimates of sharp image patches from observations that are blurred by an unknown motion kernel. Instead of regressing directly to patch…
The Wasserstein distance has become increasingly important in machine learning and deep learning. Despite its popularity, the Wasserstein distance is hard to approximate because of the curse of dimensionality. A recently proposed approach…
Image deblurring remains a central research area within image processing, critical for its role in enhancing image quality and facilitating clearer visual representations across diverse applications. This paper tackles the optimization…
The most ubiquitous form of computational aberration correction for microscopy is deconvolution. However, deconvolution relies on the assumption that the point spread function is the same across the entire field-of-view. This assumption is…
Typical blur from camera shake often deviates from the standard uniform convolutional script, in part because of problematic rotations which create greater blurring away from some unknown center point. Consequently, successful blind…
This paper concerns solving the sparse deconvolution and demixing problem using $\ell_{1,2}$-minimization. We show that under a certain structured random model, robust and stable recovery is possible. The results extend results of Ling and…
Many computer vision problems (e.g., camera calibration, image alignment, structure from motion) are solved with nonlinear optimization methods. It is generally accepted that second order descent methods are the most robust, fast, and…