Related papers: Differentiable SVD based on Moore-Penrose Pseudoin…

The image reconstruction process in medical imaging can be treated as solving an inverse problem. The inverse problem is usually solved using time-consuming iterative algorithms with sparsity or other constraints. Recently, deep neural…

We present differentiable point-based inverse rendering, DPIR, an analysis-by-synthesis method that processes images captured under diverse illuminations to estimate shape and spatially-varying BRDF. To this end, we adopt point-based…

In this paper, we propose a novel deep convolutional neural network (CNN)-based algorithm for solving ill-posed inverse problems. Regularized iterative algorithms have emerged as the standard approach to ill-posed inverse problems in the…

In this paper we address the issue of output instability of deep neural networks: small perturbations in the visual input can significantly distort the feature embeddings and output of a neural network. Such instability affects many deep…

Neural operators have emerged as a promising paradigm for learning solution operators of partial differential equa- tions (PDEs) directly from data. Existing methods, such as those based on Fourier or graph techniques, make strong as-…

Deep learning (DL) has emerged as a tool for improving accelerated MRI reconstruction. A common strategy among DL methods is the physics-based approach, where a regularized iterative algorithm alternating between data consistency and a…

We introduce Sven (Singular Value dEsceNt), a new optimization algorithm for neural networks that exploits the natural decomposition of loss functions into a sum over individual data points, rather than reducing the full loss to a single…

Generalized inverses play a fundamental role in numerical linear algebra, particularly when matrices are rectangular, singular, or rank deficient. Even when the input matrix is sparse, generalized inverses such as the M-P pseudoinverse are…

Separable nonlinear least squares problems appear in many inverse problems, including semi-blind image deblurring. The variable projection (VarPro) method provides an efficient approach for solving such problems by eliminating linear…

Inverse Problems in medical imaging and computer vision are traditionally solved using purely model-based methods. Among those variational regularization models are one of the most popular approaches. We propose a new framework for applying…

Numerical solutions of partial differential equations (PDEs) require expensive simulations, limiting their application in design optimization, model-based control, and large-scale inverse problems. Surrogate modeling techniques seek to…

Supervised learning with a convolutional neural network is recognized as a powerful means of image restoration. However, most such methods have been designed for application to grayscale and/or color images; therefore, they have limited…

We propose a new algorithm for the computation of a singular value decomposition (SVD) low-rank approximation of a matrix in the Matrix Product Operator (MPO) format, also called the Tensor Train Matrix format. Our tensor network randomized…

Single-level reformulations of (non-convex) distributionally robust optimization (DRO) problems are often intractable, as they contain semiinfinite dual constraints. Based on such a semiinfinite reformulation, we present a safe…

To quantify uncertainties in inverse problems of partial differential equations (PDEs), we formulate them into statistical inference problems using Bayes' formula. Recently, well-justified infinite-dimensional Bayesian analysis methods have…

Significant progress has been witnessed in learning-based Multi-view Stereo (MVS) under supervised and unsupervised settings. To combine their respective merits in accuracy and completeness, meantime reducing the demand for expensive…

This paper introduces the $w$-product, a novel wavelet-based tensor multiplication scheme leveraging second-generation wavelet transforms to achieve linear transformation complexity while preserving essential algebraic properties. The…

A Transformer-based deep direct sampling method is proposed for electrical impedance tomography, a well-known severely ill-posed nonlinear boundary value inverse problem. A real-time reconstruction is achieved by evaluating the learned…

We propose a stochastic gradient descent approach with partitioned-truncated singular value decomposition for large-scale inverse problems of magnetic modulus data. Motivated by a uniqueness theorem in gravity inverse problem and realizing…

When building a geometric scene understanding system for autonomous vehicles, it is crucial to know when the system might fail. Most contemporary approaches cast the problem as depth regression, whose output is a depth value for each pixel.…