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We consider an inertial primal-dual fixed point algorithm (IPDFP) to compute the minimizations of the following Problem (1.1). This is a full splitting approach, in the sense that the nonsmooth functions are processed individually via their…

We present a novel iterative algorithm for detection of binary Markov random fields (MRFs) corrupted by two-dimensional (2D) intersymbol interference (ISI) and additive white Gaussian noise (AWGN). We assume a first-order binary MRF as a…

Non-cooperative game theory provides a robust framework for analyzing distributed resource allocation in multi-user wireless networks, with \emph{Iterative Water-Filling} (IWF) emerging as a canonical solution for power control problems.…

Suppose X is a multivariate diffusion process that is observed discretely in time. At each observation time, a transformation of the state of the process is observed with noise. The smoothing problem consists of recovering the path of the…

Sample-based Bayesian inference provides a route to uncertainty quantification in the geosciences, and inverse problems in general, though is very computationally demanding in the naive form that requires simulating an accurate computer…

Partially observable Markov decision processes (POMDPs) have recently become popular among many AI researchers because they serve as a natural model for planning under uncertainty. Value iteration is a well-known algorithm for finding…

There has been an increasing interest in developing efficient immersed boundary method (IBM) based on Cartesian grids, recently in the context of high-order methods. IBM based on volume penalization is a robust and easy to implement method…

We study two fundamental optimization problems: (1) scaling a symmetric positive definite matrix by a positive diagonal matrix so that the resulting matrix has row and column sums equal to 1; and (2) minimizing a quadratic function subject…

In this paper, we study a fast approximate inference method based on expectation propagation for exploring the posterior probability distribution arising from the Bayesian formulation of nonlinear inverse problems. It is capable of…

We study the convergence of random function iterations for finding an invariant measure of the corresponding Markov operator. We call the problem of finding such an invariant measure the stochastic fixed point problem. This generalizes…

This paper presents an improved implicit sampling method for hierarchical Bayesian inverse problems. A widely used approach for sampling posterior distribution is based on Markov chain Monte Carlo (MCMC). However, the samples generated by…

Physics-informed neural network (PINN) has been successfully applied in solving a variety of nonlinear non-convex forward and inverse problems. However, the training is challenging because of the non-convex loss functions and the multiple…

Blind face restoration (BFR) is important while challenging. Prior works prefer to exploit GAN-based frameworks to tackle this task due to the balance of quality and efficiency. However, these methods suffer from poor stability and…

Fluorescence Molecular Tomography (FMT) is a widely used non-invasive optical imaging technology in biomedical research. It usually faces significant accuracy challenges in depth reconstruction, and conventional iterative methods struggle…

Existing diffusion-based methods for inverse problems sample from the posterior using score functions and accept the generated random samples as solutions. In applications that posterior mean is preferred, we have to generate multiple…

The Iterative Forecast Planner (IFP) is a geometric planning approach that offers lightweight computations, scalable, and reactive solutions for multi-robot path planning in decentralized, communication-free settings. However, it struggles…

Optical diffraction tomography relies on solving an inverse scattering problem governed by the wave equation. Classical reconstruction algorithms are based on linear approximations of the forward model (Born or Rytov), which limits their…

Infrared and visible image fusion (IVIF) is essential for integrating thermal saliency with textural details to support downstream perception. However, most existing approaches suffer from "semantic blindness," leading to the erroneous…

We develop an improved phase calibration method of a reflective spatial light modulator (SLM) using interferometry by employing novel phase masks. We generate the optimised phase masks by using Iterative Fourier Transform Algorithm (IFTA)…

We consider the estimation of the transition matrix of a hidden Markovian process by using information geometry with respect to transition matrices. In this paper, only the histogram of $k$-memory data is used for the estimation. To…