Multiresolution Parameter Choice Method for Total Variation Regularized Tomography

A Computational Framework for Total Variation-Regularized Positron Emission Tomography

In positron emission tomography, image data corresponds to measurements of emitted photons from a radioactive tracer in the subject. Such count data is typically modeled using a Poisson random variable, leading to the use of the negative-log Poisson likelihood fit-to-data function. Regularization is needed, however, in order to guarantee reconstructions with minimal artifacts. Given that tracer...

UPRE method for total variation parameter selection

Total Variation (TV) regularization is a popular method for solving a wide variety of inverse problems in image processing. In order to optimize the reconstructed image, it is important to choose a good regularization parameter. The Unbiased Predictive Risk Estimator (UPRE) has been shown to give a good estimate of this parameter for Tikhonov regularization. In this paper we propose an extensio...

Geometry of total variation regularized Lp-model

Truncated Total Least Squares Method with a Practical Truncation Parameter Choice Scheme for Bioluminescence Tomography Inverse Problem

In bioluminescence tomography (BLT), reconstruction of internal bioluminescent source distribution from the surface optical signals is an ill-posed inverse problem. In real BLT experiment, apart from the measurement noise, the system errors caused by geometry mismatch, numerical discretization, and optical modeling approximations are also inevitable, which may lead to large errors in the recons...

An optimal analytical method for nonlinear boundary value problems based on method of variation of parameter

In this paper, the authors present a modified convergent analytic algorithm for the solution of nonlinear boundary value problems by means of a variable parameter method and briefly, the method is called optimal variable parameter method. This method, based on the embedding of a parameter and an auxiliary operator, provides a computational advantage for the convergence of the approximate soluti...