Algorithms and software for total variation image reconstruction via first-order methods

Abstract

This paper describes new algorithms and related software for total variation (TV) image reconstruction, more specifically: denoising, inpainting, and deblurring. The algorithms are based on one of Nesterov's first-order methods, tailored to the image processing applications in such a way that, except for the mandatory regularization parameter, the user needs not specify any parameters in the algorithms. The software is written in C with interface to Matlab (version 7.5 or later), and we demonstrate its performance and use with examples.

Sparse Occlusion Detection with Optical Flow

“…This is done in Nesterov (2005), that has already been used profitably for noise reduction, inpainting and deblurring (Weiss et al 2009;Dahl et al 2009), and incorporated in software libraries for sparse recovery (Becker et al 2009). In our case, we write ψ(v 1 , v 2 , e 1 ) as a summation of terms…”

“…Since G T G 2 is bounded above (Dahl et al 2009) by 8, given the coefficients λ and μ, L is given by…”

Phase retrieval in in-line x-ray phase contrast imaging based on total variation minimization

“…It was initially developed for image denoising [22] and recently been introduced in such fields as deblurring, super-resolution, inpainting and tomography [23][24][25][26]. The idea underlying TV minimization is to promote a solution that has the sparsest gradient.…”

“…Any implementation of TV minimization can be chosen from a wide range of algorithms [25]. Here we will present only results acquired with an algorithm based on the so called Fast Iterative Shrinkage-Thresholding Algorithm (FISTA) [29].…”

Calculation of Relaxation Spectra from Stress Relaxation Measurements

“…Furthermore, these techniques are used in various fields of science such as in the measurement of emulsion droplet size distribution (Hollingsworth and Johns, 2003), NMR spectral analysis (van Beek et al, 2003), image deblurring (Dahl et al, 2009) or tomography (Correia et al, 2009) just to name a few. Stress relaxation experimentation is a fundamental and direct approach in the elucidation of molecular dynamics of relaxation processes, yet application of regularization methods to such measurements on biopolymer systems are not well documented in literature.…”