kkdeng/faster-fista

Source codes for paper "Faster FISTA"

Faster-FISTA

Matlab code to reproduce the results of the paper

Faster FISTA

Jingwei Liang, Carola-Bibiane Schönlieb

Quadratic problem

Consider solving the problem below $$ \min_{x\in \mathbb{R}^n} ~ \frac{1}{2} |Ax - f|^2 , $$ where $A$ is the Laplacian operator $$ A = \begin{bmatrix} 2 & -1 & & & & & & \ -1 & 2 & -1 & & & & & \ & -1 & 2 & -1 & & & & \ & & & \dotsm \ & & & & -1 & 2 & -1 & \ & & & & & -1 & 2 & -1 \ & & & & & & -1 & 2 \ \end{bmatrix} . $$

We set $n = 201$.

Relative error $|x_{k}-x_{k-1}|$	Objective function value $\Phi(x_{k}) - \Phi(x^\star)$

Linear inverse problems

Consider solving the problem below $$ \min_{x\in \mathbb{R}^n} ~ \mu R(x) + \frac{1}{2} |Ax - f|^2 . $$

$\ell_{1}$-norm

Relative error $|x_{k}-x_{k-1}|$	Objective function value $\Phi(x_{k}) - \Phi(x^\star)$

$\ell_{1,2}$-norm

Relative error $|x_{k}-x_{k-1}|$	Objective function value $\Phi(x_{k}) - \Phi(x^\star)$

$\ell_{\infty}$-norm

Relative error $|x_{k}-x_{k-1}|$	Objective function value $\Phi(x_{k}) - \Phi(x^\star)$

Total variation based image deblur

The codes only run under MacOS

Original image	Blurred image	Recovered image	Performance comparison

Principle component pursuit

Matrix example

Mixture matrix	Sparse component	Low-rank component	Performance comparison

Video example

Original frame	Foreground	Background	Performance comparison

Copyright (c) 2018 Jingwei Liang