How do I structure a total variation denoising code?

I have never use matlab before and have thrown in at the deep end with a total variation denoising question.

I have to implement the forward-backward splitting algorithm for the dual form of the total variation denoising problem. I've been sent an example code for the Lasso-primal:

wine_quality.m:

function [white_indicators, red_indicators]=wine_quality() dwhite=dlmread('../data/winequality-white.csv', ';', 1, 0); white_indicators=do_wine_quality(dwhite, 0.0003, 1000) dred=dlmread('../data/winequality-red.csv', ';', 1, 0); red_indicators=do_wine_quality(dred, 0.005, 1000) end

function x=do_wine_quality(data, lambda, iters) A=data(:, 1:11); b=data(:, 12); x0=zeros(11, 1); % L=norm(A)^2 is the factor of smoothness of g(x)=|Ax-b|^2 % This sets tau*L=0.9<=1. tau=0.9/norm(A)^2; x=lasso_fb(A, b, lambda, x0, tau, iters); end

lasso_fb.m:

function x=lasso_fb(A, b, lambda, x0, tau, iters) x=x0; for i=1:iters % z = x-tau grad g(x) x = prox_l1(tau, lambda, x - tau*A'*(A*x-b)); end end

prox_l1.m:

function xnext=prox_l1(tau, lambda, z) % Soft thresholding idx=abs(z)<=lambda; xnext=z-lambda*z./abs(z); xnext(idx)=0; end

How can I use this for the denoising problem?

Answer 1

[Sudarshan Kolar]

Hello Cath,

I understand that you want to implement total variation denoising. Have you considered other resources as well, like:

https://www.mathworks.com/matlabcentral/fileexchange/16204-toolbox-sparse-optmization?focused=5175257&tab=example

https://www.mathworks.com/matlabcentral/fileexchange/52478-the-spectral-total-variation-denoising-algorithm

http://www.mathworks.com/matlabcentral/fileexchange/16201-toolbox-image?focused=5133334&tab=function

Hope that helps. Sorry for not being able to answer your question directly.

Sudarshan