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?
