% VTISTA.m for Variant Thresholding Soft Iterative Thresholding Algorithm.

function x_output =VTISTA( y,A,lambda,Max_Iter)

%   ITSTA is a simple algorithm based on Soft-thresholding and used to solve

%   following Problem:

%       min || y - A x ||_2^2 / 2 + u(x) || x ||_1

%                   s.t.   || x ||_0 <= s

%   Input:

%   y :measure data;

%   A: sensing matrix;

%   lambda: parameter for (1/2)*(x-xk)' (A'A) (x-xk)=lambda^2 ||x-xk||_2^2;

%   Sparsity_level : || x ||_0,that is the number of the nonzero entries of

%   some vector in R^n;

%   Output:

%   x_shs: the iterative soft thresholding;

%%%%%%%%%%%%%%%

x0     = A'*y;                                       % Initialization vector;

n       = length(x0);                                % the dimension of signal;

if nargin <4

   Max_Iter = n ;

end

if nargin <3

   lambda =  sqrt(2*log(n));

end

Iter    = 0;                    % initializate iteration;

x_input = x0;

while Iter <= Max_Iter  

   %   The important loop;

   lambdax = lambda / ((sqrt(n) - 1)*norm(x_input,2));

   Tx = lambdax/2;

   zxk = x_input +A'*(y-A*x_input) ;  

   % This is soft thresholding;

   x_input = wthresh(zxk,'s',Tx) ;

  % x_input = zxk - sign(x_input).*Tx;

   %the same with wthresh(which is inner function);

   Iter = Iter+1;

end

x_output = x_input;

end