BPDN_DF_L1.m

function [x_out, time_tot] = BPDN_DF_L1(varargin)

% [x_out, time_tot] = BPDN_DF_L1(y, G, F, tau, 1000)
% 
% This function solves the BPDN optimization function on a time-varying
% signal under the assumption that only the innovations is sparse. Under
% these assumptions, BPDN is solved for the innovations at every time-step
% and used to update the state estimate.
% 
%   The inputs are:
% 
% y:       MxT matrix of measurement vectors at each time step
% G:       MxNxT array of measurement matrices at each iteration
% F:       MxMxT array of dynamics matrices for each iteration
% tau:     Sparsity tradeoff parameter for BPDN on the innovations
% maxiter: Maximum number of iterations for BPDN to run
% 
%    The outputs are:
% x_out:      NxT matrix with the estimates of the signal x
% time_tot:   total runtime
% 
%
% Code by Adam Charles, 
% Department of Electrical and Computer Engineering,
% Georgia Institute of Technology
% 
% Last updated August 21, 2012. 
% 

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Input Parsing
if nargin > 1
    y = varargin{1};
    G = varargin{2};
else
    error('Bad number of inputs!')
end
if nargin > 2
    F = varargin{3};
else
    F = eye(size(G, 2));
end

if nargin > 3
    tau = varargin{4};
else
    tau = 0.01;
end

if nargin > 4
    maxiter = varargin{5};
else
    maxiter = 1000;
end

if nargin > 5
    error('Bad number of inputs!')
end

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Initializations
x_dim = size(F, 1);
num_iters = size(y, 2) - 1;

x_out = zeros(x_dim, num_iters+1);
time_bp = zeros(num_iters + 1);

% Initial Point
[x_out(:, 1), ~, ~, time_bp(1)] = BPDN_homotopy_function(G(:, :, 1), y(:, 1), tau, maxiter);

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Run Algorithm
% Iterate through
for ii = 1:num_iters
    % Solve for sparse innovations
    [v_out, ~, ~, time_bp(ii+1)] =...
        BPDN_homotopy_function(G(:, :, ii+1),...
        (y(:, ii+1)- G(:, :, ii+1)*(F(:, :, ii+1)*x_out(:, ii) )), tau, maxiter);
    % Update state
    x_out(:, ii+1) = F(:, :, ii+1)*x_out(:, ii) + v_out;
end

time_tot = sum(time_bp);
end

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