dictionary_learning.m

function [dictionary] = dictionary_learning(image_set, D, lambda)
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% We presume the size of the images are the same (e.g. 20 x 20)

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% Input parameters:
% image_set: A cell of (grey) images provide for this algorithm
% D: Initial dictionary
% lamda: The regularization term for LARS computation

% Output:
% dictionary: dictionary for this image_set

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% Code is following the algorithm provided by the paper - Online Dictionary 
% for Sparse Coding by Julien Mairal, Francis Bach, Jean Ponce, and Guiilermo Sapiro

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[n p] = size(image_set{1}); % image size

A_now = []; B_now = []; A_old = []; B_old = [];
T = length(image_set(1,:)); % number of images to train 
for t = 1:T,
    Y = convert_image_to_vector(image_set{t});
    X = D;
    Y = zero_mean_y(Y);
    X = Normalize(X);
    [beta_hist] = lars(X, Y, lambda); % sparse coding; return the hist. of coefficients it generates
    a = beta_hist(size(beta_hist, 1),:)';

    % update A and B
    if t == 1,
        A_now = 0.5 * a * a'; 
        A_old = A_now;
        B_now = Y * a'; 
        B_old = B_now;
    else
        A_now = A_old + 0.5 * a * a'; 
        A_old = A_now;
        B_now = B_old + Y * a';
        B_old = B_now;
    end % end if

    % update dictionary
    D = dict_update(D, A_now, B_now);
end % end for loop

dictionary = D;
end