OMP_delta.m

function [x, t, Pos_h_t] = OMP_delta(Q, y, sigma, noise_en, Lp)
    % OMP Algorithm
    [M, N] = size(Q);
    h_temp = zeros(N,1);
    Pos_h_t = [];
    r_n = y; 
    Q_t = [];
    t = 0; 
    ht_LS = [];
    if(nargin == 3 || noise_en)
        delta = sigma^2;
        while(r_n'*r_n > size(y,1)*delta)
            product_t = Q'*r_n;
            [~, pos_t] = max(abs(product_t));
            Pos_h_t = [Pos_h_t pos_t];   %Qt相当于At,Pos_h_t相当于配置集合倒Vt
            Q_t = [Q_t,Q(:,pos_t)];   
            Q(:,pos_t) = zeros(M,1);
            ht_LS = Q_t\y;    %%%%为什么没有乘dft矩阵，ht_LS 相当于theta Q_t\y是最小二乘解吗？好像不是，直接除
            r_n = y -  Q_t*ht_LS;
            t = t+1;
        end
        h_temp(Pos_h_t) = ht_LS;
        x = h_temp;
    else
        while(t < Lp)
            product_t = Q'*r_n;
            [~, pos_t] = max(abs(product_t));
            Pos_h_t = [Pos_h_t pos_t];
            Q_t = [Q_t,Q(:,pos_t)];
            Q(:,pos_t) = zeros(M,1);
            ht_LS = Q_t\y;
            r_n = y -  Q_t*ht_LS;
            t = t+1;
        end
        h_temp(Pos_h_t) = ht_LS;
        x = h_temp;
    end
end