Clutter Mitigation in Echocardiography Using Sparse Signal Separation

Algorithm 1

Orthogonal Matching Pursuit.

Task. Approximate the solution to problem (4) or (5).

Input Parameters. Input parameters are dictionary , the signal , and the error threshold or

the maximum sparsity of the solution .

Initialization. Initialization is as follows:

 (i) Initialize .

 (ii) The initial solution .

 (iii) The initial residual .

 (iv) The initial support .

Main Iteration. Increment by 1 and perform the following steps:

 (i) Sweep: compute the projection values , where is the conjugate transpose of matrix .

 (ii) Update support: find element , the maximizer of , and update the support, .

 (iii) Update solution: compute , the minimizer of subject to support .

 (iv) Update residual: compute .

 (v) Stopping criterion: if (for problem (4)) or (for problem (5)), stop. Otherwise,

    continue with the next iteration.

Output. The approximated solution is obtained after iterations.