International Journal of Biomedical Imaging / 2015 / Article / Alg 1

Research Article

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.

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