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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