International Journal of Biomedical Imaging / 2015 / Article / Alg 2

Research Article

Clutter Mitigation in Echocardiography Using Sparse Signal Separation

Algorithm 2

K-SVD.
Task. Train a dictionary to sparsely represent the data by approximating the solution
to problem (6).
Input Parameters. Input parameters include a matrix containing the signals and the
maximum sparsity of the solution .
Initialization. Initialization is as follows:
 (i) Initialize .
 (ii) Initialize by either using randomly chosen examples from or using random entries.
 (iii) Normalize the columns of .
Main Iteration. Increment by 1 and apply the following:
 (i) Sparse coding: obtain the sparse representations of each signal . Use OMP to
    approximate the solution of
         
                subject to  .
    These form the matrix .
 (ii) Dictionary update: use the following steps to update the columns of the dictionary and obtain :
     repeat for .
   (a) Define the group of samples that use the atom :
            .
   (b) Compute the residual matrix , where stands for the th row of .
   (c) Restrict by choosing only the columns corresponding to , and obtain .
   (d) Apply SVD decomposition . Update the dictionary atom and the representations .
 (iii) Stopping rule: if the change in is small enough, stop.
Output. The desired result is the dictionary and the sparse representations of the signals in .

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