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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