On the Uniqueness of the Sparse Signals Reconstruction Based on the Missing Samples Variation Analysis

Algorithm 1

Sparsity limits—Theorem 1 and Corollary 2.

Require:

 (i) Set of missing sample positions

 (ii) Total number of signal samples ,

(1)

(2)

(3) for do

(4)  for do

(5)    and

(6)  end for

(7)  

(8)  if then                 Theorem 1 check

(9)  

(10) end if

(11)  if then                 Corollary 2 check

(12)  

(13)  end if

(14) end for

Output: ,

 (i) Every solution with sparsity is unique.

 (ii) Solution with sparsity is unique with probability one, excluding zero-probability event

   (when the amplitudes of signal components are related to each other with a relation defined by

   the missing sample positions).