Research Article

Pattern Synthesis for Sparse Arrays by Compressed Sensing and Low-Rank Matrix Recovery Methods

Algorithm 1

Input: the measurement matrix is , the dimension is , is the number of atoms in , is the length of an atom, sparse degree is K, and sampling signal is y.
Output: index set is , residual is , and reconfiguration of the signal is .
 (1) The initial residual is , the estimate of the signal sparse degree is K, the number of iterations is , is the index set of all the atoms, and the index value set is
 (2) Calculate the inner product of current residual and every atom in the index set to choose a candidate set:
  ,
  ,
  
Here, is definitively the relaxing factor, , and the value is close to 1 typically.
 (3) Calculate the intersection of the current candidate set and the candidate set of the last iteration, , and then put the value of into the new index
 (4) If , select an atom from by calculating the minimum residual and join the index set
  
 (5) Reset the index value and update the residual:
  ,
  
 (6) Compare the error parameters which is setup previously with the , or calculate whether the atom number of the index set meets the required value. If it does not meet the stop condition, and return to step 2.