Kaczmarz Iterative Projection and Nonuniform Sampling with Complexity Estimates

Algorithm 3

-Subspace Kaczmarz Projections.

Require: Matrix full-rank consistent measurements subject to , for .

 (1) Set to initial approximation,

 (2) while not converged do

 (3)   Select distinct linearly independent rows of relative to random rule. Construct block

     matrix comprised of rows .

 (4)   Perform Gram-Schmidt procedure on to obtain the orthonormal set of columns .

     Let

 (5)   Update as follows:

     ,

     ,

 (6)   Compute iteratively using , ,

 (7)   Update

 (8) end while