The convergence of block cyclic projection with underrelaxation parameters for compressed sensing based tomography

Area of Science:

• Medical Imaging
• Applied Mathematics
• Computer Science

Background:

• The block cyclic projection method in compressed sensing (BCPCS) is used for computed tomography (CT) image reconstruction.
• Previous convergence proofs for BCPCS were limited to unity relaxation parameters (λ=1).

Purpose of the Study:

• To extend the convergence proof of the BCPCS method to include underrelaxation parameters (λ∈(0,1)).
• To derive the convergence of related algorithms, BCAVCS and BDROPCS, under similar conditions.

Main Methods:

• Mathematical analysis to prove convergence of the BCPCS algorithm with underrelaxation.
• Derivation of convergence conditions for BCAVCS and BDROPCS algorithms using underrelaxation parameters.

Main Results:

• Convergence of the BCPCS method is proven for underrelaxation parameters λ∈(0,1).
• Convergence for BCAVCS and BDROPCS algorithms is established under specific conditions with underrelaxation.

Conclusions:

• The study successfully extends the theoretical convergence of BCPCS and related algorithms to underrelaxation parameters.
• Experimental results validate the demonstrated convergence behavior for various parameter choices.