Biconjugate gradient stabilized method in image deconvolution of a wavefront coding system

The point spread function (PSF) is a non-rotational symmetric for the wavefront coding (WFC) system with a cubic phase mask (CPM). Antireflective boundary conditions (BCs) are used to eliminate the ringing effect on the border and vibration on the edge of the image. The Kronecker product approximation is used to reduce the computation consumption. The image-formation process of the WFC system is transformed into a matrix equation. In order to save storage space, biconjugate gradient (Bi-CG) and biconjugate gradient stabilized (Bi-CGSTAB) methods are used to solve the asymmetric matrix equation, which is a typical iteration algorithm of the Krylov subspace using the two-side Lanczos process. Simulation and experimental results illustrate the efficiency of the proposed algorithm for the image deconvolution. The result based on the Bi-CGSTAB method is smoother than the classic Wiener filter, while preserving more details than the Truncated Singular Value Decomposition (TSVD) method.

► This paper analyses the iteration algorithm based on the biconjugate gradient stabilized method (Bi-CGSTAB).
► The antireflective boundary conditions (BCs) is introduced to make up the blurring operator.
► The Kronecker product approximation is analyzed to reduce the computation consumption.
► The classic Wiener filter and TSVD method are analyzed for the image restoration.