Abstract: Aiming at the problem that traditional image restoration algorithms were difficult to derive convergent splitting results when antiHermitian components dominated Hermitian components, which led to poor image restoration effect， the author proposed an image restoration algorithm based on displacement Hermitian splitting. Firstly, displacement parameter was introduced to define quasiHermitian splitting when matrix was split. Secondly, the splitting result was substituted by conjugate gradient normal residual (CGNR) algorithm for inner iteration to approximate each outer iteration, and each outer iteration was derived from the convergent splitting of coefficient matrix. Thirdly, the derived convergence splitting 
results were applied to the image restoration model. Finally, the algorithm was compared with the generalized minimum error method and the generalized preconditioned symmetric splitting method. The experimental results show that the iterative approximation results obtained by the proposed algorithm are better, the number of iterations and CPU time required are significantly reduced, the CPU occupancy time is only 0.25 s, and the image restoration effect is better.

Key words: Hermitian component, image restoration, conjugate gradient normal residual (CGNR) algorithm, coefficient matrix, convergent splitting