Fast Algorithms For Image Restoration Under Two Kinds Of Boundary Conditions

The research of ill-posed problems in image processing is a hot topic in the field of image processing and computer vision.It is widely used in many fields such as science,engineering calculation and life.Image restoration is an important branch of image processing,and its purpose is to improve a given imageNoschese et al.proposed a new modified truncated singular value decompo-sition method for the ill-posed problem of small dimension.In this paper,we use the truncation idea proposed by Noschese et al.to improve a new Tikhonov regu-larization method recently proposed by Fuhry et al.We obtain two more effective regularization methods.Furthermore,we apply the corresponding two regulariza-tion methods to the periodic side,respectively.In the problem of image restoration under boundary conditions and anti-reflective boundary conditions,especially the application of FFT algorithm to periodic boundary conditions and fast sinusoidal transform(FST)algorithm to anti-reflective boundary conditions are discussed.The feasibility and effectiveness of the proposed method are verified theoretically and ex-perimentally.