Fast Deconvolution for Motion Blur Along the Blurring Paths

In this paper, we propose a deconvolution method which removes the motion blur along the blurring paths. The 2-D blurred image is transformed into 1-D horizontal blurred vectors along the blurring paths. Hence, the deconvolution of stacked horizontal blurred vectors is implemented in an iterative deconvolution process by a 1-D image restoration method that saves computation time. The deconvolution process is usually implemented in the frequency domain by fast Fourier transform (FFT). The computation time of FFT used in the 1-D image restoration method for the blurred vectors is about two-fifths of that of 2-D FFT used in the common image restoration method. To get stacked horizontal blurred vectors, we first incorporate orthogonal Chebyshev polynomial into the proposed method to extract pixels along the blurring paths. Then, we expand horizontal blurred vectors smoothly to reduce boundary artifacts. At last, we add a nonquadratic regularization term to the Richardson-Lucy algorithm, which adaptively penalizes the image gradients, to avoid oversmoothing of details. Experimental results for real motion-blurred images demonstrate that our approach runs much faster than the 2-D deblurring algorithm, while achieving as high restoration accuracy and visual perception as the 2-D deconvolution algorithm.