Matrix analysis
A Geometric Approach to Shape from Defocus
IEEE Transactions on Pattern Analysis and Machine Intelligence
A Fast Iterative Shrinkage-Thresholding Algorithm for Linear Inverse Problems
SIAM Journal on Imaging Sciences
A Fast Iterative Shrinkage-Thresholding Algorithm for Linear Inverse Problems
SIAM Journal on Imaging Sciences
Accurate and efficient method for smoothly space-variant Gaussian blurring
IEEE Transactions on Image Processing
Richardson-Lucy Deblurring for Scenes under a Projective Motion Path
IEEE Transactions on Pattern Analysis and Machine Intelligence
Wavelets and filter banks: theory and design
IEEE Transactions on Signal Processing
IEEE Transactions on Image Processing
IEEE Transactions on Image Processing
A Generalized Accelerated Proximal Gradient Approach for Total-Variation-Based Image Restoration
IEEE Transactions on Image Processing
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Nonuniform blurring is general for image degradation. Either defocus, camera shaking, or motion would result in nonuniform blurring. However, most current image restoration algorithms were developed for restoration from image blurred with one single space-invariant convolution kernel. The computational inefficiency would be significant if we directly extend these algorithms for restoration of nonuniform blurred image. In this paper, we propose a novel fast restoration algorithm for restoration of nonuniform blurred images. In our method, we first model nonuniform blurring as a space-variant weighted summation of images blurred by a group of basis filters, and use principal component analysis (PCA) to obtain the basis filters in advance. Then, based on the total variation (TV) based model, we adapt the generalized accelerated proximal gradient (GAPG) algorithm for image restoration. Experimental results indicate that the proposed method can dramatically improve the computational efficiency while achieving satisfactory restoration performance.