Handling Noise and Outliers in Single Image Deblurring using L0 Sparsity

Camera shake during exposure leads to image blur and poses an important problem in digital photography. Blind deconvolution recovers the sharp original image from a blurred image. MAP has been the most widely used deconvolution field but naive MAP methods mostly tends to favour no-blur solution. An intermediate representation of the image called unnatural representation has been found to the main reason for success of existing MAP based methods. This paper presents a new blind deconvolution algorithm based on L0 sparsity for single image motion deblurring, which is robust to the presence of noise. Directional filtering is used for noise handling process owing to the fact that it does not interfere with blur of the image affecting the kernel estimation process adversely. Also, a non-blind deconvolution step with explicit outlier handling is incorporated in final image restoration step which ensures that the image is devoid of ringing artifacts and handles other non-linearities. This presents an efficient optimization problem which requires only a few iterations solve and provides very good visual quality images with no ringing artifacts despite the presence of noise. The results are comparable to state-of-the-art methods dealing with images affected with only blur while being robust to noise unlike state-of-the-art methods.