Blind multi-Poissonian image deconvolution with sparse log-step gradient prior.

Blind image deconvolution plays a very important role in the fields such as astronomical observation and fluorescence microscopy imaging, in which the noise follows Poisson distribution. However, due to the ill-posedness, it is a very challenging task to reach a satisfactory result from a single blurred image especially when the power of the Poisson noise is at a high level. Therefore, in this paper, we try to achieve high-quality restoration results with multi-blurred images which are contaminated by Poisson noise. Firstly, we design a novel sparse log-step gradient prior which adopts a mixture of logarithm and step functions to regularize the image gradients and combine it with the Poisson distribution to formulate the blind multi-image deconvolution problem. Secondly, we incorporate the methods of variable splitting and Lagrange multiplier to convert the original problem into sub-problems, then we alternately solve them to achieve the estimation of all the blur kernels of corresponding blurred images. Besides, we also design a non-blind multi-image deconvolution algorithm which is based on the log-step gradient prior to reach the final restored image. Experimental results on both synthetic and real-world blurred images show that the proposed prior is very capable of suppressing negative artifacts caused by ill-posedness. The algorithm can achieve restored image of very high quality which is competitive with some state-of-the-art methods.