An Adaptively Accelerated Lucy-Richardson Method for Image Deblurring

Abstract

We present an adaptively accelerated Lucy-Richardson (AALR) method for the restoration of an image from its blurred and noisy version. The conventional Lucy-Richardson (LR) method is nonlinear and therefore its convergence is very slow. We present a novel method to accelerate the existing LR method by using an exponent on the correction ratio of LR. This exponent is computed adaptively in each iteration, using first-order derivatives of the deblurred image from previous two iterations. Upon using this exponent, the AALR improves speed at the first stages and ensures stability at later stages of iteration. An expression for the estimation of the acceleration step size in AALR method is derived. The superresolution and noise amplification characteristics of the proposed method are investigated analytically. Our proposed AALR method shows better results in terms of low root mean square error (RMSE) and higher signal-to-noise ratio (SNR), in approximately 43% fewer iterations than those required for LR method. Moreover, AALR method followed by wavelet-domain denoising yields a better result than the recently published state-of-the-art methods.

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