Defocused Image Restoration with Local Polynomial Regression and IWF

Shooting a real world image with a camera through an optical device gives a 2-D image where at least some parts are affected by a blur and noise. Images can be blurred by atmospheric turbulence, relative motion between sensors and objects, longer exposures, and so on, but the exact cause of blurring may be unknown. Restoration of blurred noisy images (Spiros et al., 2009; 2010; Su et al., 2007) is one of the main topics in many processing. The literatures Alonso et al. (2008; 2005); Bar et al. (2006) have given good methods to improve image qualities. The purpose of image restoration is to reconstruct an unobservable true image from a degraded observation. An observed image can be written, ignoring additive noise, as the two-dimensional (2-D) convolution of the true image with a linear space-invariant (LSI) blur, known as the PSF. Restoration in the case of known blur, assuming the linear degradation model, is called linear image restoration and it has been presented extensively in the last three decades giving rise to a variety of solutions Chen et al. (2000); Suyash et al. (2006); Gu et al. (2009); Lu et al. (2009) . In many practical situations, however, the blur is unknown. Hence, both blur identification and image restoration must be performed from the degraded image. Restoration in the case of unknown blur is called blind image restoration Filip et al. (2003); Mario et al. (2003); Liao et al. (2005) . Existing blind restoration methods can be categorized into two main groups: (i) those which estimate the PSF a priori independent of the true image so as to use it later with one of the linear image restoration methods, such as zero sheet separation, generalized cross validation, and maximum likelihood and expectation maximization based on the ARMA image model Chang et al., (1991); Reeves et al. (1992); Lagendijk et al. (1990) , and (ii) those which estimate the PSF and the true image simultaneously, such as nonnegative sand support constraints recursive inverse filtering, maximum likelihood and conjugate gradient minimization, and simulated annealing Kundur et al. (1998); Katsaggelos et al. (1991) . Algorithms belonging to the first class are computationally simple, but they are limited to situations in which the PSF has a special form, and the true image has certain features. Algorithms belonging to the second class, which are computationally more complex, must be used for more general situations. In this paper, a kind of semi-blind image restoration algorithm is proposed in case of known the blur type (defocused blurring).