Successful blind image deconvolution algorithms require the exact estimation of the Point Spread Function size, PSF. In the absence of any priori information about the imagery system and the true image, this estimation is normally done by trial and error experimentation, until an acceptable restored image quality is obtained. This paper, presents an exact estimation of the PSF size, for both noisy and noiseless images. It is based on evaluating the detail energy of the wave packet decomposition of the blurred image. The minimum detail energy occurs at the optimum PSF size. Having accurately estimated the PSF, the paper also proposes a fast double updating algorithm for improving the quality of the restored image, by the least squares minimization of a system of linear equations describing some peak error deviations derived from the blurred image. Extension to the noisy case has also been investigated. Simulation results of several examples are verified.

Successful blind image deconvolution algorithms require the exact estimation of the Point Spread Function size, PSF. In the absence of any priori information about the imagery system and the true image, this estimation is normally done by trial and error experimentation, until an acceptable restored image quality is obtained. This paper, presents an exact estimation of the PSF size, which yields the optimum restored image quality for both noisy and noiseless images. It is based on evaluating the detail energy of the wave packet decomposition of the blurred image. The minimum detail energies occur at the optimum PSF size. Having accurately estimated the PSF, the paper also proposes a fast double updating algorithm for improving the quality of the restored image. This is achieved by the least squares minimization of a system of linear equations that minimizes some error functions derived from the blurred image. Moreover, a technique is also proposed to improve the sharpness of the deconvolved images, by constrained maximization of some of the detail wavelet packet energies. Simulation results of several examples have verified that the proposed technique manages to yield a sharper image with higher PSNR than classical approaches.

Exponential B-spline functions are more flexible than cardinal B-spline polynomials due to the extra degrees of freedom inherited by the arbitrary choice of its parameters. In this paper, independent simple proofs of some of the important features of Exponential B-spline functions are given. A novel efficient technique has also been proposed for decomposing a signal in terms of its exponential B-spline expansion. Applications of Exponential B-spline functions in spatial image compression are demonstrated. Our illustrative results show that Exponential B-splines outperform cardinal B-splines in image compression.