Box-constrained penalized likelihood image restoration

Abstract: 

Image restoration is a computationally intensive problem as a large number of pixel values have to be determined. Since the pixel values of digital images can attain only a finite number of values (e.g. 8-bit images can have only 256 gray levels), one would like to recover an image within some dynamic range. This leads to the imposition of box constraints on the pixel values. The traditional gradient projection methods for constrained optimization can be used to impose box constraints, but they may suffer from either slow convergence or repeated searching for active sets in each iteration. In this talk, we discuss a multiplicative iterative algorithm for box-constrained image restoration. This algorithm just requires pixel-wise updates in each iteration, and there is no need to invert any matrices. We apply this algorithm to TV image restoration problems where the observed blurry images contain Poisson, Gaussian or salt-and-pepper noises.