Generalized multichannel image deconvolution approach and its applications

Abstract

The validity of a multichannel deconvolution technique where both within and between channel relations are used was demonstrated using stochastic and deterministic deconvolution filters. In either case, prior knowledge about the original image and the noise is required. A generalized regularized multichannel image deconvolution approach is proposed in which no prior knowledge of the variance of the noise at each channel or a bound on the high-frequency energy of the image are assumed. This information instead is estimated iteratively, resulting also in the estimation of the regularization parameters, based on the partially deconvolved image at each iteration step. The multichannel smoothing functional to be minimized is formulated to have a global minimizer with the proper choice of the multichannel regularization functionals. With this algorithm, the regularization functional for each channel is determined by incorporating not only within-channel information but also cross-channel information. The proposed multichannel smoothing functional is shown to be convex, and therefore, has a global minimizer. The algorithm not only does not depend on initial conditions but is also shown to be much more computationally efficient than existing algorithms. The validity and efficiency of the approach is demonstrated by applying it to color image restoration, the wavelet-based image deconvolution, and the reconstruction of the higher resolution image.