| This dissertation addresses the use of the “Constant Modulus” (CM) or “Dispersion Cost” in blind gray-scale image deconvolution. The method is essentially a Two-Dimensional (2-D) version of the Constant Modulus Algorithm (CMA) that is well known in the field of communications for blind equalization. The resulting method, which is called “Blind Image Deconvolution Via Dispersion Minimization”, is computationally simple, applicable to minimum or mixed phase blurs, and requires fewer assumptions on both the true image and the Point Spread Function (PSF). A drawback of the method is that it is most applicable to six or less-bit images.; First, the CM cost is minimized through the use of an adaptive 2-D Finite Impulse Response (FIR) filter and the resulting method is shown to be useful in the deblurring images. Second, the behavior of the algorithm is examined by considering its both static and dynamic convergence analysis. A remarkable observation from the convergence analysis is that given a step-size for the adaptive algorithm and a blur, there is an optimum support for the adaptive FIR filter. Finally, the CM cost is minimized by using an adaptive 2-D Autoregressive (AR) filter, which has several advantages over the use of an adaptive FIR filter. The limitation of the AR case is the presence of regressor filtering, which makes implementation costly and analysis difficult. A simplified algorithm that bypasses regressor filtering is proposed and used in simulations. For a binary image, a sufficient condition on the PSF is obtained such that the simplified algorithm is locally stable to a desired solution. Theoretical results are supported with extensive computer simulations. |
