Iterative Identification and Restoration of Images

1 The Image Identification and Restoration Problem.- 1.1 Introduction.- 1.2 Restoration Methods.- 1.3 Identification Methods.- 1.4 Scope of the Monograph.- 2 Image Formation Models.- 2.1 Blur Models.- 2.2 Image Models.- 2.3 Common Point-spread Functions.- 3 Regularized Image Restoration.- 3.1 Ill-Conditionedness of the Image Restoration Problem.- 3.2 Stochastic Restoration.- 3.3 Algebraic Restoration.- 3.4Multiple Constraints Restoration.- 4 Iterative Image Restoration.- 4.1 VanCittert’s Iteration.- 4.2 Regularization via Truncated Iterations.- 4.3 Iterative Tikhonov-Miller Solution.- 4.4 Implementations with Faster Convergence.- 5 Image Restoration with Ringing Reduction.- 5.1 Analysis of Ringing Artifacts.- 5.2 Constrained Adaptive Iterative Restoration.- 5.3 Conjugate Gradients-based Implementation.- 5.4 Experimental Restoration Results.- 6 Maximum Likelihood Image Identification.- 6.1 Conventional Identification Methods.- 6.2 Maximum Likelihood Estimator.- 6.3Implementations for Noiseless Data.- 6.4Implementations for Noisy Data.- 7 Imáge Identification Using the EM-Algorithm.- 7.1 Review of the EM-Algorithm.- 7.2 EM-Algorithm Applied to Image Identification.- 7.3 The E-step of the Algorithm.- 7.4 The M-step of the Algorithm.- 7.5 Experimental Results.- 8 Methods for Improved Image Identification.- 8.1 Parametric Image Identification.- 8.2 Experimental Results Using Parametric Models.- 8.3 Hierarchical Image Identification.- 8.4 Experimental Results Using the Hierarchical Method.- A Eigenvalue Analysis for 2-D Systems.- B Properties of the Iteration (5.21).- C Derivation of Equation (7.14).