Multiframe Image Restoration

Outline Introduction Mathematical Models The restoration Problem Nuisance Parameters and Blind Restoration Applications

Introduction Multiframe image restoration is concerned with the improvement of imagery acquired in the presence of varying degradations. In most situations digital data are acquired, and the restoration processing is carried out by a generator special-purpose digital computer.

The general idea of restoration processing

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Image Blur and Sampling System and environmental blur detector sampling

System and Environmental Blur f is blurred by the imaging system, and the observable signal is the continuous-domain intensity is formed through a convolution relationship with the image intensity:

System and Environmental Blur The point-spread function for diffraction is modeled by the space invariant function: the inner product operation

System and Environmental Blur Imaging systems often suffer from various types of optical aberrations -imperfections in the figure of the system’s focusing element (usually a mirror or lens). The point-spread function takes the form:

System and Environmental Blur e(u) is the aberration function An out-of-focus blur induces a quadratic aberration function: where r is the distance to the scene, d is the focal setting, and f is the focal length.

System and Environmental Blur Wave propagation through an inhomogeneous medium such as the Earth’s atmosphere can induce additional distortions. These distortions are due to temperature- induced variations in the atmosphere’s refractive index, and they are frequently modeled in a manner similar to that used for system aberrations:

Sampling The detection of imagery with discrete detector arrays results in the measurement of the (time-varying) sampled intensity:

Sampling A sequence of image frames is available for detection Each frame is recorded at the time t = t k, and the blur parameter takes the value 8k = 8, during the frame so that we write

Nosie Models Electromagnetic waves such as light interact with matter in a fundamentally random way Quantum electrodynamics (QED) is the most sophisticated theory available for describing the detection of electromagnetic radiation. Electromagnetic energy is transported according to the classical theory of wave propagation, and the field energy is quantized only during the detection process

Object Category Recognition the expected photocount for the nth detector during the k-th frame is: Read-out noise

The Restoration Problem The intensity function

Restoration as an Optimization Problem An optimization problem

Methods Maximum-Likelihood Estimation Gaussian Noise Poisson Noise

Methods Sieve-Constrained Maximum-Likelihood Estimation

Methods Penalized Maximum-Likelihood Estimation

Methods Maximum a Posteriori Estimation

Methods Regularized Least-Squares Estimation

Methods Minimum I-Divergence Estimation

Linear Methods Linear methods for solving multiframe restoration problems are usually derived as solutions to the regularized least-squares problem:

Linear Methods Linear methods for solving multiframe restoration problems are usually derived as solutions to the regularized least-squares problem:

Linear Methods C is called the regularizing operator

Linear Methods In matrix-vector notation, the regularized least- squares optimization problem can be reposed as with the minimun-norm solution satisfying: or

Nonlinear (Iterative) Methods General optimization problem:

Applications Fine-Resolution Imaging from Undersampled Image Sequences Ground-Based Imaging through Atmospheric Turbulence Ground-Based Solar Imaging I with Phase Diversity

Applications Fine-Resolution Imaging from Undersampled Image Sequences

Applications Ground-Based Imaging through Atmospheric Turbulence

Applications Ground-Based Solar Imaging I with Phase Diversity