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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
Google Image Search -- monkey
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