Transcript System and Environmental Blur

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 temperatureinduced 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 leastsquares optimization problem can be reposed as
with the minimun-norm solution
or
satisfying:
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