# image processing - ch 05 - image restorationbarner/courses/eleg675/image processing...1 image...

Post on 28-Apr-2018

231 views

Embed Size (px)

TRANSCRIPT

1

Image Restoration

Image Processing with Biomedical Applications

ELEG-475/675Prof. Barner

Image ProcessingImage Restoration

Prof. Barner, ECE Department, University of Delaware 2

Image Restoration

Image enhancement is subjective Heuristic and ad hoc

Image restoration is more theoretically motivated

A priori knowledge of image degradation utilizedOptimality criteria used to formulate restoration

Image ProcessingImage Restoration

Prof. Barner, ECE Department, University of Delaware 3

Preliminaries:Correlation and Power Spectrum

Note self-convolution

Correlation results if we do not reflect one term

Note maximum at =0; also

Power Spectral Density (PSD)

Cross correlation and PSD

Assume ergotic signals (RVs) interchange time/ensemble averages, e.g.,

( ) ( ) ( ) ( )f t f t f t f t dt

=

( ) ( ) ( ) ( ) ( )fR f t f t f t f t dt

= = +

2

( ) ( )fR d f t dt

=

{ } { } 2( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) | ( ) |f fP s R f t f t F s F s F s F s F s = = = = =

( ) ( ) ( ) ( ) ( )fgR f t g t f t g t dt

= = +

( ) { ( )}fg fgP s R =

{ ( )} ( )x t x t dt

=

Image ProcessingImage Restoration

Prof. Barner, ECE Department, University of Delaware 4

Degradation and Restoration Model

Degradation is taken to be a linear spatially invariant operator

( , ) ( , ) ( , ) ( , )g x y h x y f x y x y= +

( , ) ( , ) ( , ) ( , )G u v H u v F u v N u v= +

2

Image ProcessingImage Restoration

Prof. Barner, ECE Department, University of Delaware 5

Noise Properties

Arises in acquisition, digitization, and transmission/storage processesCCD cameras are affected by:

Light levelsSensor temperatureBad sensors

Transmission noise can be due to interferenceWireless transmission interferenceLost networking packets

Statistics depend on sourceCommon assumption: White Spectrum

Correlation: R()=A()Power spectrum: P(s)=A

Image ProcessingImage Restoration

Prof. Barner, ECE Department, University of Delaware 6

Noise Probability Density Functions

Gaussian (normal) PDF

Typically models electronics and sensor noiseRayleigh PDF

Skewed distribution typically models range imaging noise

2 2( ) / 21( )2

zp z e

=

2( ) /2 ( ) for

0 for ( )

z a bz a e z ab

z ap z