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    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