ece542-8 - ECE 542-8 Digital Image Processing 5- Image...

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1 ECE 542-8 Digital Image Processing 5- Image Restoration II Dr. Z. Aliyazicioglu Cal Poly Pomona Electrical & Computer Engineering 1 Cal Poly Pomona Electrical & Computer Engineering Office 9-143 Periodic Noise reduction by Frequency Domain Filtering Bandreject Filters: An ideal bandreject filter is where D(u,v) is the distance from the origin of centered frequency rectangle 0 00 0 1i f ( ,) 2 (,) 0 i f 22 2 W Duv D WW Huv D D W D    ECE542 - 8 2 Cal Poly Pomona origin of centered frequency rectangle, W is the width of the band, and D 0 is the radial center
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2 Periodic Noise reduction by Frequency Domain Filtering Bandreject Filters: A Butterworth bandreject filter of the order n A Gaussian bandreject filter 2 22 0 1 (,) 1 n Huv DuvW Duv D    ECE542 - 8 3 Cal Poly Pomona 2 0 1 2( , ) (,) 1 Du vD e  Example a) Image heavily corrupted by sinusoidal noise of various frequencies b) Spectrum of (a), the components lie on an approximate circle about origin c) Butterworth bandreject filter of ECE542 - 8 4 Cal Poly Pomona bandreject filter of order 4 d) Result of filter
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3 Periodic Noise reduction by Frequency Domain Filtering Bandpass filter A bandpass filter performs the opposite operation of a bandreject filter bandreject filter Therefore, an ideal bandpass filter is (,) 1 (,) bp br Hu v v  0 00 0i f ( ,) 2 1 i f 22 W Duv D WW Huv D D  ECE542 - 8 5 Cal Poly Pomona You can find expressions of Butterworth and Gaussian Bandpass filter 0 2 W D  Example: Image heavily corrupted by sinusoidal noise of various frequencies Spectrum of (a), the components lie on an approximate circle about origin ECE542 - 8 6 Cal Poly Pomona Butterworth bandpass filter of order 4 Result of the filter
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4 Periodic Noise reduction by Frequency Domain Filtering Notch Filter A notch filter rejects (or passes) frequencies in predefined neighborhood about a center frequency . 3-D plots of Ideal, Butterworth, and Gaussian notch (reject) filter They appear in symmetric ECE542 - 8 7 Cal Poly Pomona pairs about the origin Periodic Noise reduction by Frequency Domain Filtering Ideal notch reject filter The transfer function of an ideal notch reject filter of radius D 0 with center at (u 0 ,v 0 ) and, by symmetry, at (-u 0 ,-v 0 ), is Where 10 20 0i f ( ,) o r ( (,) 1 otherwise D u vD D u vD Huv  1/ 2 MN  Assume that the center of ECE542 - 8 8 Cal Poly Pomona 22 0 ( ) ( ) Duv u u v v    1/ 2 0 ( ) u u v v frequency rectangular has been shifted to the point (M/2,N/2)
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5 Periodic Noise reduction by Frequency Domain Filtering Notch Filter A Butterworth notch reject filter
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This note was uploaded on 10/24/2010 for the course ECE 542 taught by Professor Zeki during the Spring '10 term at Cal Poly Pomona.

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ece542-8 - ECE 542-8 Digital Image Processing 5- Image...

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