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**Unformatted text preview: **Nonlinear Filtering for Noise Smoothing Frequency Domain Method for Noise Smoothing Example: Picture with lines on it. Can we get rid of lines? Think of the image as desired image + noise (lines). Consider working in transformed domain: take DTFT or DFT. Exploit separability of noise and image. EEE 508 1 Nonlinear Filtering for Noise Smoothing Consider DTFT of noise image: 2 d ( n 1 , n 2 )= d ( n 2 )1 D ( 1 , 2 )=2 ( 1 ) D ( 2 ) (1 ( constant along n 1 ) 1 - (1) DTFT of the desired image:- 1 - (2) EEE 508 2 Nonlinear Filtering for Noise Smoothing DTFT of original (noisy) image: 2 1 - (1)+(2) In the frequency domain, the signal and noise are separable - (approximately) null out noise component by removing dots in frequency domain, then take inverse transform the noise is gone or significantly reduced. EEE 508 3 Nonlinear Filtering for Noise Smoothing DTFT of filtered image: 2 1 - (1)+(2)- EEE 508 4 Edge Enhancement Motivation: Edges are very important for intelligibility, segmentation, analysis, and identification. Transform Compression 1. Root Filtering x ( n 1 n 2 ) l X ( K 1 , K 2 ) = Transform (such as DFT) 1 ; , , , 2 1 1 2 2 1 d d D D K K X K K X K K X 1 ; , 2 1 , 2 1 2 1 2 1 2 1 d d D T D K K j o e K K X Note : Since 0 D 1 | X ( K 1 , K 2 )| D = D root of magnitude of X ( K 1 , K 2 ). EEE 508 5 Edge Enhancement Observation : (about behavior) y = a y 0 < D < 1 y = a D a Effect of D-rooting: boosts low-amplitude components or coefficients and de-emphasizes highamplitude components or coefficients. EEE 508 6 Edge Enhancement For natural or common images, high-frequency components, which correspond to edges, tend to have low amplitudes, and low- frequency components tend to have high amplitudes. D rooting boosts highfrequency components which correspond to edges to edges....

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