image noise ii - university of arizona

ECE/OPTI533 Digital Image Processing class notes 256 Dr. Robert A. Schowengerdt 2003

IMAGE NOISE IIPHOTOELECTRONIC NOISE

• Frame averaging

If available, average N frames of same object

If noise is independent frame-to-frame, variance will be reduced by

Requires multiple, co-registered frames

What will happen if the frames are not co-registered?

ση2 N⁄


IMAGE NOISE IIsimulation example of frame averaging

N = 1σbackground = 19.86

σbackground = 13.98N = 2




IMAGE NOISE II• Low-pass smoothing

Reduces high-frequency noise

Smooths image

Set filter cutoff at about ρc ρc SNR 1==

10-4

10-3

10-2

10-1

100

101

102

103

0 0.1 0.2 0.3 0.4 0.5

frequency domain profile - noise image

poweramplitude

pow

er o

r am

plit

ude

spatial frequency (cycles/pixel)


IMAGE NOISE IIideal low-pass filtered examples

ρc = 0.2

ρc = 0.1


IMAGE NOISE II• Sigma filter

Average selected pixels within moving window

Average only those pixels that are within a threshold difference ∆ from the DN of the center pixel, DNc

One type of “edge-preserving smoothing” algorithm

DNc ∆±


IMAGE NOISE IIsigma filter near edges and lines

c

c

edge feature

5 x 5 window:

row m, column n

row m, column n+1

c

c

crow m, column n+2

line feature

only the green

pixels are

averaged for

the output

pixel c


IMAGE NOISE II• Nagao-Matsuyama filter

Calculate the variance of 9 subwindows within a 5 x 5 moving window

Output pixel is the mean of the subwindow with the lowest variance

The nine subwindows used in the Nagao-Matsuyama filter

c

c c c c

c c cc


IMAGE NOISE IIExample of SAR (Synthetic Aperture Radar) noise filtering

original 5 x 5 LPF


IMAGE NOISE II

original 5 x 5 sigma (k=2)


IMAGE NOISE II

original Nagao-Matsuyama


IMAGE NOISE IIImpulse Noise

• Salt and pepper noise DN is “outlier” relative to neighboring pixel DNs

• Use algorithms that compare test pixel to neighbors


IMAGE NOISE II• Noise cleaning

Set threshold ∆ = kσglobal

Noise Cleaning (pixels)

• DNneighbors = average DN (8-neighbors)

• If ,

• If ,

DN test DNneighbors– ∆> DN test DNneighbors=

DN test DNneighbors– ∆≤ DN test DN test=

Noise Cleaning (lines)

• DNneighbors = average DN (2-neighbors above and below)

• If ,

• If ,

DN test DNneighbors– ∆> DN test DNneighbors=

DN test DNneighbors– ∆≤ DN test DN test=


IMAGE NOISE II• Median filtering

Example of rank filtering

Output DN = median(DNwindow)

• Length of window must be odd

• Sort input DNs within window and select middle DN for output

median filter preserves 1-D edges

-5

0

5

10

15

-8 -6 -4 -2 0 2 4 6 8

input signal

1x3 median

amplit

ude

index

-5

0

5

10

15

-8 -6 -4 -2 0 2 4 6 8

input signal

1x3 LPF

amplit

ude

index


IMAGE NOISE IImedian filter removes impulse noise

-2

0

2

4

6

8

10

12

-8 -6 -4 -2 0 2 4 6 8

input signal

1x5 LPF

amplit

ude

index

-2

0

2

4

6

8

10

12

-8 -6 -4 -2 0 2 4 6 8

input signal

1x5 median

amplit

ude

index

median filter window length should be at least 2 x width impulse noise

-2

0

2

4

6

8

10

12

-8 -6 -4 -2 0 2 4 6 8

input signal

1x3 median

amplit

ude

index


IMAGE NOISE II“separable” 2-D median filter preserves 2-D edges

n

m

n

m

3 x 3 2-D median filter

n

m

3 x 3 2-D separable median filter

1 x 3 median filter along m, then 3 x 1 median filter along n


IMAGE NOISE IIexample bad line removal with median filter (Schowengerdt, 1997)

single noisy partial scanline(Landsat MSS)

after 3 x 1 median filter


IMAGE NOISE IIexample line drop removal

3 x 1 median filter

difference


IMAGE NOISE IIMedian filter doesn’t work as well on photoelectronic noise

3 x 3 median filter

Why isn’t median filter effective for this type of noise?


IMAGE NOISE IISTRUCTURED NOISE

Periodic, stationary

• Periodicity means noise power is isolated into a few frequencies

• Difficulty is in detecting noise power “spikes”

• Visual detection works, but not practical for processing large number of images

Automated periodic, sta-tionary noise removal

• Apply “soft” (Gaussian) high-pass filter to noisy image to remove image components

• Threshold HPF-filtered spectrum to isolate noise frequency components

• Convert thresholded spectrum to 0 (noise) and 1 (non-noise) to create noise amplitude “notch” filter

• Apply filter to noisy image


IMAGE NOISE IIexample Mariner 6 image (Rindfleish et al, 1971)

noisy image power spectrum

noise spikes

noise pattern

filtered image


IMAGE NOISE IIexample automated periodic noise removal (Schowengerdt, 1997)

noise spikes

zeros in filter

high-pass filtered noisy image

notch-filtered image

notch filter

power spectrum


IMAGE NOISE II

• Not really automated filter design

Two parameters must be supplied:

• width of Gaussian HPF

• power spectrum threshold for notch filter

image noise ii - university of arizona

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