Image Noise I

IMAGE NOISE I

• APPLICATIONS

• Signal estimation in presence of noise

• Detecting known features in a noisy background

• Coherent (periodic) noise removal

ECE/OPTI533 Digital Image Processing class notes 238 Dr. Robert A. Schowengerdt 2003 IMAGE NOISE I

TYPES OF NOISE

• photoelectronic

• photon noise

• thermal noise • impulse

• salt noise

• pepper noise

• salt and pepper noise

• line drop • structured

• periodic, stationary

• periodic, nonstationary

• aperiodic

• detector striping

• detector banding

ECE/OPTI533 Digital Image Processing class notes 239 Dr. Robert A. Schowengerdt 2003 IMAGE NOISE I

Photoelectronic noise

• Photon noise

Photon arrival statistics

Low-light levels (nightime imaging, astronomy)

• Poisson density function

• Standard deviation = square root mean (signal-dependent)

High-light levels (daytime imaging)

• Poisson distribution —> Gaussian distribution

• Standard deviation = square root mean • Thermal noise

Electronic

White (flat power spectrum), Gaussian distributed, zero-mean (signal-independent)

ECE/OPTI533 Digital Image Processing class notes 240 Dr. Robert A. Schowengerdt 2003 IMAGE NOISE I • Photoelectronic noise model

Photon noise is signal-dependent

Thermal noise is signal-independent

One model for a combined noise field fh (m, n) is:

fh (m, n) = h P(m, n) fs(m, n) + h T(m, n)

where

h P(m, n) and h T(m, n) are independent white, zero-mean Gaussian noise fields

fs(m, n) is the noiseless signal (may not be measurable)

Note, h P(m, n) has unit standard deviation and is scaled by square root of signal

• Approximates photon noise component for large signals

ECE/OPTI533 Digital Image Processing class notes 241 Dr. Robert A. Schowengerdt 2003 IMAGE NOISE I • Noisy image model

f(m, n) = fs(m, n) + fh (m, n) = fs(m, n) + h P(m, n) fs(m, n) + h T(m, n)

additive signal-dependent and signal-independent random noise

• Note, this model may not apply in particular situations!

ECE/OPTI533 Digital Image Processing class notes 242 Dr. Robert A. Schowengerdt 2003 IMAGE NOISE I Examples of simulated thermal noise for different noise standard deviations s h

20 10

ECE/OPTI533 Digital Image Processing class notes 243 Dr. Robert A. Schowengerdt 2003 IMAGE NOISE I Examples of simulated photon + thermal noise for different standard deviations s h

10 20

ECE/OPTI533 Digital Image Processing class notes 244 Dr. Robert A. Schowengerdt 2003 IMAGE NOISE I IMPULSE NOISE pepper noise (0.05% and 2%)

• Data loss or saturation

• Definitions

• Salt noise: DN = maximum possible

• Pepper noise: DN = minimum possible

• Salt and pepper noise: mixture of salt and pepper noise

• Line drop: part or all of a line lost

ECE/OPTI533 Digital Image Processing class notes 245 Dr. Robert A. Schowengerdt 2003 IMAGE NOISE I

Line drop

ECE/OPTI533 Digital Image Processing class notes 246 Dr. Robert A. Schowengerdt 2003 IMAGE NOISE I STRUCTURED NOISE simulation example

Periodic, stationary

• Noise has fixed amplitude, frequency and phase

• Commonly caused by interference between electronic components

ECE/OPTI533 Digital Image Processing class notes 247 Dr. Robert A. Schowengerdt 2003 IMAGE NOISE I Mars Mariner example - multiple frequencies (Rindfleish et al, 1971)

ECE/OPTI533 Digital Image Processing class notes 248 Dr. Robert A. Schowengerdt 2003 IMAGE NOISE I Periodic, nonstationary

• noise parameters (amplitude, frequency, phase) vary across the image

• Intermittant interference between electronic components simulation example

ECE/OPTI533 Digital Image Processing class notes 249 Dr. Robert A. Schowengerdt 2003 IMAGE NOISE I

Mars Mariner 9 example - single frequency, variable amplitude (Chavez and Soderblum, 1975)

ECE/OPTI533 Digital Image Processing class notes 250 Dr. Robert A. Schowengerdt 2003 IMAGE NOISE I Aperiodic

• JPEG noise

JPEG-compressed (low quality)

difference (noise)

ECE/OPTI533 Digital Image Processing class notes 251 Dr. Robert A. Schowengerdt 2003 IMAGE NOISE I • ADPCM (Adaptive Pulse Code Modulation) noise

• IKONOS 1-m panchromatic imagery

• Kodak proprietary compression algorithm

lake in Reid Park, Tucson DN 200-220 contrast-stretched

ECE/OPTI533 Digital Image Processing class notes 252 Dr. Robert A. Schowengerdt 2003 IMAGE NOISE I Detector Striping example with 4 detectors

• Calibration differences among individual scanning detectors

detector 1 2 . scan j i . N detectors/ N scan 1 2 . i scan direction . reverses N

• For detector i:

DNi = gainiE + offseti

where E is the scanned optical image

ECE/OPTI533 Digital Image Processing class notes 253 Dr. Robert A. Schowengerdt 2003 IMAGE NOISE I Detector Banding

• Calibration changes from scan-to-scan (whiskbroom scanner)

detector 1 2 . scan j i . N detectors/scan N 1 2 . scan direction i reverses . N

• For detector i, scan j:

DNij = gainj(gainiE + offseti) + offsetj

where E is the scanned optical image irradiance (W-m-2)

• Changes in gainj or offsetj from scan-to-scan can be caused by detector saturation at one end of scan

ECE/OPTI533 Digital Image Processing class notes 254 Dr. Robert A. Schowengerdt 2003 IMAGE NOISE I

example Landsat Thematic Mapper (Schowengerdt, 1997) - 16 detectors/scan

original (San Francisco Bay) water mask

masked contrast- original stretched

ECE/OPTI533 Digital Image Processing class notes 255 Dr. Robert A. Schowengerdt 2003