IMAGE NOISE I - University of Arizonadial/ece533/notes12.pdf · ECE/OPTI533 Digital Image...
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ECE/OPTI533 Digital Image Processing class notes 238 Dr. Robert A. Schowengerdt 2003
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 239 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 240 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 Ñ> 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 241 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 is:
where
and are independent white, zero-mean Gaussian noise fields
is the noiseless signal (may not be measurable)
Note, has unit standard deviation and is scaled by square root of signal
• Approximates photon noise component for large signals
fη m n,( )
fη m n,( ) ηP m n,( ) fs m n,( ) ηT m n,( )+=
ηP m n,( ) ηT m n,( )
fs m n,( )
ηP m n,( )
ECE/OPTI533 Digital Image Processing class notes 242 Dr. Robert A. Schowengerdt 2003
IMAGE NOISE I• Noisy image model
additive signal-dependent and signal-independent random noise
• Note, this model may not apply in particular situations!
f m n,( ) fs m n,( ) fη m n,( )+ fs m n,( ) ηP m n,( ) fs m n,( ) ηT m n,( )+ += =
ECE/OPTI533 Digital Image Processing class notes 243 Dr. Robert A. Schowengerdt 2003
IMAGE NOISE IExamples of simulated thermal noise for different noise standard deviations ση
1020
5
ECE/OPTI533 Digital Image Processing class notes 244 Dr. Robert A. Schowengerdt 2003
IMAGE NOISE IExamples of simulated photon + thermal noise for different standard deviations ση
10 20
5
ECE/OPTI533 Digital Image Processing class notes 245 Dr. Robert A. Schowengerdt 2003
IMAGE NOISE IIMPULSE NOISE
• 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
pepper noise (0.05% and 2%)
ECE/OPTI533 Digital Image Processing class notes 246 Dr. Robert A. Schowengerdt 2003
IMAGE NOISE I
Line drop
ECE/OPTI533 Digital Image Processing class notes 247 Dr. Robert A. Schowengerdt 2003
IMAGE NOISE ISTRUCTURED NOISE
Periodic, stationary
• Noise has fixed amplitude, frequency and phase
• Commonly caused by interference between electronic components
simulation example
ECE/OPTI533 Digital Image Processing class notes 248 Dr. Robert A. Schowengerdt 2003
IMAGE NOISE IMars Mariner example - multiple frequencies (Rindfleish et al, 1971)
ECE/OPTI533 Digital Image Processing class notes 249 Dr. Robert A. Schowengerdt 2003
IMAGE NOISE IPeriodic, nonstationary
• noise parameters (amplitude, frequency, phase) vary across the image
• Intermittant interference between electronic components
simulation example
ECE/OPTI533 Digital Image Processing class notes 250 Dr. Robert A. Schowengerdt 2003
IMAGE NOISE IMars Mariner 9 example - single frequency, variable amplitude (Chavez and Soderblum, 1975)
ECE/OPTI533 Digital Image Processing class notes 251 Dr. Robert A. Schowengerdt 2003
IMAGE NOISE IAperiodic
• JPEG noise
JPEG-compressed (low quality)
difference (noise)
ECE/OPTI533 Digital Image Processing class notes 252 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 253 Dr. Robert A. Schowengerdt 2003
IMAGE NOISE IDetector Striping
• Calibration differences among individual scanning detectors
• For detector i:
where E is the scanned optical image
detector 1
2.i
N12.
.
i.
N
scan direction reverses
scan j
N detectors/scan
DN i gain iE offset i+=
example with 4 detectors
ECE/OPTI533 Digital Image Processing class notes 254 Dr. Robert A. Schowengerdt 2003
IMAGE NOISE IDetector Banding
• Calibration changes from scan-to-scan (whiskbroom scanner)
• For detector i, scan j:
where E is the scanned optical image irradiance (W-m-2)
• Changes in or from scan-to-scan can be caused by detector saturation at one end of scan
detector 1
2.i
N12.
N detectors/scan.
i.
N
scan direction reverses
scan j
DN ij gain j gain iE offset i+( ) offset j+=
gain j offset j