ECE/OPTI533 Digital Image Processing class notes 238 Dr. Robert A. Schowengerdt 2003IMAGE NOISE I• APPLICATIONS• Signal estimation in presence of noise• Detecting known features in a noisy background• Coherent (periodic) noise removalECE/OPTI533 Digital Image Processing class notes 239 Dr. Robert A. Schowengerdt 2003IMAGE NOISE ITYPES 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 bandingECE/OPTI533 Digital Image Processing class notes 240 Dr. Robert A. Schowengerdt 2003IMAGE NOISE IPhotoelectronic noise• Photon noisePhoton arrival statisticsLow-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 noiseElectronicWhite (flat power spectrum), Gaussian distributed, zero-mean (signal-independent)ECE/OPTI533 Digital Image Processing class notes 241 Dr. Robert A. Schowengerdt 2003IMAGE NOISE I• Photoelectronic noise modelPhoton noise is signal-dependentThermal noise is signal-independentOne 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 signalsfηm n,( )fηm n,( ) ηPm n,( ) fsm n,( ) ηTm n,( )+=ηPm n,( )ηTm n,( )fsm n,( )ηPm n,( )ECE/OPTI533 Digital Image Processing class notes 242 Dr. Robert A. Schowengerdt 2003IMAGE NOISE I• Noisy image modeladditive signal-dependent and signal-independent random noise• Note, this model may not apply in particular situations!f m n,( ) fsm n,( ) fηm n,( )+ fsm n,( ) ηPm n,( ) fsm n,( ) ηTm n,( )+ += =ECE/OPTI533 Digital Image Processing class notes 243 Dr. Robert A. Schowengerdt 2003IMAGE NOISE IExamples of simulated thermal noise for different noise standard deviations ση 10205ECE/OPTI533 Digital Image Processing class notes 244 Dr. Robert A. Schowengerdt 2003IMAGE NOISE IExamples of simulated photon + thermal noise for different standard deviations ση 10205ECE/OPTI533 Digital Image Processing class notes 245 Dr. Robert A. Schowengerdt 2003IMAGE 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 lostpepper noise (0.05% and 2%)ECE/OPTI533 Digital Image Processing class notes 246 Dr. Robert A. Schowengerdt 2003IMAGE NOISE ILine dropECE/OPTI533 Digital Image Processing class notes 247 Dr. Robert A. Schowengerdt 2003IMAGE NOISE ISTRUCTURED NOISEPeriodic, stationary• Noise has fixed amplitude, frequency and phase• Commonly caused by interference between electronic componentssimulation exampleECE/OPTI533 Digital Image Processing class notes 248 Dr. Robert A. Schowengerdt 2003IMAGE NOISE IMars Mariner example - multiple frequencies (Rindfleish et al, 1971)ECE/OPTI533 Digital Image Processing class notes 249 Dr. Robert A. Schowengerdt 2003IMAGE NOISE IPeriodic, nonstationary• noise parameters (amplitude, frequency, phase) vary across the image• Intermittant interference between electronic componentssimulation exampleECE/OPTI533 Digital Image Processing class notes 250 Dr. Robert A. Schowengerdt 2003IMAGE 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 2003IMAGE NOISE IAperiodic• JPEG noiseJPEG-compressed (low quality)difference (noise)ECE/OPTI533 Digital Image Processing class notes 252 Dr. Robert A. Schowengerdt 2003IMAGE NOISE I• ADPCM (Adaptive Pulse Code Modulation) noise• IKONOS 1-m panchromatic imagery• Kodak proprietary compression algorithm lake in Reid Park, TucsonDN 200-220 contrast-stretchedECE/OPTI533 Digital Image Processing class notes 253 Dr. Robert A. Schowengerdt 2003IMAGE NOISE IDetector Striping• Calibration differences among individual scanning detectors • For detector i: where E is the scanned optical imagedetector12.iN12..i.Nscan direction reversesscan jN detectors/scanDNigainiE offseti+=example with 4 detectorsECE/OPTI533 Digital Image Processing class notes 254