Image NoiseDr. Robert A. Schowengerdt

Techniques for Image Processing and Classifications in Remote SensingRemote Sensing

By Ke Tang

APPLICATIONSSignal estimation in presence of noiseDetecting known features in a noisy backgroundCoherent (periodic) noise removal

TYPES OF NOISEPhotoelectronic

photon noisethermal noise

Impulsesalt noisepepper noisesalt and pepper noiseline drop

Structuredperiodic, stationaryperiodic, nonstationaryaperiodicdetector stripingdetector banding

Photonelectronic noisePhoton noise

Photon arrival statistics Low-light levels (nighttime imaging, astronomy)• Poisson density function• Standard deviation = (signal-dependent)High-light levels (daytime imaging)• Poisson distribution > Gaussian distribution• Standard deviation = square root mean

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

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Photoelectronic noise modelPhoton noise is signal-dependentThermal noise is signal-independentOne model for acombined noise field

are independent white, zero-mean Gaussian noise fieldsfs is the noiseless signal (may not be measurable)

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Noisy image model

additive signal-dependent and signal-independent random noise

Note, this model may not apply in particular situations!

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Examples of simulated thermal noise for different noise standard deviations

Examples of simulated photon + thermal noise for different standard deviations

Impulse NoiseData loss or saturationDefinitionsSalt noise:

DN = maximum possiblePepper noise:

DN = minimum possibleSalt and pepper noise:

mixture of salt and pepper noise

Line drop: part or all of a line lost

Structured NoisePeriodic, stationary

Noise has fixed amplitude, frequency and phase Commonly caused by interference between electronic components

Structured NoiseMars Mariner Example

Structured NoisePeriodic, nonstationary

noise parameters (amplitude, frequency, phase) vary across the imageIntermittent interference between electronic components

Structured NoiseMars Mariner 9 example

single frequency, variable amplitude (Chavez and Soderblum,1975)

Structured NoiseAperiodic

JPEG noiseADPCM (Adaptive Pulse Code Modulation) noise

Structured NoiseDetector StripingCalibration differences among individual scanning detectors

Structured NoiseDetector BandingCalibration changes from scan-to-scan (whiskbroom scanner)

Photoelectronic NoiseFrame averagingIf available, average N frames of same objectIf noise is independent frame-to-frame, variance will be reduced byRequires multiple, co-registered frames

N/2ησ

Simulation Example Of Frame Averaging

Low-pass Smoothing

Low-pass smoothingReduces high-frequency noiseSmooths imageSet filter cutoff at about SNR = 1

Sigma Filter

Average selected pixels within moving windowAverage only those pixels that are within a threshold difference ∆ from the DN of the center pixel, DNcDNc+∆

sigma filter near edges and lines

Nagao-Matsuyama filterCalculate the variance of 9 subwindows within a 5 x 5 moving windowOutput pixel is the mean of the subwindow with the lowest variance

Example of SAR (Synthetic Aperture Radar) Noise Filtering

Example of SAR Noise Filtering

Example of SAR Noise Filtering

Impulse Noise

Salt and pepper noise DN is “outlier” relative to neighboring pixel DNsUse algorithms that compare test pixel to neighbors

Noise cleaning

Set threshold ∆ = kσglobal

Median filteringExample of rank filteringOutput DN = median(DNwindow)Length of window must be oddSort input DNs within window

and select middle DN for output

Median Filter

Median Filterseparable 2-D median filter preserves 2-D edges

Median Filter

Line Drop Removal

Median Filter on Photoelectronic Noise

Structured NoisePeriodic, stationary

Periodicity means noise power is isolated into a few frequenciesDifficulty is in detecting noise power “spikes”Visual detection works, but not practical for processing large number of images

Structured NoiseNot really automated filter designTwo parameters must be supplied:

width of Gaussian HPFpower spectrum threshold for notch filter