Investigation of Noise and Dimensionality Reduction Investigation of Noise and Dimensionality Reduction Transforms on Hyperspectral Data Transforms on Hyperspectral Data

as Applied to Target Detectionas Applied to Target Detection

Brian StaabEmmett Ientilucci

Digital Imaging and Remote Sensing LaboratoryCenter for Imaging Science

Rochester Institute of Technology

OverviewOverviewBackgroundBackground

Dimension & Noise Reduction TransformsDimension & Noise Reduction TransformsPrincipal Components Analysis (PCA)Principal Components Analysis (PCA)Maximum Noise Fraction (MNF)Maximum Noise Fraction (MNF)

Target Detection AlgorithmsTarget Detection AlgorithmsSpectral Angle Spectral Angle MapperMapper (SAM)(SAM)Orthogonal Subspace Projection (OSP)Orthogonal Subspace Projection (OSP)

Experiment Experiment

ResultsResultsA small sampleA small sample

ConclusionsConclusions

The TransformsThe Transforms

VarianceVariance

σσ22

PCA/MNF BandsPCA/MNF Bands1 2 3 4 5 …. 200

““NoiseNoise”” BandsBands

Too Much DataToo Much DataSimplify and Speed up AnalysisSimplify and Speed up Analysis

Without Throwing Away Information?Without Throwing Away Information?

Principal Components Analysis (PCA)Principal Components Analysis (PCA)Compress Variance to Few BandsCompress Variance to Few BandsDeDe--correlation via linear transformscorrelation via linear transforms

The TransformsThe Transforms

PCA maximizes variance of bandsPCA maximizes variance of bandsSignal & Signal & NoiseNoise MaximizedMaximized

Maximum Noise Fraction (MNF)Maximum Noise Fraction (MNF)Attempt to Attempt to ““separateseparate”” Noise and SignalNoise and SignalMaximize Signal to Noise RatioMaximize Signal to Noise RatioRequires Estimate of NoiseRequires Estimate of Noise

Dimension ReductionDimension Reduction

Noise ReductionNoise ReductionPCA/MNF SpacePCA/MNF Space

Zero the Noise BandsZero the Noise Bands

Inverse Transform to Original SpaceInverse Transform to Original Space““Noise Cleaned DataNoise Cleaned Data””

Only use the First Few PCA/MNF BandsOnly use the First Few PCA/MNF BandsContains the Most Variance or Information (compressed)Contains the Most Variance or Information (compressed)

Remaining Bands = Noise (Low Variance)Remaining Bands = Noise (Low Variance)

ConsiderConsider

How many dimensions do you keep?How many dimensions do you keep?

How will it affect target detection How will it affect target detection performance?performance?

Target Detection AlgorithmsTarget Detection AlgorithmsSpectral Angle Spectral Angle MapperMapper –– SAMSAM

Detection Statistic = Angle Detection Statistic = Angle

,

,

cos( )T

i j

i j

θ =t xt x

t

Target spectra

Xi,j

Test pixel

Band 1

Band 2

Target Detection AlgorithmsTarget Detection AlgorithmsOrthogonal Subspace Projection (OSP)Orthogonal Subspace Projection (OSP)

Geometrical ApproachGeometrical Approach

Matrix operatorMatrix operatorEliminate undesired spectral signatures (background) Eliminate undesired spectral signatures (background) contributioncontributionHow unlike the BackgroundHow unlike the Background

Vector operatorVector operatorMaximizes the contribution of desired target spectraMaximizes the contribution of desired target spectraHow TargetHow Target--LikeLike

HypothesisHypothesis

Dimension and Noise reduction Dimension and Noise reduction transforms on hyperspectral imagery transforms on hyperspectral imagery have no effect on target detection have no effect on target detection performanceperformance

Testing an AssumptionTesting an Assumptionthat there is no Effectthat there is no Effect

Radiance orRadiance orDC SpaceDC Space

ReflectanceReflectanceSpaceSpace

PCA/MNFPCA/MNFSpaceSpace

ELMELM PCAPCA

MNFMNF

ExperimentExperimentHyperspectral Hyperspectral Image CubeImage Cube

145

Band

s

145

Band

s

Atm

osph

eric

Atm

osph

eric

Com

pens

ation

Com

pens

ation

Experiment:Experiment:Band ReductionBand Reduction

Trim PCA/MNFTrim PCA/MNFDataData

PCA/MNFSpace

PCA/MNFsame transform

TargetTargetReflectanceReflectance

Target Detection-SAM-OSP

Record Detection Statistic

Iterate Number of Dimensions Trimmed

Experiment:Experiment:Noise ReductionNoise Reduction

Zero PCAZero PCADataData

Noise Noise Reduced Reduced ReflectanceReflectanceInverse

PCA

Target ReflectanceTarget Reflectance

Target Detection-SAM-OSP

Record StatisticIterate Number of Bands Zeroed

Experiment:Experiment:Band/Noise ReductionBand/Noise Reduction

Vary No. Bands Kept or ZeroedVary No. Bands Kept or ZeroedExamine Trends:Examine Trends:

Low and High Contrast TargetsLow and High Contrast TargetsSAM & OSPSAM & OSP

DetectionDetectionStatisticStatisticθθ

Number of Dimensions Kept Number of Dimensions Kept Or % Variance KeptOr % Variance Kept

100 % = All BandsLess % or Bands

Reference: Detection using all bands

AB

HydiceHydice Forest Radiance SceneForest Radiance Scene

141 x 116 Subset141 x 116 Subset145 Bands145 Bands.4 to 2.4 .4 to 2.4 µµmmELM AppliedELM Applied9 9 mbmb

High Contrast30 Fully Resolved pixels

Low Contrast15 Fully Resolved pixels

Zoom

Noise EstimateNoise EstimateNeeded for MNF TransformNeeded for MNF Transform20x17 pixel calibration panel20x17 pixel calibration panel

Homogeneous RegionHomogeneous RegionDifference of Original and Spatially Difference of Original and Spatially Shifted Version = NoiseShifted Version = Noise

Noise Std. Dev.

Vs. Band

Noise Covariance Matrix

ResultsResults

To compare with the trends of target pixelsTo compare with the trends of target pixels3 background classes were used as test 3 background classes were used as test pixelspixels

8 Graphs per Experiment: Dimension and Noise Reduction8 Graphs per Experiment: Dimension and Noise ReductionPCA & MNFPCA & MNFSAM & OSPSAM & OSPHigh & Low Contrast TargetsHigh & Low Contrast Targets

Results: PCA Band ReductionResults: PCA Band Reduction

High ContrastHigh ContrastVery Little EffectVery Little EffectMean of 30 PixelsMean of 30 Pixels

BackgroundBackgroundGrassGrassRoadRoadDirtDirt

PCA Band Reduction: SAM: Mean High Contrast

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

0 5 10 15 20

Number of Dimensions

Ang

le (R

adia

ns) Mean Target

GrassRoadDirtO

| 94.6% | 99.15% | 99.6 % | 99.69% % Variance Kept

Results: MNF Band ReductionResults: MNF Band Reduction

High ContrastHigh ContrastMore Separation More Separation with Background with Background ClassesClasses

Mean of 30 PixelsMean of 30 Pixels

MNF Band Reduction: SAM: Mean High Contrast

0.1

0.3

0.5

0.7

0.9

1.1

1.3

1.5

1.7

0 20 40 60 80 100 120 140

Number of Dimensions

Angl

e (r

adia

ns)

Target MeanGrassRoadRock/DirtG

| 73.6% | 97.99% | 99.37 % | 99.89% % Variance Kept

Results: MNF Noise ReductionResults: MNF Noise Reduction

Low ContrastLow Contrast

Improvement in Improvement in AngleAngle

Increase in Increase in background background separationseparation

IdealIdeal

MNF Noise Reduction: SAM: Mean Low Contrast

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

0 20 40 60 80 100 120 140

Number of Bands Kept

Angl

e (r

adia

ns)

MeanGrassRoadDirt/Rock

| 73.6% | 97.99% | 99.37 % | 99.89% % Variance Kept

Summary: SAMSummary: SAM

+ Improves / Better target Angle till significant noise reduction then:

++ Improves separation from background (Target Improves/ Background Worsens)

+ Target angle improves+ Improves separation from background

Low Contrast

+ Improves / Better target angle till significant noise reduction then:

+ Improves separation from background slightly

- Improves background angles

- Worsens target angle High Contrast

MNFPCANoiseReduction

- Worsens target angle- Confusion with background

+ Improves target Angle and+ Improves separation from background

slightly

Low Contrast

+ Improves target angle+ Improves separation from

background

+ Improves target angle- Improves background angles

High Contrast

MNFPCABandReduction

Target relatively constant till significant Target relatively constant till significant band/noise reduction then:band/noise reduction then:

Summary: OSPSummary: OSP

- Worsens target till 99.8% variance (~110 bands) kept then:

• Constant target/backgrounds till significant noise reduction then:

- Worsens target statistic+ Small area of improvement of target &

background separation

Low Contrast

- Worsens target statistic

+ Small area of improvement of target & background separation

• Target Relatively Constant till significant noise reduction then:

- Worsens Target statistic

High Contrast

MNFPCANoiseReduction

- Confusion with background• Target relatively constant till significant

band reduction then:- Worsens Target Angle

+ Improves Target and + Improves Separation from background

till significant band reduction then:- Background Increase but at lower rate

Low Contrast

+ Improves target slightly + Improves Separation from Background

till significant band reduction

+ Improves target slightly + Improves separation from Background

till significant band reduction

High Contrast

MNFPCABand

Reduction

EndmemberEndmember changes cause drastic fluctuations, some changes cause drastic fluctuations, some cause background confusioncause background confusion

ConclusionConclusion

Band ReductionBand ReductionDetection statistic remains relatively Detection statistic remains relatively constant or improvesconstant or improvesSome cases: Increase in separationSome cases: Increase in separation

Noise ReductionNoise ReductionSAM angle constant or improvesSAM angle constant or improves

Background Separation increasesBackground Separation increases

OSP statistic constant or deterioratesOSP statistic constant or deterioratesDrastic fluctuations (Drastic fluctuations (EndmembersEndmembers))

ConclusionConclusion

Future Considerations:Future Considerations:Use of varyingUse of varying

Data setsData setsTarget Detection AlgorithmsTarget Detection AlgorithmsTargetsTargets

Better Noise EstimatesBetter Noise Estimates

QuestionsQuestions