Adaptive Algorithms for Optimal Classification and Compression of Hyperspectral Images

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Adaptive Algorithms for Optimal Classification
and Compression of Hyperspectral Images

• Tamal Bose and Erzsébet Merényi
• Wireless_at_VT
• Bradley Dept. of Electrical and Computer
  Engineering
• Virginia Tech
• Electrical and Computer Engineering
• Rice University

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Outline

• Motivation
• Signal Processing System
• Adaptive Differential Pulse Code Modulation
  (ADPCM) Scheme
• Transform Scheme
• Results
• Conclusion

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Status-Quo
Raw data (limited onboard processing) Unreliable
links Unacceptable latencies Delay in science
and discovery Restricts deep space missions
Mission Scientists
Mission Control
High stress Reduced productivity
KNOWLEDGE
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High-Speed Real-Time On-Board Signal Processing

• Impact on Science
• State-of-the-art signal processing algorithms to
• enable onboard science
• detect events and take necessary action e.g.
  collecting and processing data as a result of
  detecting dust storms in Mars
• process and filter science data with machine
  intelligence e.g. data compression with signal
  classification metrics, so that that certain
  features can be preserved

• Objectives
• Computationally efficient signal processing
  algorithms with the following features
• Adaptive filter based algorithms that
  continuously adapt to new environments, inputs,
  events, disturbances, etc.
• Modular algorithms suitable for implementation in
  distributed processors
• Cognitive algorithms that learn from its
  environments high degree of artificial
  intelligence built-in for mission technology and
  for science data gathering/processing

Concept

• Current science/technology plans
• Scientific processing and data analysis
• Data compression/filtering
• Autonomous mission control e.g. automatic
  landing site identification, instrument control,
  etc.
• Cognitive radio based communications to optimize
  power, cost, bandwidth, processing speed, etc.

DSP Algorithms
11/12/2007
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Impact

• Large body of knowledge developed for on-board
  processing. Two main classes (Filtering and
  Classification)
• Adaptive filtering algorithms (EDS, FEDS, CG, and
  many variants)
• Algorithms for 3-D data de-noising, filtering,
  compression, and coding.
• Algorithms for hyperspectral image clustering,
  classification, onboard science (HyperEye)
• Algorithms for joint classification and
  compression.

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Intelligent Data Understanding in on-board context
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HyperEye Intelligent Data Understanding
environment Precision manifold learning system
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Specific Goals (this talk)

• Maximize compression ratio with classification
  metrics
• Minimize mean square error under some constraints
• Minimize classification error

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Signal Processing System
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TOOLS ALGORITHMS

• Digital filters
• Coefficient adaptation algorithms
• Neural nets, SOMs
• Pulse code modulators
• Image transforms
• Nonlinear optimizers
• Entropy coding

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Scheme-I

• ADPCM is used for compression
• SOM mapping is used for clustering
• Genetic algorithm is used to minimize the minimum
  cost function
• Compression is done along spatial and/or spectral
  domain

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ADPCM system

• Prediction error Reconstruction
  Reconstruction error quantization error
• Cost function

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• Several different algorithms are used for
  adaptive filtering
• Least Mean Square (LMS)
• Recursive Least Squares (RLS)
• Euclidean Direction Search (EDS)
• Conjugate Gradient (CG)
• The Quantizer is Adaptive
• Jayant quantizer
• Lloyd-Max optimum quantizer
• Custom quantizer as needed

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Predictor Footprint

• C(i,j,k) represents prediction coefficients
• R is a prediction window over which C(i,j,k) is
  nonzero

i
j
Filter coefficient position
Cubic Filter
Position to be predicted
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EDS Algorithm
The least squares cost function
An iterative algorithm for minimizing has
the form
The cost function at the next step is
Now we find a such that the above is minimized
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EDS Algorithm
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Self-organzing map SOM

• Unsupervised neural network
• A mapping from high-dimensional input data space
  onto a regular two-dimensional array of neurons
• The neurons of the map are connected to adjacent
  neurons by topology (rectangular or hexagonal)
• One neuron wins the competition then change its
  weights and its neighborhood
• Sourcehttp//www.generation5.org/content/2004/ais
  ompic.asp

Competition layer (output layer)
weights
Input layer
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The learning process of the SOM

• Competition
• A winning neuron is selected when
  output(i)ltinput, weightgt
• the shortest Euclidean distance between input
  vector and weights
• Update
• Update the weight values of the winning neuron
  and its neighborhood
• Repeat
• As the learning proceeds, the learning
• rate and the size of the neighborhood
• decreases gradually

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GA-ADPCM Algorithm

• Apply SOM mapping to the original image.
• Generate initial population of ADPCM
  coefficients.
• Implement ADPCM (LMS, EDS, RLS, etc.) processing
  using these sets of coefficients.
• Apply SOM mapping to the decompressed images.
• Calculate the fitness scores (clustering errors)
  between the decompressed images and the original
  image.

Fitness Scores 4 2 3 1
ADPCM
SOM
Coefficients 1 2 3
Population 1 2 3 4
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• Sort the fitness scores and choose the 50
  fittest individuals.
• Apply the genetic operations (crossover and
  mutation) and create the new coefficient
  population.
• Go to Step 2 and repeat this loop until the
  termination condition is achieved.
• The termination condition is when the clustering
  error smaller than a certain threshold

Coefficients 1 2 3
Fitness Scores 1 2
Population 4 2
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Fitness function

• FCe/N.
• Ce is the number of pixels clustered incorrectly.
• N is the total pixels in the image.
• F is the percentage of incorrectly clustered
  pixels.
• Ce is obtained by the following steps
• Calculate CmCo-Cg, where Co is the matrix
  containing the clustering result of the original
  image. Cg is the matrix containing clustering
  result of the image after ADPCM compression and
  decompression. Cm is the difference between the
  two clustered images.
• Assign all the nonzero points in Cm matrix to be
  1 and add them together to get the clustering
  error Ce.

0 0 1 1 0 0 1 0 1 Cm
1 2 3 2 1 3 3 1 2 Co
1 2 2 1 1 3 1 1 3 Cg
0 0 1 1 0 0 2 0 -1 Cm

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Transform Domain Scheme

• Image transform is used for compression
• DFT, DCT, DST, DWT, etc.
• Parameters (block size, number of bits) can be
  adjusted by cost function
• Compression is done along
• spectral domain, spatial domain, or both
• Quantization
• Uniform, non-uniform, optimum, custom, etc.
• Bit allocation
• non-uniform

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Transform-Domain Algorithm
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• Method I fix the number of quantization bits,
  adjust block size (DCT length)
• Method II fix block size (DCT length), adjust
  the number of quantization bits
• Several other combinations

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Results
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Hyperspectral cube- Lunar Crater Volcanic Field
(LCVF)
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Jasper Ridge (JR)
One frame of the hyperspectral cube
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Clustered results comparison between ADPCM and
GA-ADPCM

• One block of the original image Clustered image
  by LMS Clustered image by EDS
• Clustered original image Clustered image by
  GA-LMS Clustered image by GA-EDS

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Fitness score for GA-LMS Fitness score for
GA-EDS fitness scores clustering errors
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Clustering error comparison between ADPCM and
GA-ADPCM
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Clustering error comparison between LMS and GA-LMS

• Block size16 Classes4 Block size32
  Classes4 Block size64 Classes4
• Block size16 Classes3 Block size32
  Classes6 Block size64 Classes8

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Clustering error comparison between EDS and GA-EDS
Block size16 Classes4 Block size32
Classes4 Block size64 Classes4
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Clustering results between uncompressed image and
transformed image
Clustered image of original image Clustered
image after transform
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Mean spectral signatures of the SOM clusters
identified in the Jasper Ridge image.
Left from the original image. Right
from the image after applying DCT compression and
decompression
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Clustering Errors using Different Block Sizes in
JR
Clustering Errors using Different Number of Bits
in JR
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Spectral signature comparison (Mean, STD,
Envelope) of whole hyperspectral data
LCVF Uncompressed Data
LCVF after ADPCM compression LCVF
after DCT compression
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LCVF Uncompressed Data LCVF after
ADPCM compression LCVF after DCT
compression
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Classification accuracy
Measuring the effect of compression on
classification accuracy. Data Hyperspectral
image of Lunar Crater Volcanic Field, 196
spectral bands, 614 x 420 pixels.
Classifications were done for 23 known surface
cover types. Original uncompressed data are
labeled with LCVF, a compressed-uncompressed
data set with D1c16 using ADPCM, a
compressed-uncompressed data set with
DCT194b8hb4 using DCT (8-bit quantization for
significant data, 4-bit for insignificant data).
D1c8b3 is using ADPCM with 3-bit Jayant
quantization.
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Conclusion

• New algorithms have been developed and
  implemented that use the concept of
  classification metric driven compression
• GA-ADPCM algorithm was simulated
• Optimized the adaptive filter in an ADPCM using
  GA
• Reduced clustering error
• Drawback increased computational cost
• Feedback-Transform algorithm was simulated
• Select the optimal block size (DCT length) and
  number of quantization bits to achieve a balance
  between a low clustering error, and computational
  complexity, and memory usage
• Compression along spectral domain preserves the
  spectral signatures of the clusters
• Results using the above algorithms are promising

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Acknowledgments

• Graduate students
• Mike Larsen (USU)
• Kay Thamvichai (USU)
• Mike Mendenhall (Rice)
• Li Ling (Rice)
• Bei Xei (VT)
• B. Ramkumar (VT)
• NASA AISR Program