Low-Complexity Lossless Compression of Hyperspectral Imagery via Linear Prediction

Presented by: Robert Lipscomb and Hemalatha Sampath

What is a hyperspectral image?

• Think of a hyperspectral image as series of pictures (or bands) of the same target in a single state

– Each band represents a view of that target using a different wave length

– Details not visible to the human eye can be determined from these additional views and become beneficial when predicting the weather, studying geology, etc.

– When the bands are stacked together they create a 3-Dimensional cube that represents the image

– Each band can be accessed and processed individually

Our Image Data

• 512 pixels x 512 pixels x 224 bands

• Used a block of 128x128 pixels from each band due to large processing times

• 16-bit representation used for each pixel

• The results from the paper used all of the pixels in each band and the image size was 512x614x224

Example

Original Bands 4,14,18,30,50,100,150,160,200 of the Moffett Field Image

Low-Complexity Algorithms

• A large majority of these images are obtained from detectors aboard spacecrafts which have strict power limitations

• Other more advanced methods have been proposed, but most are of a high complexity

• Algorithms must be of low complexity because low processing times lead to a smaller power consumption

Dimensions

• A hyperspectral image has 2 types of correlations

• Spatial (Intraband correlation)– ith(row) and jth(column) dimension

• Spectral (Interband correlation)– Kth(band) dimension

LP (Linear Prediction) Step: 1

Xi,j-1 Xi,j

Xi-1,j-1 Xi-1,j

a

bc

d IB = {1….8} so the first eight bands are predicted using the intraband median predictor

-each band will be encoded within the spatial domain so the kth dimension will not be used

Xi,j predicted = median[ c, a, c + a – b]

Ei,j (Error) = (Xi,j - Xi,j predicted)

-The errors are stored for each predicted value and this matrix of value is sent to the encoder to be compressed

-This predictor takes advantage of the spatial correlation within the band

LP (Linear Prediction) Step: 2

X i,j-1,k-1 X i,j,k-1

X i-,j-1,k-1 X i-1,j,k-1

X i,j-,k X i,j,k

X i-1,j-,k X i-1,j,k

-The remaining 216 bands need to be predicted using interband linear predictor

-Because this is now an interband predictor the kth dimension will be used

a

b c

d e h

f g

K-1 band K band (current band)

Difference 1,k = e - aDifference 2,k = g - cDifference 3,k = f - b

X i,j,k predicted = d + (Diff1+Diff2+Diff3)/3

E i,j (Error) = (Xi,j,k - Xi,j,k predicted)

-Once again the Error values are stored in a matrix and sent to the encoder

-This method takes advantage of the spectral correlation in the images

SLSQ(Linear Prediction) Step: 1

X i,j-1,k-1 X i,j,k-1

X i-,j-1,k-1 X i-1,j,k-1

a

b c

d

K-1 band

X i,j-1,k-1 X i,j,k-1

X i-,j-1,k-1 X i-1,j,k-1

a

b c

d

K-1 bandX i,j-1,k-1 X i,j,k-1

X i-,j-1,k-1 X i-1,j,k-1a

b c

d

K-1 band

X i,j-1,k-1 X i,j,k-1

X i-,j-1,k-1 X i-1,j,k-1

a

b c

d

K-1 band

X i,j-1,k-1 X i,j,k-1

X i-,j-1,k-1 X i-1,j,k-1

a

b c

d

K-1 band