This document presents methods for predictive quantization of dechirped spotlight-mode synthetic aperture radar (SAR) raw data in the transform domain. It discusses previous work on SAR data compression, analyzes the characteristics of spotlight SAR data in the inverse discrete Fourier transform (IDFT) domain, and proposes three predictive encoding schemes - transform domain block predictive quantization (TD-BPQ), transform domain block predictive vector quantization (TD-BPVQ), and predictive trellis coded quantization (TD-PTCQ) - to take advantage of correlations in the transformed data. Numerical results on an example dataset show SNR improvements of up to 6 dB compared to baseline block adaptive quantization.

1. Predictive Quantization of
Dechirped Spotlight-Mode SAR Raw Data in
Transform Domain
Takeshi Ikuma, Mort Naraghi-Pour*
Department of Electrical and Computer Engineering
Louisiana State University
Baton Rouge, LA
Thomas Lewis
Air Force Research Laboratory
Dayton, OH

2. 2
Presentation Outline
 Circular spotlight-mode SAR, Motivation
 Previous work
 Autoregressive modeling of IDFT transformed SAR data
 Predictive encoding
 Block predictive quantization: scalar, vector
 Predictive trellis coded quantization
 Numerical results
 Conclusions

3. 3
Circular Spotlight-Mode SAR
 We are interested in circular spotlight-mode SAR
 Radar periodically emits a linear FM chirp pulse and receives,
dechirps, and samples the reflected pulses
 A large volume of data is generated that must be downlinked
for processing and archiving
 Downlink channel has limited bandwidth z
 Need on-board compression
q: azimuth angle
of SAR RAW* data q
* Not SAR Image Compression
y
x

4. 4
Previous Work
 Block Adaptive Quantization (BAQ)
 Simple scalar quantizer, adapted to the signal power
 Implemented in exiting systems
 NASA Magellan Mission
 NASA Shuttle Imaging Radar Mission C
 More Effective Method?
 Samples of both I and Q channels of SAR raw data are
largely uncorrelated
 However, SAR image exhibits some correlation
 Transformed data may exhibit some correlation

5. 5
Previous Work, cont’d
Paper Method Pre-Proc. Quantize Post-Proc.
r
Kwon (1989) BAQ Normalization SQ
Arnold (1988) CCT VQ
Franceschetti SC-SAR 1-bit SQ
(1991)
Benz (1995) FFT-BAQ Normalization & SQ w/bit
2-D FFT allocation
Bolle (1997) R & AZ comp DCT SQ Huffman
Owens (1999) TCVQ Trellis coding VQ
Baxter (1999) Gabor/TCQ Gabor trans. VQ Huffman
Trellis coding
Poggi (2000) Range VQ
compression
Magli (2003) NPAQ LPC SQ Arithmetic

6. 6
Spotlight CSAR Data
 CSAR data samples are uncorrelated
 Zero-mean Gaussian distributed
 Signal power varies slowly over time
Example: AFRL Gotcha data set (about 42,000 returns from full 360°)
Magnitude of Raw Data Formed SAR Image (CBP, 512 returns)

7. 7
Transformed Data
 If there are strong reflectors in the scene, range-wise IDFT of
CSAR data exhibits correlation along azimuth.
 Isotropic reflectors appear as sinusoidal traces in the
transformed data. Anisotropic reflectors appear as partial
sinusoidal traces.
IDFT of SAR data
High magnitude sinusoidal trace from metallic cylinder object

8. 8
Transformed Data, cont’d
 Develop block adaptive AR model for IDFT data across returns
(azimuth) for each fixed IDFT bin
 AR model can capture strong reflectors and homogeneous field
Example: AR(1) Model of Gotcha Data
 Blocks with higher signal power  AR poles close to the unit circle
Companion Paper:
T. Ikuma, M. Naraghi-Pour and T.
Lewis,
“Autoregressive Modeling of
Dechirped Spotlight-Mode Raw
SAR Data in Transform Domain,”
Poster presentation today.

9. 9
Block Predictive Coding
 Using the AR modeling, we develop predictive coding techniques
for compression of SAR data
 AR Estimator: Burg’s method
 Predictive Encoder:
 Predictive quantization Encoder
 Scalar: TD-BPQ (DPCM)
 Vector: TD-BPVQ
 Predictive Trellis Coded Quantization
Decoder

10. 10
Transform Domain Block Predictive Quantization
 All signals are complex-valued
ikMv i ,q
 Q(x) : 2 identical scalar quantizers
rkMb i ,q Q(x) ˆ
ekMb i ,q
for I and Q channels
 Designed for zero-mean
2 2
k ,q Gaussian input with variance k ,q
 Predictor states initialization
rkMb i ,q  First block : BAQ encoded.
A(z)
ˆ
rkMb i ,q
 Subsequent blocks: Last L
a k ,q coded samples of previous
block
DPCM Encoder
L: Predictor Order

11. 11
TD-Block Predictive VQ
 There is some correlation between neighboring IDFT bins
 Code multiple (Nb) IDFT bins together to take advantage of
this correlation Predictive VQ
 Model a block of data as a vector AR process
 Treat each IDFT bin as a separate channel. Use generalized AR
estimators for vector process. Each AR coefficient is now a matrix
 Innovation process comprises independent circular complex Gaussian
processes with zero mean and different variances
 Vector quantizer codebook
 Basic codebook designed with LBG algorithm for circular complex
Gaussian training samples with zero mean and unit variance
 For each data block, basic codebook is transformed according to
estimated covariance matrix given by vector AR estimator

12. 12
Predictive Trellis Coded Quantization
 We have also applied predictive trellis-coded quantization
(PTCQ) for coding of IDFT data
Two design considerations: Trellis and codebook
 Amplitude Modulation Trellises
 Exhibit reasonable resistance against error propagation
 Codebook Design:
 Based on 32QAM symbol constellation
 Scaled according to variance estimation from AR analysis
 (Can be optimized by training it with LBG)
 Viterbi algorithm is used for encoding

13. 13
Example: 2-Bit/S PTCQ Configuration
Codebook Structure Trellis Structure
B0 0
0
32QAM 1
2 3
B1 1
3
0
1 2
B0 2 3
2
0
TCQ set partitioning 1
1
B1 3
2
3
0
0
B0 B0 4
1
2
3
3
D0 D2 D4 D6 B1 5 1
0
2
2
3
B0 6
0
B1 1
2 1
D1 D3 D5 D7 B1 3
0
7

14. 14
Numerical Results
 Numerical Results are obtained for AFRL Gotcha dataset
 Performance measure: Average SNR of formed SAR
images
 119 images are formed each from 352 returns (roughly 3° azimuth)
using convolution back-projection algorithm
 Bit Rate: Fixed to 2 bits per real sample
 TD-BPQ, TD-BPVQ, TD-BPTCQ, & BAQ are compared in
terms of
 Average SNR
 Per-Image SNR
as prediction order and block size are varied

15. 15
TD-BPQ: SNR vs. Predictor Order
M = 256
SNR improves by 2.5 dB by introducing prediction
(from L = 0 to L = 1)

16. 16
TD-BPQ: SNR vs. Block Size
Prediction order L = 4
Reasons for SNR loss:
Mb small – poor AR estimates
Mb large – data non-stationary

17. 17
Performance Results
L = 4, M = 256, TD-BPVQ: 2 IDFT bins together
1 dB 1.5 dB
BAQ
TD-BPQ
5 dB TD-BPVQ
TD-BPTCQ
SNR for each of the three schemes experiences fluctuations across
images due to the anisotropic nature of the scene

18. 18
Formed SAR Image Comparison
BAQ TD-BPVQ
9.7 dB 14.4dB
Original
TD-BPQ TD-BPTCQ
13.5 dB 14.9 dB

19. 19
Conclusions
 Significant correlation is observed in IDFT of dechirped
CSAR data
 Three predictive encoding algorithms are applied to
transformed data:
 TD-BPQ: Scalar DPCM coding in IDFT domain
 TD-BPVQ: Vector predictive coding in IDFT domain
 TD-PTCQ: Predictive Trellis Coded Quantization
 The predictive quantization can provide up to 6 dB
improvement in average SNR
Any Questions?