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

Predictive Quantization of

Dechirped Spotlight-Mode SAR Raw Data in

Transform Domain

Presentation Outline

2

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

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

Need on-board compression

of SAR RAW* data

* Not SAR Image Compression

3

x

y

q

z

q: azimuth angle

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

4

Previous Work, cont’d

5

Paper Method Pre-Proc. Quantize

r

Post-Proc.

Kwon (1989) BAQ Normalization SQ

Arnold (1988) CCT VQ

Franceschetti

(1991)

SC-SAR 1-bit SQ

Benz (1995) FFT-BAQ Normalization &

2-D FFT

SQ w/bit

allocation

Bolle (1997) R & AZ comp DCT SQ Huffman

Owens (1999) TCVQ Trellis coding VQ

Baxter (1999) Gabor/TCQ Gabor trans.

Trellis coding

VQ Huffman

Poggi (2000) Range

compression

VQ

Magli (2003) NPAQ LPC SQ Arithmetic

CSAR data samples are uncorrelated Zero-mean Gaussian distributed Signal power varies slowly over time

6

Example: AFRL Gotcha data set (about 42,000 returns from full 360°)

Magnitude of Raw Data Formed SAR Image (CBP, 512 returns)

Spotlight CSAR 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.

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Transformed Data

IDFT of SAR data

High magnitude sinusoidal trace from metallic cylinder object

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

8

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.

Transformed Data, cont’d

Block Predictive Coding

Using the AR modeling, we develop predictive coding techniques

for compression of SAR data

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Encoder

Decoder

AR Estimator: Burg’s method

Predictive Encoder:

Predictive quantization

Scalar: TD-BPQ (DPCM)

Vector: TD-BPVQ

Predictive Trellis Coded Quantization

Transform Domain Block Predictive Quantization

All signals are complex-valued

Q(x) : 2 identical scalar quantizers

for I and Q channels

Designed for zero-mean

Gaussian input with variance

Predictor states initialization

First block : BAQ encoded.

Subsequent blocks: Last L

coded samples of previous

block

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,bkM i qr Q(x)

A(z)

,ˆbkM i qe

,ˆbkM i qr

,bkM i qr

,k qa

2,k q

,vkM i qi

DPCM Encoder L: Predictor Order

2,k q

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

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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

12

Predictive Trellis Coded Quantization

Example: 2-Bit/S PTCQ Configuration

13

D6 D0

D1

D2

D3

D4

D5 D7

32QAM

1

0

1

2

3

4

5

6

7

B0

B1

B0

B1

B0

B1

B0

B1

0

3

2

1

0

3 2

1

0

3

2

1

0

3

2

0

3

2

1

0

2

1

0

3

2

1

0

3 2

1

3

B0

B1

Codebook Structure

TCQ set partitioning

Trellis Structure

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

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TD-BPQ: SNR vs. Predictor Order

15

SNR improves by 2.5 dB by introducing prediction (from L = 0 to L = 1)

M = 256

TD-BPQ: SNR vs. Block Size

16

Reasons for SNR loss:

Mb small – poor AR estimates

Mb large – data non-stationary

Prediction order L = 4

Performance Results

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L = 4, M = 256, TD-BPVQ: 2 IDFT bins together

SNR for each of the three schemes experiences fluctuations across

images due to the anisotropic nature of the scene

5 dB

1 dB 1.5 dB

BAQ

TD-BPQ

TD-BPVQ

TD-BPTCQ

Formed SAR Image Comparison 18

Original

BAQ

TD-BPQ

TD-BPVQ

TD-BPTCQ

9.7 dB

13.5 dB

14.4dB

14.9 dB

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

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Any Questions?