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- 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?

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