Wavelet-based compression of SAR raw data Enrico Magli, Gabriella Olmo, Barbara Penna Dip. di Elettronica - Politecnico di Torino Corso Duca degli Abruzzi, 24 - 10129 Torino - ITALY Ph.: +39 011 5644195 - Fax: +39 011 5644149 E-mail: magli(olmo)@polito.it,
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Abstract— In this paper we compare two compression methods for SAR raw data, based on the Discrete Wavelet Transform (DWT). In the former, the data are subject to blockwise normalization prior to be transformed by means of the DWT processor; then, an optimal rate allocation is performed for each subband. The latter employs the well known JPEG 2000 to perform the DWT and the subsequent quantization, rate allocation and coding steps; both the cases of normalized and non normalized data are considered. The performance of the algorithms have been tested on SIR-C/X-SAR data, and FBAQ is employed as the term of comparison for both quality and compression ratio. The obtained results show that the if the samples are normalized, the performance of the DWT-based algorithms is more predictable, and less subject to statistical fluctuations related to the characteristics of the input data. I. I NTRODUCTION Synthetic Aperture Radar (SAR) is a dedicated high resolution sensor employed in several Earth observation applications. A significant characteristic of this system is the generation of a large amount of data, that involves major problems related to on-board data storage and communication bandwidth towards the receiving ground station. Consequently, lossy compression of SAR raw data must be adopted. The most popular method for SAR data compression is the FBAQ (Flexible Block Adaptive Quantization) [1], [2]. In this technique, the real and imaginary components of the raw data are divided into blocks; the standard deviation of each block is evaluated, and the data block samples are coded by a Lloyd-Max quantizer, which employs the optimal quantization thresholds to obtain minimum distortion. However, in spite of its simplicity, the FBAQ does not exploit the (anyway slight) correlation among the samples of the raw signal. Several methods exist [3] in which the principle of transform coding is applied to the compression of SAR raw data. These methods apply some type of frequency decomposition (e.g. the fast Fourier transform or the discrete cosine transform) to the data prior to quantization and coding. Most of these algorithms apply a blockwise normalization of the I and Q coefficients, so that the normalized data can be modelled as stationary Gaussian processes, whose power spectral densities (psd) in the range and azimuth directions are related to the SAR system parameters [3]. In particular, the psd in the range direction is dictated by the chirp bandwidth, whereas the psd in the azimuth direction is proportional to the azimuth antenna pattern. These pdf’s exhibit a weak lowpass behaviour, more evident in the range direction, showing that some amount of correlation among samples does exist, and can be exploited to design efficient compression algorithms based on the transform prin-
ciple. The most important practical consequence of blockwise normalization is that the bit allocation to each frequency band can be computed once and for all. Moreover, the normalization task itself is not computationally intensive, as it can be performed by means of low complexity algorithms (e.g. the BAQ). Therefore, the proposed algorithms based on normalization and frequency decomposition can be classified as (relatively) low complexity. The objective of this paper is to ascertain if these concepts also apply if the discrete wavelet transform (DWT) is used as the decorrelation stage. In particular, we want to verify the impact of data normalization on the performance of DWT-based algorithms. To this end, we compare two algorithms: the former works on blockwise normalized data, and implements an optimal static rate allocation to the subbands of the DWT. The latter algorithm is the well known JPEG 2000 compression standard [7], which is operated on both normalized and non normalized data. It is worth noticing that the use of the DWT for SAR raw data compression has already been proposed in [4]. However, in this paper a computationally intensive rate allocation making use of Lagrangian optimization is employed. II. THE DWT AND THE PROPOSED SCHEMES The basic principle of transform coding [5] is that, if the sequence to be compressed is correlated, it is possible to reduce the number of encoded bits as some information carried by each sample can be inferred from other elements in the sequence. Actually, it can be shown that the maximum amount of compaction can be achieved if the data are subject to a transform that decorrelates the input sequence. The transformed sequence has different statistical properties with respect to the original one, and it exhibits a markedly unbalanced energy distribution. The Karhunen Lo`eve Transform [5] is known to yield perfect data decorrelation. However, it exhibits very high computational complexity, and is often replaced by other reversible transforms which, although being suboptimal, are more affordable from the complexity point of view. The most popular of them are the discrete cosine transform [5] and the DWT. The DWT is based on the principle that efficient decorrelation can be achieved by splitting the data into two subsequences, carrying information respectively on the low and highpass half bands of the original signal. In fact, most of the signal energy is carried by the low pass sequence, so achieving the necessary energy compaction. The process can be iterated on the low pass sequence, yielding a representation in terms of subsequences, each of which carries information on a constant-Q subband of the original signal. In practice, this operation
is performed by means of a filter bank configuration. At each stage, the input signal is processed by means of a lowpass and a highpass filter, whose outputs are downsampled by a factor of two, maintaining the whole structure critically sampled. The filters must satisfy the socalled perfect reconstruction properties [5]. The selection of the filters strongly affects the compression performance of the DWT, and numerous selections of good filters for image and video applications can be found in the literature [6]. The first algorithm proposed in this paper is depicted in Fig. 1. The input data are segmented into blocks of dimension 32 × 32, and each block is normalized dividing each sample by the standard deviation (considered constant over the block). In order to reduce the computational complexity, the standard deviation is obtained as the output of an FBAQ quantizer with a high number of quantization levels, as proposed in [3].
lar blocks (typically 64 × 64), or code-blocks, which are independently encoded with EBCOT (Embedded Block Coding with Optimized Truncation), which is based on a bit-plane approach, context modeling and arithmetic coding. The bit stream output by EBCOT is obtained from the independent embedded bit streams generated for every block; basically, it is organized as a succession of layers, each layer containing the additional contributions from each code block. The block truncation points associated with each layer are optimal in the rate distortion sense. If the bit stream is randomly truncated, the departure from optimality can be small if the number of layers is large. The final JPEG 2000 bit stream consist of a global header, followed by one or more sections corresponding to tiles. Each tile section encompasses a tile header and a layered representation of the code-blocks, organized into packets. III. EXPERIMENTAL RESULTS
NORMALIZATION
DISCRETE WAVELET TRANSFORM
RATE ALLOCATION & QUANTIZATION
Fig. 1. Block scheme of the first proposed algorithm
After the normalization step, the DWT is applied to the data. Experimental evaluations have led to the selection of 2 levels of filter decomposition; moreover, the I and Q samples are interlaced prior to be transformed, in order to maximize the short term correlation. As for the filter bank, we have selected the LeGall (5,3) filters [6], which, besides yielding excellent compression performance, exhibit a high computational efficiency, and are suitable for hardware implementation. As already mentioned, the theoretically optimal bit allocation has been applied to each subband, with a given average number of bits per sample as the constraint of the optimization problem. The analytical solution can be easily worked out, as the transformed coefficients are still characterized by a Gaussian ddp; details of the bit allocation procedure can be found in [6]. It is worth noticing that, as the number of bits allocated to each subband is related to the subband standard deviation, the allocation can be performed once and for all thanks to the data normalization. Once defined the optimal number of quantization levels allocated to each subband, the quantization itself is performed by means of a Lloyd Max quantizer optimized for Gaussian distribution. The second compression scheme considered is the well known JPEG 2000 ISO/ITU-T standard for still image coding [7]. JPEG 2000 is intended to provide innovative solutions according to the new trends in multimedia technologies, and should yield not only superior performance with respect to existing standards in terms of rate distortion capability and subjective quality, but also numerous additional functionalities developed to match the needs of applications such as wireless transmission, medical imagery, digital library, e-commerce. Lossless and lossy compression, progressive transmission, encoding of very large images, robustness to the presence of bit errors and region of interest coding are some representative examples of its features. The architecture of the JPEG 2000 is similar to every transformbased coding scheme. The DWT is first applied to the source image data; then, the transform coefficients are quantized and entropy coded; finally, the output codestream is generated. The DWT is applied to rectangular partitions of the image or tiles. Quantization with an embedded dead-zone scalar approach is then applied independently to each subband, in such a way that all the information content is preserved in the case of reversible transform. Each subband of the wavelet decomposition is divided into rectangu-
The performance of the two algorithms described in Sec. II has been evaluated on real-world SIR-C/X-SAR raw data. These data are prequantized on 4 or 6 bit/sample. We have selected two scenes, named Jesolo and Innsbruck, which are quantized on 6 bit/sample, and tested the algorithms at rates of 2 and 3 bit/sample. Data normalization has been made on 32 × 32 blocks. The LeGall(5,3) filter has been used throughout our tests. The selected quality metric is SNR between the original and decoded raw data. In Table I, the performance of the classical FBAQ algorithm is reported for the sake of comparison. The two cases of compression at 2 and 3 bits/sample are addressed; results are expressed in terms of the SNR on the I and Q components of the signal, and of the absolute phase error expressed in degrees; this latter information is particularly significant in case of interferometric applications. TABLE I PERFORMANCE
2 bit/sample Jesolo Innsbruck 3 bit/sample Jesolo Innsbruck
OF THE
FBAQ
Real (dB) 8.53 9.22 Real (dB) 12.62 14.47
ALGORITHM ON
SIR-C/X-SAR
FBAQ Imag. (dB) 8.21 9.14 Imag. (dB) 12.49 14.36
DATA
Phase (degree) 14.89 16.29 Phase (degree) 12.40 10.80
Tables II and III report the performance results of the proposed algorithms applied to the Jesolo and Innsbruck scenes respectively. The label “DWT” refers to the first proposed algorithm, whereas “Jpeg2000” refers to the standard applied to non normalized data, and “Jpeg2000(*)” to the standard applied to normalized data. It can be noticed that, for both scenes, the performance of DWT and JPEG 2000 with data normalization are almost equivalent. A different situation can be appreciated in the case of JPEG 2000 without data normalization; the performance of this algorithm turns out to be heavily dependent on the scene at hand, ranging from a loss of more than 2 dB with respect to DWT, in the case of Jesolo and 2 bit/pixel compression, to the gain of 1,2 dB in the same situation with the Innsbruck scene. This behaviour can be explained considering that the non normalized data represent a non stationary process, whose statistical characteristics are subject to fluctuations which affect also the compression performance.
TABLE II PERFORMANCE
OF THE PROPOSED ALGORITHMS APPLIED TO THE
J PEG 2000:
NON NORMALIZED DATA .
2 bit/sample DWT Jpeg2000 Jpeg2000(*) 3 bit/sample DWT Jpeg2000 Jpeg2000(*)
J PEG 2000(*):
JESOLO Real (dB) Imag.(dB) 8.03 7.89 5.98 5.88 8.48 8.46 Real (dB) Imag.(dB) 13.06 12.91 13.30 13.25 14.30 14.20
JESOLO
SCENE .
NORMALIZED DATA
Phase (degree) 20.89 20.52 20.17 Phase (degree) 15.87 10.99 14.34
timal. Moreover, since the local psd varies from image to image, the rate allocation must be computed for each image, thus leading to high computational complexity. The most important benefit of normalizing the data prior to waveletbased compression lies in the fact that the resulting performance is much more predictable, as can be inferred from the results shown in the previous section; this makes it easier to design the compression algorithm, and results in a much more robust system. Moreover, blockwise normalization of the data provides a signal that is stationary in range and azimuth. As a consequence, the rate allocation to wavelet subbands can be performed once and for all, and need not be recomputed for each image, thus alleviating the overall computational burden of a wavelet-based scheme. V. CONCLUSIONS
TABLE III PERFORMANCE SCENE .
OF THE PROPOSED ALGORITHMS APPLIED TO THE
J PEG 2000:
2 bit/sample DWT Jpeg2000 Jpeg2000(*) 3 bit/sample DWT Jpeg2000 Jpeg2000(*)
NON NORMALIZED DATA .
J PEG 2000(*):
INNSBRUCK Real (dB) Imag. (dB) 8.70 8.54 9.92 9.74 8.38 8.21 Real (dB) Imag.(dB) 13.78 13.62 14.09 13.87 14.18 14.14
INNSBRUCK
NORMALIZED DATA
Phase (degree) 19.51 20.79 19.55 Phase (degree) 14.00 14.60 13.09
It can also be noticed that the performance of DWT and JPEG 2000 are comparable with that of FBAQ at the same bit rate. However, it must be remarked that the SNR evaluated on the raw data is not directly related to the quality of the images formed from them. Due to the frequency shaping of the quantization error, the compression algorithms based on frequency decomposition usually exhibit noticeable performance gains with respect to FBAQ on the image data, although this cannot be appreciated on the raw data. This behaviour should also hold for the DWT-based algorithms, which are a particular class of frequency decomposition. IV. DISCUSSION In the previous section we have presented experimental results on real-world SIR-C/X-SAR data compressed with our wavelet-based algorithm that performs static rate allocation, as well as the JPEG 2000 algorithm in case of normalized and non-normalized data. There are a few observations that can be made on the basis of these results. In general, wavelet-based algorithms have turned out to be suitable for the compression of SAR raw data. However, some caveats are worth being pointed out. Remarkably, when applied to the original SAR data, i.e. without normalization, wavelet-based algorithms exhibit a very high degree of performance variability if applied to different images, or even on the same image at different bit-rates. Although there are cases when they outperform FBAQ, at times they provide much poorer SNR. The reason for this behavior lies in the nonstationarity of the SAR raw data, whose local psd may significantly vary over the scene. As a consequence, the rate allocation for each subband, computed by JPEG 2000, reflects its “average” energy content, which is not necessarily op-
In this paper we have compared two compression methods for SAR raw data, based on the Discrete Wavelet Transform (DWT). The former is applied to normalized input data, which can be considered stationary; therefore, the bit allocation to each subband can be evaluated statically, with a major computational advantage. The latter employs the JPEG 2000 ISO/ITU-T standard for still image coding; both the cases of normalized and non normalized data are considered. Performance evaluation of the algorithms on SIR-C/X-SAR data reveals that the blockwise normalization strongly mitigates the fluctuation of the algorithm performance, so making this latter more predictable and less dependent on the particular scene being compressed. Besides this advantage, the possibility of performing the rate allocation once and for all reduces the algorithm computational complexity. R EFERENCES [1] R. Kwok, W.T.K. Johnson, “Block adaptive quantization of Magellan SAR data”, IEEE Trans. Geosc. Remote Sens., vol.27, n.4, pp. 375-383, July. 1989 [2] I.H. McLeod, I.G. Cumming, “On-board encoding of the ENVISAT wave mode data”, Proc. of IEEE IGARSS 1995 [3] U. Benz, K. Strodl, A. Moreira, “A comparison of several algorithms for SAR raw data compression”, IEEE Trans. Geosc. Remote Sens., vol.33, n.5, pp. 1266-1276, Sept. 1995 [4] V. Pascazio, G. Schirinzi, “Wavelet transform coding for SAR raw data compression”, Proc. of IEEE IGARSS 1999 [5] Sayood K., ”Introduction to data compression”, Morgan Kaufmann Publishers, 2000 [6] Vetterli M., Kovaˇcevi´c J., “Wavelets and subband coding”, Prentice Hall PTR, Englewood Cliffs, New Jersey, 1995 [7] D.S. Taubman, M.W. Marcellin, JPEG2000: image compression fundamentals, standards, and practice, Kluwer, 2001
