The amount of data collected from spaceborne remote sensing has substantially increased in the last years. During same time period, the ability to store or transmit data has not increased as quickly. At this time, there is a growing interest in developing compression schemes that could provide both higher compression ratios and lower encoding/decoding errors. In the case of the spaceborne Synthetic Aperture Radar (SAR) earth observation system developed by the French Space Agency (CNES), the volume of data to be processed will exceed both the on-board storage capacities and the telecommunication link. The objective of this paper is twofold: to present various compression schemes adapted to SAR data; and to define a set of evaluation criteria and compare the algorithms on SAR data. In this paper, we review two classical methods of SAR data compression and propose novel approaches based on Fourier Transforms and spectrum coding

Besson, O.

Lambert-Nebout, C.

Massonnet, D.

Rogron, B.

English

NASA Technical Reports Server

A Comparative Study of SAR Data Compression Schemes
N94- 28259
Dr. C.Lambert-Nebout
CNES CT/AE/SEA/TB
18 av Edouard Belin
31055 Toulouse
e_mail • lambert@hathor.cnes.fr
phone • 33.61.27.33.08
fax • 33.61.28.19.96
Dr. O.Besson
ENS1CA
49 av Leon Blum
31056 Toulouse
Dr. D.Massonnet, Dr. B. Rogron
CNES CT/IA/QTIS/PR
18 av Edouard Belin
31055 Toulouse
I)INTRODUCTION
In spaceborne remote sensing, the amount of data collected has substantially increased ill
the last years. In the same time, the ability to store or transmit it has not increased as fast, so that
there is a growing interest in developing compression schemes that could provide both higher
compression ratios and lower encoding/decoding errors. In the case of the spaceborne Synthetic
Aperture Radar (SAR) earth observation system developped by tile French Space Agency
(CNES), the volume of data to be processed is planned to exceed on-board storage capacities or
telecommunication link. The objective of this paper is twofold:
data.
- to Present various compression schemes adapted to SAR data
- to define a set of evaluation criteria and compare the algorithms on SAR
In this paper, we review two classical methods of SAR data compression and propose
novel approaches based on Fourier Transforms and spectrum coding.
II),pESCR!pTION OF ALGORITHMS
a) Block Adaptive Quantizer
The first algorithm presented in this paper is the Block Adaptive Quantizer (BAQ)
which was first proposed for tile Magellan mission to Venus ([1]). This method encodes data into
2 bits in the following way: one bit is the sign bit, the other indicates the signal level. The signal-
level bit indicates whether the signal is above or below arms dependant threshold S:
x(n) ="1 1" if x < S
x(n)="10" ifx e_-S,O]
x(n) = "00" if x e[O,S]
x(n) ="01" ifx > S
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https://ntrs.nasa.gov/search.jsp?R=19940023756 2020-06-16T15:03:42+00:00Z
In tile decoding process, tile signal y(n) is reconstructed as follows:
y(n) = (sign). ct.S if magnitude bit=0
y(n) = (sign). 13.S if magnitude bit=l
The parameters (Z,I_,S are chosen so as to minimize the encoding-decoding error:
f; LE= (x- Ct.S)2.p(x) dx + (x- [_S) 2.p(x) dx
where p(x) is the probability density function (pdf) of the data. In the case of SAR data,
one can assume a normal distribution N(0, 0"2). By setting £=k O, it can be shown that the optimal
choise kopt of k is given by the nlinimizer of the following function
J(k) = ..k _ (1-e-k:/2)2
2 7t.erf(k/_')
The optimal values ot'_ 13are given by:
o_op t = _(-2_.(l-e -k"2_"/2)
kopt.'C_-.erf(kopt/_")
13opt _ 1/'2-.c-k::'l"/:2
kopt.'C"ff".erfc (kopt/_-)
Therefore, BAQ consists of the following steps:
1) select N samples
2) estimate o from these samples
3) encode each sample as indicated above
The estimation of o fiom the samples is not a direct estimation: it uses a mapping fiom
the rms value to the average magnitude of the data ([1 ]): this method avoids nmltiplications and is
therefore more attractive fiom an on-board point of view.
b) Block Floating Point Quantizer
The BFPQ method was proposed originally by Joo and Held ([2]) for the Magellan
mission. As for BAQ, BFPQ uses results on gausian signals quantization: it is known ([3]) that
for a k-bit uniform quantizcr, there exists an optimal value O_pt that minilnizcs the quantization
82:
and saturation noise. The principle of BFPQ is to adapt the rms level of data to this optimal
value while decreasing the number of quantization bits. If x(i) denotes the original m-bit
quantized signal, the compressed signal y(i) is obtained by a simple division:
y(i) = x(i___))
C
The constant C is determined using the fact that:
i) y(i) Should be quantized on k bits
ii) the rms ofy is optimal
Then, it is straigtforward to show that C is given by:
C = 2.0,:
(2 k _ 1). O__'l
where Ox is the rms level of input data. The BFPQ encoding scheme consists of the following
steps:
1) acquire N samples x(i) i=l ..N
2) estimate Ox
3) calculate C
4) divide the original data by C
There exists numerous versions of this algorithm that can sirnplify it:
i) Ox can be estimated either directly either using the mapping method
ii) C is rounded to the nearest power of 2: this enables the division to become a
simple bit shift
An interesting implementation of the algorithm is to establish a direct mapping of Ox to
C's nearest power of 2. In this case, BFPQ can be resumed by:
1) acquire N samples
2) estimate the average magnitude
3) read in a table the corresponding value of tile scaling factor
This version requires only simple operations on integers and can be directly implemented
on board.
c) FFT
In this section, we propose a generalisation of the popular Discrete Cosine
Transform method of image compression ([4]) to the case of SAP, data. As a matter of fact, DCT
concerns real data and can not be applied directly to SAR data, which, by definition, is complex.
We then propose to replace tile Discrete Cosine Transform by a 2D Fast Fourier Transform
(FFT), the compression scheme being now modeled by the following figure:
83
FFT Quantization
aencoded
Figure 1: Block Diagram ofl,7;7' based SAR data compre.s:s'ion
The original image is first partitioned into NxN pixel blocks and each block is
independently transformed using the 2D Fourier Transform. The entropy of the transformed data
is then estimated and the spectrum is quantized using 8 bits of resolution: given the original
entropy, the quantization factor is chosen so that the entropy after quantization exactly matches
the desired output bit rate. It is therefore supposed that the quantizalion process is optimal. Data
is then coded using a loseless encoding algorithm (for instance, Huflinan codes): since coding is
supposed to be error free, it has not been simulated in this study. As can be seen, the algorithm
used gives the optimal performance that can be acheived by this kind of method It is to be noted
that all the computations needed for this method were run using a floating point arithmetic, the
analysis of errors due to fixed point implementation being beyond the scope of this study.
d) Presumming
The knowledge of some features of the radar signal suggests a more sensitive way to
reduce the data flow in the spectral domain In the range direction, the signal is shaped by the
chirp generation which results in the spectral signature shown in tigure 2
2.0
1.5
].o'
0.5"
- , , WN -- 1
Figure 2: range .v)ec/ral signa/ttre
84
The signaloutsidethe "top hat" shapeis noiseand doesnot needencoding.In the azimuth
direction, the signalis shapedby the antennapatternonce it hasbeenaliasedby the sampling
phenomenon.Figure3 showsanactualazimuthspectrumand,in dotted line, theactualshapeof
the antennapattern once turned from the standardangular representationto the spectral
representation.This spectral representationcannot be achieved in the real world due to
unsufficientpulserateof the instrument.As a result, the outermost contribution of the antenna
pattern is aliased in the actual spectrum. The signal can then be modelled into three parts :
- a white noise floor WN
- a useful radar signal RS
- a ambiguous radar signal AS
l,'igure 3: a,zimulh spectrum
The latter causes "ghosts" in the radar images, also called ambiguities, and should be
eliminated. Standard compression schemes cannot make out a useful signal such as RS and an
ambiguous signal AS since they have the same structure. It is also obvious that the signal to noise
ratio is systematically greater in the central part of the spectrum.
The idea of presumming [5] is therefore to have a supervised coding of the 2D Fouricr
transform of the image. There would be no coding of the range region outside the useful signal
(which results in a moderate saving of 20% or so). The coding in the azimuth spectrum would
apply only to the central part where the signal to noise ratio is the highest. The toss of signal
would amount to the vertically striped surfaces of figure 3, and the uscful signal to the
horizontally striped surface (the presommation span PS represented in figure 3 is just an
illustration, not an actual value).
Presumming could easily achieve a factor of two in data compression with a minimal
signal loss and an imprownent of the quality due to the elimination of most of the ambiguous
signal. This is true regardless of any further encoding of the conserved data.
85
lid EVALUATION CRITERIA
a) SAR data
In order to evaluate the performances of the different algorithms, a set of criteria
were developped for both SAR data and SAR image. In the following, we suppose an image of
width LX and height LY and note z(i,j) (resp. z'(i,j)) the pixel of the itn raw and the jth colurnn of
the original (resp. encoded-decoded) data. The following criteria are considered for SAR data:
Mean Square Error (MSE): MSE = --
1 LY LX 2
LX. LY _ Y'lz(i' j) - z' (i, j)
i=lj=l
Maximum error: [lz(i,j)- z'(i,j) ]E,,+,x = maxt ....
' L I o,.i)l
Phase Mean Square Error:
1 I.Y I .X 2
MSE+- ZZ d_(i,j)- _p'(i, j)[
LX. LY i=l .i=l
Peak Signal to Quantization Noise Ratio:
, [max( z(i,j)l:')]j
Average Signal to Quantization Noise Ratio: ASQNR = 10. log
] I.Y I ,X 2
Z Z z(i, J)l
LX. LY i=t .i=_
MSE
b) SAR image
An inaage acquired by ERS1 over southwest France in september 1991 was used as a
testbed for the methods described in this paper, The iillage features ocean surface, homogeneous
areas of forested or agricultural surfaces, highly contrasted areas such as the city of Bordeaux and
some individual objects which are corner reflectors (two corner reflectors were placed in low
backscatter regions) and which were shown to behave as corner reflectors (point targets).
A number of radar image quality criteria [6], which exceed the scope of this paper, were
computed in addition to more standard data compression criteria, we may cite :
86
- rangeor azimuthresolution
- integrated sideiobe ratio
- ambiguous target ratio
- standard deviation/mean ratio over homogenous areas
More details about the results of this study are available in [7].
V) APPLICATION
The four above described methods were applied to an image provided from ERSI and
representing the scene of Cazaux (France). The original data had the following characteristics:
* data precision: 5 bits per I and Q sample
* data type: unsigned byte
* data range: [0,31 ]
* data entropy: approximately 4,7 bits
* data properties: approximately Gaussian distributed with mean and rms:
m = 15.31866 +j 15.37417
a = 6.733508 + j 6.706872
* signal size: 10240 lines x 5616 complex samples
For all the methods, the image was partitioned into 128x128 blocks and each block was
independently compressed and decompressed. The encoded/decoded data was then compared to
original data by means of the above described criteria. The programs were written in Ansi C and
run on a Sparc IPX station. The following tables show the SAR data evaluation criteria:
Criterion BAQ BFPQ(5,2) FFT(5,2) PRE(5,2)
mean 15.51 +j15.56 15.23 +j15.27 15.32 +j15.37 15.32 +j15.37
rms 6.94 +j6 92 4.67 +j4.64 6.86 +j6.83 6.4 j6.,_86
MSE ....... 9.758 19.625 7.044 12.8
Ema x 6.4 1 9.487 14.56
MSE, 1.13E-I 1.17 6.65E- 1 8.36E-1
PSQNR(dB) 17.2 14.165 18.615 16.02
ASQNR(dB) 9.7 6.67 11.12 8.53
7'able I." SAR data evaluation criteria for 2 bit compression
87
Criterion BFPQ(5,3) FFT(5,3) PRE(5,3) PRE(5,3)
no coding
mean 15.31 +j 15.35 15.32 +j 15.37 15.32 +j 15.37 15.32 +j 15.37
rms 5.7 +j 5.7 6.76 +j 6.74 5.23 +j 5.22 5.89 +j 5.88
MSE 5.28 1.8s 9.957 19.048
Ema x 1 5.385 13.93 17.09
MSE¢ 7.11 E- 1 3.573E-1 7.41 E- 1 9.547E- 1
PSQNR(dB) 19.87 24.42 17.11 14.294
ASQNR(dB) 12.37 16.92 9.62 6.8
Table II." SAR data evaluation criteria for 3 bit compression
Concerning SAR data, it seems that the FFT provides either for 2 or 3 bits the best
results. Nevertheless, in the case of 2 bit compression, BAQ is shown to perform nearly as well as
FFT: more, the computational requirements for BAQ are very inferior compared to FFT.
Consequently, for a 2 bit compression scheme, BAQ seems to provide the best trade-off between
performance and complexity. In the case of 3 bit compression, it is more difficult to establish a
hierarchy between the methods: if FFT is shown to have the best performances, this algorithm is
more complicated than BAQ, BFPQ and Presumming with no coding.
The major conclusions of SAR image criteria [7] could be itemized below "
- all algorithms produce errors on the phase of image pixei,
- FFT algorithm reproduces images better than the other algorithms,
- Presumming algorithm is a very interesting algorithm : its performance is very
near to FFT (its complexity is lower),
- BFPQ (5,3) and BAQ (5,2) are however very similar to FFT in terms of image
quality for a city.
The images before and at2er compression-decompression can be found at the end of the
paper.
V) CONCLUSION
We have presented in this paper four compression algorithms for raw SAP, data. These
algorithms have been developped in C language on a SUN station. Their performances have been
studied and compared through image quality criteria, data criteria and complexity criteria on data
supplied from ERS-1. The choice of the best algorithm (specially for space on-board application)
is indeed a trade-offbetween performance and complexity.
References:
[1] R.Kwok,W.T.K.Johnson, "Block Adaptive Quantization of Magellan SAR Data", IF_EE
Trans. Geo. Remote Sensing, vol 27, n°4, pp 375-383, July 89
[2] T.H.Joo,D.N.Held, "An Adaptive Quantization Method for Burst Mode Synthetic Aperture
Radar Data", IEEF, hst. Radar Col_, pp 385-390, 1985
[3] G.A.Gray, G.W.Zeoli, "Quantization and Saturation Noise Due to Analog-to-Digital
Conversion", IEEE Trans. Aerospace Electronic Systems, pp 222-223, Jan 71
[4] M.Rabbani,P.W.Jones, Digital Image Compressioo Techniques, Donald O'Shea
Editors, 1991
[5] D, Massonnet ,"lnt6r& d'une Pr6sommation embarqu6e sur un syst6me SAR", hlteroal
memo CT/IA/QTIS/PR, n° 178 6-3-1992
[6] D. Massonnet, "Radar Image Quality White Paper", Proc. of the SAR cafibration workshop
Oberpfaffenhofen, Germany, October 9th-1 lth 1991
[7] B. Rogron ,"Compression des donn6es brutes SAR et Qualit6 des Images synth6tis6es",
lnternal memo CT/IA/QTIS/PR n°646 18-10-1993
Figure 4: Reference image from ERS-1
89
Figure 5." lmage after 2 bit compression and decompression
9O
Figure 6." Image after 3 bit compression and decompression
91



A comparative study of SAR data compression schemes

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