ISPRS COMMISSION II SYMPOSIUM (WG II.5)
Baltimore, Maryland, U.S.A.
May 26-30, 1986
Rate distortion functions of SAR imagery
R.W. Okkes
European Space Research & Technology Center (ESTEC)
Noordwijk, The Netherlands
W. Huisman
National Aerospace Laboratory (NLR)
Emneloord, The Netherlands
INTRODUCTION
As a result of digital processing operations SAR imagery is commonly
represented by time discrete quantized samples (or pixels), where
quantization inevitably introduces distortion of the imagery data.
This paper investigates optimum encoding and processing schemes which
provide the minimum number of bits per pixel representation for a given
amount of encoder induced quantization distortion.
The main parameters which efect the bit per pixel versus disortion
relationship are image characteristics, the speckle reduction algorithm
(if applied) and the encoder performance. The encoder and processing
Scheme analyzed in this paper consists of an optimum encoder, performing
according to rate distortion theory, preceded and followed by two-
dimensional linear arbitrary complex filters, which may represent speckle
suppression processing or any other processing operation applied.
Evaluation results of the minimum bit/pixel versus distortion relationship
are given for representative SAR imagery generated by a two dimensional
first order Gaussian-Markov ground model, in case of applying either an
optimum pre- or post filter, where both type or filters optimally suppress
the inherent speckle noise.
Also results are provided using a practical encoding scheme.
IMAGE CHARACTERISTICS
As shown by Raney [1] the pixel intensity [i(x,y)] of a multi-look SAR
image, optimally processed with non-overlapping subapertures, can be
represented accurately by:
L 0 2
Cy] - ZE [{ro)+ A} * A, (X, y) x K:(xy)/ (1)
where,
xy = Image sample coordinates
r(x,y) = Speckle average ground reflectivity signal
Mn = Equivalent thermal noise power
nj(x,y)= Complex Gaussian noise variable (unit power)
Ki(x,y)= Two dimensial Fourier transform of the weighting function
effected by the SAR sensor antenna pattern and the i-th look
subaperture filter
L - Number of looks applied.
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