# Lossless compression of synthetic aperture radar images Page: 3 of 5

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equalization, it is used as a one-step predictor.

This method should be useful in particular for

SAR magnitude images, which have a rayleigh-

shaped pixel distribution, as the RLSL is very

effective at decorrelating data and providing a

residue with gaussian characteristics. The latter is a

simpler source model to manipulate. Similarly,

a linear predictor (with fixed least-squares

coefficients) [4] can be utilized to transform input

image data into a residue sequence with gaussian

characteristics.

Other methods proposed for lossless

image compression involve the frequency domain

representation of the image. In [5], the DCT was

performed on image blocks, a subset of the DCT

coefficients were retained, and then an error

residual was formed by taking the difference

between the original data block and its lossy

reconstruction (formed from the retained

coefficients). The DCT itself has proven useful

for lossy compression of SAR imagery [6], due to

its ability to compact low frequency information

into a few coefficients. However, the loss of high

frequency detail in lossy DCT schemes (e.g.

JPEG) can lead to severe distortion [7].

Therefore, lossless schemes based on the DCT are

attractive.

3. ENTROPY CODING

Entropy coding is a useful, fully-

reversible method for data compression. The aim

of entropy coding is to reduce the size of the

input data sequence to its overall entropy, which

can be thought of as a theoretical limit to the data

sequence's compressibility. One of the most

popular methods for entropy coding is arithmetic

coding, which basically involves mapping strings

of symbols to the interval of real numbers

between 0 and 1. The arithmetic coding method

proposed in [8] is often used due to its capability

for incremental transmission and its lack of

overhead in the form of a symbol frequency

table. However, as the quantization of the input

increases past 12 bits (often seen in SAR

imagery), the internal memory requirements for

this method become cumbersome. A

modification has been proposed in [9] to address

this issue, in which an interval frequency table is

formed, rather than a symbol frequency table.

Arithmetic coding has also been shown to provide

near-optimal results for gaussian data [8].

Another type of entropy encoder uses

variable-length codewords to reduce entropy,

assigning shorter codewords to symbols which

have a greater probability of occurrence. One

such method under development at SandiaNational Labs for use with complex SAR imagery

takes advantage of the gaussian shape of the in-

phase and quadrature pixel distribution. An

image's clutter standard deviation is estimated;

those pixels whose values fall within a certain

number of standard deviations of the mean are

termed clutter, and those without are non-clutter.

This models the data as a 2-state discrete

memoryless source. The clutter pixels are

encoded with a sufficient number of bits to meet

their dynamic range, while the non-clutter pixels

are transmitted as is. This method can be

employed in a lossless scheme, as it was for this

paper, or as a lossy technique when it is necessary

to transmit man-made objects (i.e., pixel values

farther from the mean) without loss, while clutter

may be quantized with fewer than the number of

bits necessary.

A third entropy coding technique is bi-

level sequence coding, presented in [4]. This

method, developed for white gaussian residue

sequences, is a type of run-length code. The

residue sequence is encoded into an alternating

sequence of two different "levels", based on the

number of bits required to represent successive

consecutive runs of residue values. This should

prove useful with SAR images as the vast majority

of pixels in an image fall within a small range of

low pixel values, which may provide long runs of

the lower level.

4. SIMULATIONS

In order to see the effectiveness of

different lossless compression techniques on SAR

imagery, various techniques were applied to 9

image swaths (820x226 pixels) in the form of

either 16-bit magnitude or 32-bit complex (in-

phase and quadrature) data. The methods used

were the DCT-based method described in [5]

(using the arithmetic coder described in [9]), the

arithmetic coder from [9] without any

preprocessing, the bilevel coding scheme using a

linear predictor to generate the gaussian residue

sequence described in [4] as well as the linear

predictor of [4] followed by the arithmetic coder

of [9], the 2-state discrete memoryless source

technique (lossless case) and the RLSL method

described in [10] (also using the arithmetic coder

described in [9]). The criteria used for

comparison was the compression ratio, which is

simply the size of the input file (in bytes) divided

by the size of the output (compressed) file. Also

included is the theoretical compression limits,

calculated for magnitude data by modeling it as a

rayleigh distribution with the rayleigh parameter

computed empirically, and by modeling the real

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Ives, R.W.; Magotra, N. & Mandyam, G.D. Lossless compression of synthetic aperture radar images, article, February 1, 1996; Albuquerque, New Mexico. (digital.library.unt.edu/ark:/67531/metadc666534/m1/3/: accessed January 22, 2019), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.