Data compression and storage formats

In order to deal efficiently with data from the AIRSAR and SIR-C polarimetric radars, scientists at the Jet Propulsion Lab (JPL) sought a way of storing and distributing the data that was simple, compact and contained all the essential information for data interpretation and classification. Rather than storing the four complex elements of the scattering matrix, possibly using 32 bytes per pixel, they chose the Stokes

Did you Know?

Did you know that the Stokes and covariance matrices contain phase information, even though they are power representations? This is because the cross terms such as the expected value of (Ehh Evv*) are complex numbers, and the angle of the complex number depends upon the phase angle between the HH and VV channels.

(Kennaugh) matrix for the AIRSAR data, and compressed each sample (or group of averaged samples) into a 10-byte word. Other radar systems have used the covariance matrix for data compression Boerner et al, page 292.

In the JPL scheme, the total power of each sample is computed and stored in 2 bytes, one for the mantissa and one for the exponent. The remaining 8 unique elements of the Stokes matrix are normalized by the top left element, M11, and stored in 1 byte each. The four smallest of these, related to the cross-products of the co-pol and cross-pol channels, are square rooted as well. The original elements of the Stokes matrix are easily recovered from the stored values Dubois & Norikane.

With higher storage capacities becoming available, it is possible to store the full scattering (Sinclair) matrix for each sample, without averaging to reduce the data volume. More sophisticated methods of compressing radar image data have been developed for single channel data, e.g. based upon the DCT or wavelets, but these methods have not been fully tested on polarimetric data yet.

Whiz quiz

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Question 1: What is meant by a "scattering mechanism"? The answer is...

Question 2: How is a "scattering mechanism" defined? The answer is...

Question 3: Why is the covariance matrix considered to be a "power" representation? The answer is...

Whiz quiz - answer

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Answer to question 1: Every feature or structure on the ground scatters radar energy in a certain way. Examples are water, a cornfield, a farmhouse, or a car. Most of these features scatter energy in a different way from the others. The term "scattering mechanism" is an attempt to characterize the scattering from a given feature in terms of simple elements for which we know or can model the scattering behaviour. Examples of scattering mechanisms are a sphere, a dihedral, a helix, and composite scatterers such as a random distribution of dipoles.

Answer to question 2: There are two basic ways of defining a "scattering mechanism". The first is to create a physical model of a scatterer, such as a dipole or a trihedral corner reflector. Then mathematical and physical principles (such as Maxwell's equations) are used to derive how the EM waves scatter off the surface. The scattering is then expressed as a scattering matrix, or its derivatives such as the Stokes or covariance matrix. The term "mechanism" refers to the elemental scatterer or model, plus its associated mathematical definition of scattering behaviour.

The second method is to make an explicit measurement of the scattering, either in the field or under laboratory conditions (e.g. in an anechoic chamber). In this case, the measured echo is usually made up of a number of elemental mechanisms, and mathematical procedures have been developed to separate the signal into its constituent components (e.g. eigenvalue decomposition of the coherency matrix). Each component is then referred to as a scattering mechanism, and hopefully can be related to a physical model mentioned in the previous paragraph.

Answer to question 3: Because the scattering matrix elements relate the "voltage" of the scattered EM wave (the Electric Field strength) to the "voltage" of the incident wave, and the covariance matrix is formed from "products" of these elements. In other words, the covariance matrix relates the power of the scattered EM wave to the power of the incident wave.