Logarithmic Compression Methods for Spectral Data

Abstract

A companding operation applied to the homomorphic data output from a Gabor processor. This system avoids suppression of additive signal components, while gaining the benefits of constant relative precision that a logarithmic transform affords. The result is a compandor system that uses the common properties of images and signals and that can be run at a wide variety of compression ratios, depending on tolerable degradation of the information.

Description

Modern communications have a need to transmit increasingly large amounts of data through transmission channels that are constrained in time and frequency range. The general term for this problem is data compression and expansion, or "companding." Algorithms and hardware that deal with companding must address the properties of images, audio, data, and RF communication signals. The present invention deals with a "lossy" companding algorithm, which is suited to the transmission of images, audio, and RF signals, but not to binary computer data, where a lossy scheme can result in an unacceptable high bit error rate. 

Sensor derived data often divides into two classes: those that provide constant absolute precision regardless of input level, and those where the desired data is actually a modulation of an underlying brightness, generating a constant relative precision. Most images are high frequency contrast modulations of an underlying scene brightness, where the contrast modulation remains much smaller than the total brightness range seen over the entire observation time. Similarly, most RF signals are intentionally modulated as the mathematical product of the information and an underlying carrier, whose brightness can vary dramatically upon reception. Therefore, the great majority of practical sensor applications are multiplicative modulation processes, and only require constant relative precision. This, in turn, implies that either floating point or logarithmic representations may be used without loss of resolution, as long as they are properly scaled. 

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