Abstract

This work focuses on estimating the information conveyed to a user by multi-dimensional digitised signals. The goal is establishing the extent to which an increase in radiometric resolution, or equivalently in signal-to-noise ratio (SNR), can increase the amount of information available to users. Lossless data compression is exploited to measure the “useful” information content of the data. In fact, the bit-rate achieved by the reversible compression process takes into account both the contribution of the “observation” noise, i.e. information regarded as statistical uncertainty, whose relevance is null to a user, and the intrinsic information of hypothetically noise-free samples. Once the parametric model of the noise, assumed to be possibly non-Gaussian, has been preliminarily estimated, the mutual information between noise-free signal and recorded noisy signal is easily estimated. However, it is desirable to know what is the amount of information that the digitised samples would convey if they were ideally recorded without observation noise. Therefore, an entropy model of the source is defined and such a model is inverted to yield an estimate of the information content of the noise-free source from the code rate and the noise model. Results are reported and discussed both on a simulated noisy image and on true hyperspectral data (220 spectral bands) recorded by the AVIRIS imaging spectrometer.

Keywords: Airborne Visible/InfraRed Imaging Spectrometer (AVIRIS); Correlation analysis; Generalised Gaussian PDF; Hyperspectral imagery; Information-theoretic assessment; Lossless compression; Multivariate regression; Noise estimation; Noise modelling; Parametric entropy modelling

Article Outline

1. Introduction

2. Information-theoretic problem statement

3. Information assessment procedure

3.1. Noise modelling

3.2. Source de-correlation via DPCM

3.3. Entropy modelling

3.4. Generalised Gaussian PDF

3.4.1. Higher-order moment method

3.4.2. Mallat's method

3.4.3. Entropy matching method

3.5. GG modelling of correlated noise

3.6. Information-theoretic assessment

4. Experimental results

4.1. Simulated data

4.2. AVIRIS hyperspectral data

5. Concluding remarks

Acknowledgements

References