Predicting the lossless compression ratio of remote sensing images with configurational entropy

Abstract

Compression of remote sensing images is beneficial to both storage and transmission. For lossless compression, the upper and lower limits of compression ratio are defined by Shannon's source coding theorem with Shannon entropy as the metric, which measures the statistical information of a dataset. However, the calculation of the actual Shannon entropy of a large image is not an easy task, which limits the practicality of predicting the lossless compression ratio with Shannon entropy. On the other hand, most recently developed compression techniques take into consideration the configurational information of images to achieve a high compression ratio. This leads us to hypothesize that a metric capturing configurational information can be employed to build mathematical models for predicting compression ratios. To test this hypothesis, a two-step investigation was carried out, i.e., to find the most suitable metric through extensive experimental tests and to build a model upon this metric. A total of 1850 8-b images with 15 compression techniques were used to form the experimental dataset. First, 29 metrics were analyzed in terms of correlation magnitude, distinctiveness, and model contribution. As a result, the configurational entropy outperformed the rest. Second, six configurational entropy-based prediction models for predicting the compression ratio were established and tested. Results illustrated that these models work well. The PolyRatio model with 9.0 as a numerator, which was in a similar form to Shannon's theorem, performed best and was thus recommended. This article provides a new direction for building a theoretical prediction model with configurational entropy.