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Mutual Information Loss in Pyramidal Image Processing

by Jerry Gibson *,‡ and Hoontaek Oh
Department of Electrical and Computer Engineering, University of California, Santa Barbara, CA 93106-9560, USA
*
Author to whom correspondence should be addressed.
This paper is an extended paper presented at the Multimedia Information Processing and Research conference in San Jose, CA, USA, in April 2019.
These authors contributed equally to this work.
Information 2020, 11(6), 322; https://doi.org/10.3390/info11060322
Received: 19 May 2020 / Revised: 2 June 2020 / Accepted: 4 June 2020 / Published: 15 June 2020
Gaussian and Laplacian pyramids have long been important for image analysis and compression. More recently, multiresolution pyramids have become an important component of machine learning and deep learning for image analysis and image recognition. Constructing Gaussian and Laplacian pyramids consists of a series of filtering, decimation, and differencing operations, and the quality indicator is usually mean squared reconstruction error in comparison to the original image. We present a new characterization of the information loss in a Gaussian pyramid in terms of the change in mutual information. More specifically, we show that one half the log ratio of entropy powers between two stages in a Gaussian pyramid is equal to the difference in mutual information between these two stages. We show that this relationship holds for a wide variety of probability distributions and present several examples of analyzing Gaussian and Laplacian pyramids for different images. View Full-Text
Keywords: Gaussian pyramids; Laplacian pyramids; pyramidal image processing; multiresolution image processing; log ratio of entropy powers Gaussian pyramids; Laplacian pyramids; pyramidal image processing; multiresolution image processing; log ratio of entropy powers
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Gibson, J.; Oh, H. Mutual Information Loss in Pyramidal Image Processing. Information 2020, 11, 322.

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