Relation between entropys of spatial and frequency domain

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SUMMARY

The discussion focuses on the measurement of entropy in visual data, specifically comparing spatial domain entropy with frequency domain entropy obtained through Discrete Cosine Transform (DCT). The user notes a discrepancy between the entropy values calculated from pixel data and those derived from DCT coefficients. They seek clarification on the relationship between these two forms of entropy, referencing Parseval's theorem as a potential connection. The user has not found satisfactory explanations in existing literature or online resources.

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  • Understanding of entropy in information theory
  • Familiarity with Discrete Cosine Transform (DCT)
  • Knowledge of spatial and frequency domain concepts in signal processing
  • Basic grasp of Parseval's theorem
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  • Explore the implications of Parseval's theorem in relation to signal energy
  • Investigate the differences between spatial and frequency domain representations of images
  • Examine case studies or papers on entropy measurement in image compression techniques
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Researchers, signal processing engineers, and data scientists interested in image analysis, compression algorithms, and the theoretical underpinnings of entropy in visual data.

Chriszz
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Dears,

I wish to measure the entropy of visual data such as image and video.
I did transform these image and videos into frequency domain such as DCT, then measured the entropy with these pdfs for each AC components of image and videos.

However, when I measured the entropy over spatial domain such as pixel, this entropy is differ to the entropy from DCT domain.

What is the relationship between the entropy of spatial and frequency domains? (Such as Parseval's theorem)
I couln't find this relation in the textbook for signal processing or the google.

Please give a comments for this relation.

Thanks!
 
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