A Theory for Multiresolution Signal Decomposition: The Wavelet Representation
IEEE Transactions on Pattern Analysis and Machine Intelligence
What does the retina know about natural scenes?
Neural Computation
What is the goal of sensory coding?
Neural Computation
Digital images and human vision
Multiresolution Signal Decomposition: Transforms, Subbands, and Wavelets
Multiresolution Signal Decomposition: Transforms, Subbands, and Wavelets
Digital Coding of Waveforms: Principles and Applications to Speech and Video
Digital Coding of Waveforms: Principles and Applications to Speech and Video
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The second-order statistics of natural images can be well characterized by a "self-similar" I/F2 power spectrum and the bandpass decomposition in biological vision systems is characterized by a self-similar, wavelet-like structuring of the "frequency channels". It has thus often been suggested that there might exist a systematic interrelationship between these two properties, but a complete formal derivation of this relation has not yet been provided. Using rate-distortion arguments and a complexity measure, we first show that a self-similar bandpass decomposition can achieve a desired level of distortion with a less complex system structure than required for a decomposition in bands of equal linear bandwidth. A closer analysis reveals that the true optimum decomposition is approximately selfsimilar but shows a systematic decrease of the logbandwidths with increasing center frequency of the subbands. Since this effect has also been observed in neurophysiological experiments, we conclude that the typical properties of visual neurons may infact result from an optimized exploitation of the statistical redundancies of the natural environment.