Homomorphic filtering is a generalized technique for signal and image processing, involving a nonlinear mapping to a different domain in which linear filter techniques are applied, followed by mapping back to the original domain.
This concept was developed in the 1960s by Thomas Stockham, Alan V. Oppenheim, and Ronald W. Schafer at MIT[1] and independently by Bogert, Healy, and Tukey in their study of time series.
Illumination variations can be thought of as a multiplicative noise, and can be reduced by filtering in the log domain.
[3] Homomorphic filtering can be used for improving the appearance of a grayscale image by simultaneous intensity range compression (illumination) and contrast enhancement (reflection).
Where, m = image, i = illumination, r = reflectance We have to transform the equation into frequency domain in order to apply high pass filter.
Thus homomorphic filtering happens accidentally (unintentionally) whenever we process pixel values f(q) on the true quantigraphic unit of light q.
[5] [6] [7] [8] Homomorphic filtering is used in the log-spectral domain to separate filter effects from excitation effects, for example in the computation of the cepstrum as a sound representation; enhancements in the log spectral domain can improve sound intelligibility, for example in hearing aids.
[10] How individual neurons or networks encode information is the subject of numerous studies and research.
[11][12] Time encoding consists of altering the random inter-spikes intervals (ISI) of the stochastic impulse train in output from a neuron.
The ISI variations were caused by an input sinusoidal signal of unknown frequency and small amplitude, i.e. not sufficient, in absence of noise to excite the firing state.
The frequency of the sinusoidal signal was recovered by using homomorphic filtering based procedures.
Stockham "Nonlinear Filtering of Multiplied and Convolved Signals" Proceedings of the IEEE Volume 56 No.