On the homomorphic filtering by channels´ summation

A simple method to reduce the speckle in the multichannel SAR images consists in channel summation. Developed, originally, for the multi-look treatment, this method may be used also for other multi-channel images, if features´ integrity is not a first concern. In the case of the multi-temporal sets, the channel summation leads, usually, to a non-uniform speckle reduction. This nonstationarity of the residual noise is a negative effect since it excludes a series of speckle specific treatments that could be applied subsequently. Our paper shows that this drawback can be removed if the summation is realised in the homomorphic space. More precisely, by taking the logarithm of the images, before summation, and the exponential, subsequently, we obtain a uniformly denoised image, disregarding the channels´ content. We give the mathematical support for the calculation of the coefficient of variation of the residual noise in the case of the homomorphic summation, and we test our result by comparing this theoretical value with the coefficient measured with the radial sector method.