Noise of a multiplicative nature is encountered in many applications such as coherent imaging, remote sensing and signal processing for communication systems. This thesis is concerned with the problem of reducing the multiplicative noise corrupting a signal. A generalization of the existing sampled function weighted order (SFWO) filter is proposed by relaxing the symmetry condition for the probability density function (PDF) of the noise to the filter. This generalized SFWO (GSFWO) filter is then used within a homomorphic system to reduce the multiplicative noise. It is shown that the output from such a system is biased, and hence, a suitable bias compensation technique is suggested. An unbiased homomorphic system, whose design is based on the PDF of the corrupting multiplicative noise, is proposed to reduce the noise. Images and videos generated by coherent imaging systems are always corrupted by speckle, which is a multiplicative noise having a lognormal distribution. A filter called the mean median (MM) filter to reduce additive white Gaussian noise (AWGN) is first proposed and this filter is then used within the unbiased homomorphic system to reduce the speckle in images. Fast filters to reduce AWGN in videos are also proposed in this thesis. Novel techniques for temporal estimation employing a change detection technique to determine the interframe motion are developed for their use in these filters. A new method is proposed to appropriately combine the spatial and spatiotemporal estimates of the original signal in order to obtain the final output. Finally, the MM-filter along with a novel temporal estimation scheme are used within the unbiased homomorphic system to reduce the speckle in videos. The effectiveness of the various proposed algorithms is demonstrated and compared with that of some of the existing schemes through extensive simulation
