In this paper, we study the potential of the quaternionic wavelet transform for the analysis and processing of multispectral images with strong structural information. This new representation gives a very good division of the coefficients in terms of magnitude and three-phase angles and generalizes better the concept of analytic signal to image. Furthermore, it retains the property of shift invariant and directivity. We show an application of this transform in satellite image denoising. The proposed approach relies on the adaptation of thresholding procedures based on the dependency between magnitude quaternionic coefficients in local neighborhoods and phase regularization. In addition a non-marginal aspect of multispectral representation is introduced. Thanks to coherent analysis provided by the quaternionic wavelet transformation, the results obtained indicate the potential of this multispectral representation with magnitude thresholding and phase smoothing in noise reduction and edge preservation compared with classical wavelet thresholding methods that do not use phase or multiband information.

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Abstract-In this paper, we study the Doppler effect on a GPS(Global Positioning System) on board of an observation satellite that receives information on a carrier wave L1 frequency 1575.42 MHz .We simulated GPS signal acquisition. This allowed us to see the behavior of this type of receiver in AWGN channel (AWGN) and we define a method to reduce the Doppler Effect in the tracking loop which is wavelet de-noising technique.

In Global Positioning System (GPS), receivers use FFT-based convolvers to acquire the signals. This paper shows a robust substitute algorithm for calculating the convolution that is less sensitive to additive noise.