Denoising and compression of data with Gaussian errors

1 Denoising and compression of data with Gaussian errors 

FIR filtering. Finite impulse response (FIR) filters are linear low-pass filters which can be represented as 

The mean filter can also be thought of as a convolution of the measured signal with a vector of I constant coefficients, each equals l/I. A schematic diagram of the weights used by a mean filter of length I = 5 is shown in Fig. 3(a). 

Nonlinear filtering techniques have been developed to overcome the inability of linear filters to capture features at different scales. Nonlinear filtering methods include FIR-Median Hybrid filtering and multiscale filtering, and 

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