Wavelet signal estimation in coloured noise with extension to transfer function estimation

For the estimation of inhomogeneous signals in noise, the nonlinear technique of wavelet thresholding has become popular. It has provably superior properties to linear methods. However the method is severely affected by coloured noise. Here we reformulate wavelet thresholding as an L₁ regularised least squares problem and then extend that formulation to handle coloured noise. We use a modification of the CLEAN algorithm of radiophysics to solve the resulting L₁ optimisation problem. We also apply our method to transfer function estimation in coloured noise with Kautz type models and nonwhite input signals