Least squares deconvolution in wavelet domain for 1/f driven LTI systems

In this paper we propose a least squares deconvolution method in the wavelet domain for linear time-invariant (LTI) systems with 1/f type input signals. We model the output of the system as convolution of the impulse response and the input signal, which exhibits 1/f type spectral behavior. Our aim in solving the deconvolution problem is to estimate a filter which approximates the inverse of the impulse response, so that by applying this filter to the output data we can estimate the input signal. In order to achieve this objective, we use the wavelet transform and its properties for 1/f signals, where the logarithm of the variance of the wavelet coefficients in each stage progresses linearly. We define an error criterion in the wavelet domain whose minimization yields the optimum inverse filter. We present the error minimization algorithm and the simulation results.