Noise robust one-dimensional deconvolution of medical ultrasound images

Abstract

Homomorphic filtering can be used for blind deconvolution of signals which are located in separate time bands in the cepstrum domain. However, in the literature the noise sensitivity of this filtering is frequently mentioned as a problem for its application to real signals. The noise sensitivity has its origin in the ill-posed problem of frequency domain phase unwrapping, or equivalently, in the computation of the derivative of the signal in the frequency domain. To make the phase-unwrapping well-posed, we implemented a Markov model based Bayesian method for noise robust one-dimensional (1D) phase unwrapping. A prior regularization term was used to model the stochastic noise. The resulting homomorphic filtering method was used for blind deconvolution of medical ultrasound images. Visual evaluation of ultrasound image sequences processed with this new method showed that Markov model based 1D phase unwrapping within a Bayesian framework in the frequency domain improves the best homomorphic deconvolution methods substantially.