Homomorphic deconvolution of medical ultrasound images using a Bayesian model for phase unwrapping

Radial homomorphic deconvolution algorithms for medical ultrasound images based on the complex cepstrum or the generalized cepstrum are the best of several cepstral deconvolution methods. However, the frequency domain phase unwrapping, which is an essential part of both methods, is sensitive to the stochastic noise that always degrades sensor data. The sensitivity causes variable spatial and gray scale resolution in image sequences following deconvolution. This paper introduces a robust Bayesian phase unwrapping method using a Markov random field model. The prior regularizing term accounts for the noise. The phase unwrapping is formulated as a least mean squares optimization problem. The optimization is done non-iteratively by solving a differential equation using the cosine transform. The ordinary complex cepstrum and the generalized cepstrum methods with the new phase unwrapping procedure were compared to the same methods with the standard phase unwrapping procedure, and to the logarithmic derivative cepstrum method. Both radial and lateral deconvolution were tested on several sequences of in vivo ultrasound images recorded with a 5.0 MHz or a 3.25 MHz probe. The homomorphic deconvolution methods, with the Markov model based phase unwrapping gave images with the same degree of deconvolution through the sequence and better spatial resolution and gray scale resolution than the old methods.