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Recently, several blind cepstral deconvolution methods for medical ultrasound images were compared experimentally. The results indicated that the generalized cepstrum or the complex cepstrum with phase unwrapping give the blind homomorphic deconvolution algorithms with the best performance. However, the frequency domain phase unwrapping for pulse estimation, which is an essential part of both methods, is sensitive to the sensor noise when the values of the spectrum are small due to the randomness of the tissue response. The noise introduces abrupt changes in the phase. The phase degradation due to the noise causes variable spatial and gray scale resolution in image sequences following deconvolution. This paper introduces a noise robust Bayesian phase unwrapping method using a noncausal Markov random chain model. The prior regularizing term accounts for the noise and smoothes the phase. The phase unwrapping is formulated as a least mean square optimization problem. The optimization is done noniteratively by solving a difference equation using the cosine transform. The resulting improvement in radial and lateral blind deconvolution is demonstrated on six short ultrasound image sequences recorded in vitro or in vivo.