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Spectral estimation is a major component in studies aiming at characterizing biological tissues through the analysis of backscattered radio frequency (RF) ultrasonic signals and images. However, conventional spectral estimation techniques yield a well-known trade-off between spatial resolution and variance. The backscattered signals are stochastic by nature, so short-term local analysis results in a high variance of the estimates, which cannot efficiently be reduced through conventional spatial averaging. We address this issue by describing a spectral estimation technique that reduces the variance of the estimates (by smoothing the local estimates in spectrally homogeneous regions) while preserving spectral discontinuities (i.e., the smoothing is not performed across regions with different spectral contents). The proposed approach is set in a Bayesian framework and is based on local autoregressive (AR) estimation, constrained by smoothness priors. These smoothness priors are introduced through a Markov random field in which the associated potential functions are nonquadratic, allowing thereby to preserve discontinuity. The method is validated on simulated RF images and tested on echocardiographic images acquired in vivo. The results are compared to the estimates provided by the conventional Burg technique. These results clearly demonstrate the ability of the proposed approach to improve spectral estimation in terms of variance reduction and discontinuity detection.