Adaptive learning of tissue reflectivity statistics and its application to deconvolution of medical ultrasound scans

Image deconvolution is an important post-processing methodology allowing a substantial improvement it terms of both the resolution and contrast of medical ultrasound scans. Unfortunately, the intrinsic bandlimitedness of ultrasound scanners renders the problem of image deconvolution ill-posed, and, as a result, the latter rarely admits a stable and unique solution, unless properly regularized. To be successful, the regularization needs to properly reflect the actual reflectivity properties of insonified tissues. Unfortunately, the inherent complexity of biological tissues makes it extremely difficult (if at all possible) to justify the use of a single statistical model for the description of their acoustic reflectivity structure. Thus, for example, Gaussian and Laplacian statistical priors can provide adequate description of the characteristics of diffusive scattering and specular reflection, respectively, while yielding inaccurate estimates when either of the two is used exclusively for concurrent description of both reflectively types. To overcome this difficulty, we propose to use a concomitant scale estimation framework, which allows one to learn the parameters of a prior model along with its associated reflectivity properties directly from the data. The proposed method is formulated in the form of a convex optimization problem that admits a unique and efficiently computable solution.