New advances within the recently rediscovered field of Compressed Sensing (CS) have opened for a great variety of new possibilities in the field of image reconstruction and more specifically in medical image reconstruction. In this work, a new approach using a CS-based algorithm is proposed and used in order to solve limited-angle problems (LAPs), like the ones that typically occur in computed tomography or electron microscope. This approach is based on a variant of the Robbins-Monro stochastic approximation procedure, developed by Egaziarian, using regularization by a spatially adaptive filter. This proposal consists on filling the gaps of missing or unobserved data with random noise and enabling a spatially adaptive denoising filter to regularize the data and reveal the underlying topology. This method was tested on different 3D transmission electron microscope datasets that presented different missing data artifacts (e.g, wedge or cone shape). The test results show a great potential for solving LAPs using the proposed technique.
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