Techniques which exploit properties such as sparsity and total variation have provided the ability to reconstruct images that surpass the conventional limits of imaging. This leads to difficulties in assessing the result, as conventional metrics for resolution are no longer valid. We develop a numerical approach to evaluating the second-order statistics of the estimate by relating a confidence interval on the solution to a confidence interval on a pixel value, and from this we formulate an approach to estimating the spatial resolution. With this estimate, we can calculate the resolution at each point subject to chosen bounds on the desired precision and confidence.
We demonstrate the method for limited-angle tomographic reconstructions utilizing nonnegativity, sparse regularization, total-variation minimization, and their combinations. This provides a means to visualize and understand the effect on the image inherent in these penalties and constraints. Examples are provided using simulated data for different methods, and the results are shown to agree with resolution calculated empirically via the local edge response.
K. Dillon, Y. Fainman, and Y.-P. Wang, “Computational estimation of resolution in reconstruction techniques utilizing sparsity, total variation, and nonnegativity,” J. Electron. Imaging, vol. 25, no. 5, pp. 053016–053016, 2016. (pdf)