Parameter Selection for Regularized Electron Tomography Without a Reference Image

Regularization has been introduced to electron tomography for enhancing the reconstruction quality. Since over-regularization smears out sharp edges and under-regularization leaves the image too noisy, finding the optimal regularization strength is crucial. To this end, one can either manually tune regularization parameters by trial and error, or compute reconstructions for a large set of candidate values and compare them to a reference image. Both are cumbersome in practice. In this paper, we propose an image quality metric Q to quantify the reconstruction quality for automatically determining the optimal regularization parameter without a reference image. Specifically, we use the oriented structure strength described by the highest two responses in orientation space to simultaneously measure the sharpness and noisiness of reconstruction images. We demonstrate the usefulness of Q on a recently introduced total nuclear variation regularized reconstruction technique using simulated and experimental datasets of core-shell nanoparticles. Results show that it can replace the full-reference correlation coefficient to find the optimal. Moreover, observing that the curve of Q versus has a distinct maximum attained for the best quality, we adopt the golden section search for the optimum to effectively reduce the computational time by 85%.