To increase the temporal resolution and maximal imaging time of super-resolution (SR) microscopy, we have developed a deconvolution algorithm for structured illumination microscopy based on Hessian matrixes (Hessian-SIM). It uses the continuity of biological structures in multiple dimensions as a priori knowledge to guide image reconstruction and attains artifact-minimized SR images with less than 10% of the photon dose used by conventional SIM. Hessian-SIM enables spatiotemporal resolution of 88 nm and 188 Hz, and hour-long time-lapse SR imaging of actin filaments in live cells. Finally, we observed the structural dynamics of mitochondrial cristae and structures that, to our knowledge, have not been observed previously, such as enlarged fusion pores during vesicle exocytosis.
Penalized weighted least-squares (PWLS) iterative algorithm with a total variation penalty (PWLS-TV) has shown potential to improve cone-beam CT (CBCT) image quality, particularly in suppressing noise and preserving edges. However, it sometimes suffers from the well-known staircase effect, which produces piece-wise constant areas in images. In order to remove the staircase effect, there is an increasing interest in replacing TV by higher-order derivative operations such as Hessian. Unfortunately, Hessian tends to blur the edges in the reconstruction results. In this study, we proposed a new penalty, namely the TV-H penalty, which combines the TV penalty and the Hessian penalty for CBCT reconstruction. The TV-H penalty retains some of the most favorable properties of the TV penalty like suppressing noise and preserving edges and has a better ability in preserving the structures of gradual intensity transition in images. The penalized weighted least-squares (PWLS) criterion with the majorization-minimization (MM) approach was used to minimize the objective function. Two simulated digital phantoms were used to compare the performance of TV, Hessian penalty and TV-H penalties. Our experiments indicated that the TV-H penalty outperformed the TV penalty and the Hessian penalty.
Statistical iterative reconstruction in Cone-beam computed tomography (CBCT) uses prior knowledge to form different kinds of regularization terms. The total variation (TV) regularization has shown state-of-the-art performance in suppressing noises and preserving edges. However, it produces the well-known staircase effect. In this paper, a method that involves second-order differential operators was employed to avoid the staircase effect. The ability to avoid staircase effect lies in that higher-order derivatives can avoid over-sharpening the regions of smooth intensity transitions. Meanwhile, a fast iterative shrinkage-thresholding algorithm was used for the corresponding optimization problem. The proposed Hessian Schatten norm-based regularization keeps lots of favorable properties of TV, such as translation and scale invariant, with getting rid of the staircase effect that appears in TV-based reconstructions. The experiments demonstrated the outstanding ability of the proposed algorithm over TV method especially in suppressing the staircase effect.