In super-resolution microscopy methods based on single-molecule switching, the rate to accumulate single-molecule activation events often limits the time resolution. Here, we developed a sparse-signal recovery technique using compressed sensing to analyze images with highly overlapping fluorescent spots. This method allows an activated fluorophore density an order of magnitude higher than what conventional single-molecule fitting methods can handle. Using this method, we have demonstrated imaging microtubule dynamics in living cells with a time resolution of 3 s.

Image registration is the process of establishing a common geometric reference frame between two or more image data sets possibly taken at different times. In this paper we present a method for computing elastic registration and warping maps based on the Monge-Kantorovich theory of optimal mass transport. This mass transport method has a number of important characteristics. First, it is parameter free. Moreover, it utilizes all of the grayscale data in both images, places the two images on equal footing and is symmetrical: the optimal mapping from image to image ¡ being the inverse of the optimal mapping from ¡ to £ ¢ The method does not require that landmarks be specified, and the minimizer of the distance functional involved is unique; there are no other local minimizers. Finally, optimal transport naturally takes into account changes in density that result from changes in area or volume. Although the optimal transport method is certainly not appropriate for all registration and warping problems, this mass preservation property makes the Monge-Kantorovich approach quite useful for an interesting class of warping problems, as we show in this paper. Our method for finding the registration mapping is based on a partial differential equation approach to the minimization of the ¤ ¦ ¥ Kantorovich-Wasserstein or "Earth Mover's Distance" under a mass preservation constraint. We show how this approach leads to practical algorithms, and demonstrate our method with a number of examples, including those from the medical field. We also extended this method to take into account changes in intensity, and show that it is well suited for applications such as image morphing.

An X-ray system with a large area detector has high scatter-to-primary ratios (SPRs), which result in severe artifacts in reconstructed computed tomography (CT) images. A scatter correction algorithm is introduced that provides effective scatter correction but does not require additional patient exposure. The key hypothesis of the algorithm is that the high-frequency components of the X-ray spatial distribution do not result in strong high-frequency signals in the scatter. A calibration sheet with a checkerboard pattern of semitransparent blockers (a "primary modulator") is inserted between the X-ray source and the object. The primary distribution is partially modulated by a high-frequency function, while the scatter distribution still has dominant low-frequency components, based on the hypothesis. Filtering and demodulation techniques suffice to extract the low-frequency components of the primary and hence obtain the scatter estimation. The hypothesis was validated using Monte Carlo (MC) simulation, and the algorithm was evaluated by both MC simulations and physical experiments. Reconstructions of a software humanoid phantom suggested system parameters in the physical implementation and showed that the proposed method reduced the relative mean square error of the reconstructed image in the central region of interest from 74.2% to below 1%. In preliminary physical experiments on the standard evaluation phantom, this error was reduced from 31.8% to 2.3%, and it was also demonstrated that the algorithm has no noticeable impact on the resolution of the reconstructed image in spite of the filter-based approach. Although the proposed scatter correction technique was implemented for X-ray CT, it can also be used in other X-ray imaging applications, as long as a primary modulator can be inserted between the X-ray source and the imaged object.

Cone-beam CT ͑CBCT͒ is being increasingly used in modern radiation therapy for patient setup and adaptive replanning. However, due to the large volume of x-ray illumination, scatter becomes a rather serious problem and is considered as one of the fundamental limitations of CBCT image quality. Many scatter correction algorithms have been proposed in literature, while a standard practical solution still remains elusive. In radiation therapy, the same patient is scanned repetitively during a course of treatment, a natural question to ask is whether one can obtain the scatter distribution on the first day of treatment and then use the data for scatter correction in the subsequent scans on different days. To realize this scatter removal scheme, two technical pieces must be in place: ͑i͒ A strategy to obtain the scatter distribution in on-board CBCT imaging and ͑ii͒ a method to spatially match a prior scatter distribution with the on-treatment CBCT projection data for scatter subtraction. In this work, simple solutions to the two problems are provided. A partially blocked CBCT is used to extract the scatter distribution. The x-ray beam blocker has a strip pattern, such that partial volume can still be accurately reconstructed and the whole-field scatter distribution can be estimated from the detected signals in the shadow regions using interpolation/extrapolation. In the subsequent scans, the patient transformation is determined using a rigid registration of the conventional CBCT and the prior partial CBCT. From the derived patient transformation, the measured scatter is then modified to adapt the new on-treatment patient geometry for scatter correction. The proposed method is evaluated using physical experiments on a clinical CBCT system. On the Catphan©600 phantom, the errors in Hounsfield unit ͑HU͒ in the selected regions of interest are reduced from about 350 to below 50 HU; on an anthropomorphic phantom, the error is reduced from 15.7% to 5.4%. The proposed method is attractive in applications where a high CBCT image quality is critical, for example, dose calculation in adaptive radiation therapy.

By providing effective shading correction, our approach has the potential to improve the accuracy of more advanced CBCT-based clinical applications for IGRT, such as tumor delineation and dose calculation.