Four-dimensional fluorescence microscopy-which records 3D image information as a function of time-provides an unbiased way of tracking dynamic behavior of subcellular components in living samples and capturing key events in complex macromolecular processes. Unfortunately, the combination of phototoxicity and photobleaching can severely limit the density or duration of sampling, thereby limiting the biological information that can be obtained. Although widefield microscopy provides a very light-efficient way of imaging, obtaining high-quality reconstructions requires deconvolution to remove optical aberrations. Unfortunately, most deconvolution methods perform very poorly at low signal-to-noise ratios, thereby requiring moderate photon doses to obtain acceptable resolution. We present a unique deconvolution method that combines an entropy-based regularization function with kernels that can exploit general spatial characteristics of the fluorescence image to push the required dose to extreme low levels, resulting in an enabling technology for high-resolution in vivo biological imaging.4D microscopy | low dose microscopy | noise-suppressing regularization T he study of dynamic processes is an important facet of cell biology research. Fluorescently tagged proteins combined with four-dimensional fluorescence microscopy, which records 3D image information as a function of time, provide a powerful framework for studying the dynamics of molecular processes in vivo. One of the most crucial challenges in 4D fluorescence microscopy is to ensure that normal biological function is not significantly perturbed as a result of the high doses of illumination (phototoxicity) incurred during 4D imaging. Recent work indicates that the maximal photon dose that avoids biological perturbation is 100-to 1,000-fold lower than that typically used for in vivo imaging (1). Dose limitations are even more challenging, given the desire to densely sample in time or to record over extended periods, especially in the context of analyzing multiple subcellular components via multiwavelength imaging.Under normal imaging conditions, widefield microscopy combined with image restoration using deconvolution methods provides an excellent modality for multiwavelength 4D imaging as it makes very efficient use of the illuminating photons. However, its effectiveness, in particular its ability to resolve subcellular detail sufficiently in the presence of noise, is limited by the performance of the deconvolution method. Such limitations can seriously degrade image quality at the low signal levels required for unperturbed in vivo imaging. The noise behavior of the deconvolution algorithm is determined by the efficiency of the noise stabilization term, known as the regularization functional. In particular, the functional's ability to discriminate the noise-related high frequencies from weak high frequencies in the signal ultimately determines the final resolution of the deconvolution. Currently used noise-stabilization techniques are largely based on ad hoc form...

Abstract-The quantitative assessment of cardiac motion is a fundamental concept to evaluate ventricular malfunction. We present a new optical-flow-based method for estimating heart motion from two-dimensional echocardiographic sequences. To account for typical heart motions, such as contraction/expansion and shear, we analyze the images locally by using a local-affine model for the velocity in space and a linear model in time. The regional motion parameters are estimated in the least-squares sense inside a sliding spatiotemporal B-spline window. Robustness and spatial adaptability is achieved by estimating the model parameters at multiple scales within a coarse-to-fine multiresolution framework. We use a wavelet-like algorithm for computing B-spline-weighted inner products and moments at dyadic scales to increase computational efficiency. In order to characterize myocardial contractility and to simplify the detection of myocardial dysfunction, the radial component of the velocity with respect to a reference point is color coded and visualized inside a time-varying region of interest. The algorithm was first validated on synthetic data sets that simulate a beating heart with a speckle-like appearance of echocardiograms. The ability to estimate motion from real ultrasound sequences was demonstrated by a rotating phantom experiment. The method was also applied to a set of in vivo echocardiograms from an animal study. Motion estimation results were in good agreement with the expert echocardiographic reading.

Abstract-We propose a novel method for image reconstruction from nonuniform samples with no constraints on their locations. We adopt a variational approach where the reconstruction is formulated as the minimizer of a cost that is a weighted sum of two terms: 1) the sum of squared errors at the specified points and 2) a quadratic functional that penalizes the lack of smoothness. We search for a solution that is a uniform spline and show how it can be determined by solving a large, sparse system of linear equations. We interpret the solution of our approach as an approximation of the analytical solution that involves radial basis functions and demonstrate the computational advantages of our approach. Using the two-scale relation for B-splines, we derive an algebraic relation that links together the linear systems of equations specifying reconstructions at different levels of resolution. We use this relation to develop a fast multigrid algorithm. We demonstrate the effectiveness of our approach on some image reconstruction examples.

Abstract-We present a new computational method for reconstructing a vector velocity field from scattered, pulsed-wave ultrasound Doppler data. The main difficulty is that the Doppler measurements are incomplete, for they do only capture the velocity component along the beam direction. We thus propose to combine measurements from different beam directions. However, this is not yet sufficient to make the problem well posed because 1) the angle between the directions is typically small and 2) the data is noisy and nonuniformly sampled. We propose to solve this reconstruction problem in the continuous domain using regularization. The reconstruction is formulated as the minimizer of a cost that is a weighted sum of two terms: 1) the sum of squared difference between the Doppler data and the projected velocities 2) a quadratic regularization functional that imposes some smoothness on the velocity field. We express our solution for this minimization problem in a -spline basis, obtaining a sparse system of equations that can be solved efficiently. Using synthetic phantom data, we demonstrate the significance of tuning the regularization according to the a priori knowledge about the physical property of the motion. Next, we validate our method using real phantom data for which the ground truth is known. We then present reconstruction results obtained from clinical data that originate from 1) blood flow in carotid bifurcation and 2) cardiac wall motion.Index Terms-Color Doppler imaging, color flow imaging, echocardiography, nonuniform sampling, projected sampling, pulsed wave Doppler, regularized reconstruction, shift-invariant spaces, tissue Doppler imaging, ultrasound Doppler, variational reconstruction, vector field reconstruction, velocity field reconstruction.