…… Frame 01 f Y Y' Frame 02 Frame 46 Frame 91 Frame 92 …… …… …… …… …… e d a b c Y Y' Fig. 1. X-ray tomographic reconstruction of a rose undergoing significant wilting during the scan due to loss of water. Images (a) and (b) show photographs of the rose directly before and directly after the scanning process. Traditional CT reconstruction (c) from all 5520 projections in the scan sequence show significant distortions due to misalignment of features. When grouping the projections into 92 frames of 60 projections each (d), the deformation over each frame becomes negligible, but now the number of projections per frame is insufficient for high-quality reconstruction of the corresponding volumes (e, Y). By comparison, our full space-time reconstruction algorithm yields a time sequence of highly detailed volumes for different time steps (f, Y ′ ).X-ray computed tomography (CT) is a valuable tool for analyzing objects with interesting internal structure or complex geometries that are not accessible with optical means. Unfortunately, tomographic reconstruction of complex shapes requires a multitude (often hundreds or thousands) of projections from different viewpoints. Such a large number of projections can only be acquired in a time-sequential fashion. This significantly limits the ability to use x-ray tomography for either objects that undergo uncontrolled shape change at the time scale of a scan, or else for analyzing dynamic phenomena, where the motion itself is under investigation.In this work, we present a non-parametric space-time tomographic method for tackling such dynamic settings. Through a combination of a new CT image acquisition strategy, a space-time tomographic image formation model, and an alternating, multi-scale solver, we achieve a general approach that can be used to analyze a wide range of dynamic phenomena. We demonstrate our method with extensive experiments on both real and simulated data.

Despite significant recent progress, dense, time-resolved imaging of complex, non-stationary 3D flow velocities remains an elusive goal. In this work we tackle this problem by extending an established 2D method, Particle Imaging Velocimetry, to three dimensions by encoding depth into color. The encoding is achieved by illuminating the flow volume with a continuum of light planes (a "rainbow"), such that each depth corresponds to a specific wavelength of light. A diffractive component in the camera optics ensures that all planes are in focus simultaneously. With this setup, a single color camera is sufficient for tracking 3D trajectories of particles by combining 2D spatial and 1D color information. For reconstruction, we derive an image formation model for recovering stationary 3D particle positions. 3D velocity estimation is achieved with a variant of 3D optical flow that accounts for both physical constraints as well as the rainbow image formation model. We evaluate our method with both simulations and an experimental prototype setup.

Optical coherence tomography (OCT) is a non-invasive technique with a large array of applications in clinical imaging and biological tissue visualization. However, the presence of speckle noise affects the analysis of OCT images and their diagnostic utility. In this article, we introduce a new OCT denoising algorithm. The proposed method is founded on a numerical optimization framework based on maximum-a-posteriori estimate of the noise-free OCT image. It combines a novel speckle noise model, derived from local statistics of empirical spectral domain OCT (SD-OCT) data, with a Huber variant of total variation regularization for edge preservation. The proposed approach exhibits satisfying results in terms of speckle noise reduction as well as edge preservation, at reduced computational cost.

Computed tomography has emerged as the method of choice for scanning complex shapes as well as interior structures of stationary objects. Recent progress has also allowed the use of CT for analyzing deforming objects and dynamic phenomena, although the deformations have been constrained to be either slow or periodic motions. In this work we improve the tomographic reconstruction of time-varying geometries undergoing faster, non-periodic deformations. Our method uses a warp-and-project approach that allows us to introduce an essentially continuous time axis where consistency of the reconstructed shape with the projection images is enforced for the specific time and deformation state at which the image was captured. The method uses an efficient, time-adaptive solver that yields both the moving geometry as well as the deformation field. We validate our method with extensive experiments using both synthetic and real data from a range of different application scenarios.

Visible light tomography is a promising and increasingly popular technique for fluid imaging. However, the use of a sparse number of viewpoints in the capturing setups makes the reconstruction of fluid flows very challenging. In this paper, we present a state-of-the-art 4D tomographic reconstruction framework that integrates several regularizers into a multi-scale matrix free optimization algorithm. In addition to existing regularizers, we propose two new regularizers for improved results: a regularizer based on view interpolation of projected images and a regularizer to encourage reprojection consistency. We demonstrate our method with extensive experiments on both simulated and real data.

We propose IntraTomo, a powerful framework that combines the benefits of learning-based and model-based approaches for solving highly ill-posed inverse problems in the Computed Tomography (CT) context. IntraTomo is composed of two core modules: a novel sinogram prediction module, and a geometry refinement module, which are applied iteratively. In the first module, the unknown density field is represented as a continuous and differentiable function, parameterized by a deep neural network. This network is learned, in a self-supervised fashion, from the incomplete or/and degraded input sinogram. After getting estimated through the sinogram prediction module, the density field is consistently refined in the second module using local and non-local geometrical priors. With these two core modules, we show that IntraTomo significantly outperforms existing approaches on several ill-posed inverse problems, such as limited angle tomography with a range of 45 degrees, sparse view tomographic reconstruction with as few as eight views, or super-resolution tomography with eight times increased resolution. The experiments on simulated and real data show that our approach can achieve results of unprecedented quality.

We present a flexible framework for robust computed tomography (CT) reconstruction with a specific emphasis on recovering thin 1D and 2D manifolds embedded in 3D volumes. To reconstruct such structures at resolutions below the Nyquist limit of the CT image sensor, we devise a new 3D structure tensor prior, which can be incorporated as a regularizer into more traditional proximal optimization methods for CT reconstruction. As a second, smaller contribution, we also show that when using such a proximal reconstruction framework, it is beneficial to employ the Simultaneous Algebraic Reconstruction Technique (SART) instead of the commonly used Conjugate Gradient (CG) method in the solution of the data term proximal operator. We show empirically that CG often does not converge to the global optimum for tomography problem even though the underlying problem is convex. We demonstrate that using SART provides better reconstruction results in sparse-view settings using fewer projection images. We provide extensive experimental results for both contributions on both simulated and real data. Moreover, our code will also be made publicly available.

We use structured monochromatic volume illumination with spatially varying intensity profiles, to achieve 3D intensity particle tracking velocimetry using a single video camera. The video camera records the 2D motion of a 3D particle field within a fluid, which is perpendicularly illuminated with depth gradients of the illumination intensity. This allows us to encode the depth position perpendicular to the camera, in the intensity of each particle image. The light intensity field is calibrated using a 3D laser-engraved glass cube containing a known spatial distribution of 1100 defects. This is used to correct for the distortions and divergence of the projected light. We use a sequence of changing light patterns, with numerous sub-gradients in the intensity, to achieve a resolution of 200 depth levels.