Multiple Projection Optical Diffusion Tomography with Plane Wave Illumination

We describe a new data collection scheme for optical diffusion tomography in which plane wave illumination is combined with multiple projections in the slab imaging geometry. Multiple projection measurements are performed by rotating the slab around the sample. The advantage of the proposed method is that the measured data can be much more easily fitted into the dynamic range of most commonly used detectors. At the same time, multiple projections improve image quality by mutually interchanging the depth and transverse directions, and the scanned (detection) and integrated (illumination) surfaces. Inversion methods are derived for image reconstructions with extremely large data sets. Numerical simulations are performed for fixed and rotated slabs

Non-Local Compressive Sensing Based SAR Tomography

Tomographic SAR (TomoSAR) inversion of urban areas is an inherently sparse reconstruction problem and, hence, can be solved using compressive sensing (CS) algorithms. This paper proposes solutions for two notorious problems in this field: 1) TomoSAR requires a high number of data sets, which makes the technique expensive. However, it can be shown that the number of acquisitions and the signal-to-noise ratio (SNR) can be traded off against each other, because it is asymptotically only the product of the number of acquisitions and SNR that determines the reconstruction quality. We propose to increase SNR by integrating non-local estimation into the inversion and show that a reasonable reconstruction of buildings from only seven interferograms is feasible. 2) CS-based inversion is computationally expensive and therefore barely suitable for large-scale applications. We introduce a new fast and accurate algorithm for solving the non-local L1-L2-minimization problem, central to CS-based reconstruction algorithms. The applicability of the algorithm is demonstrated using simulated data and TerraSAR-X high-resolution spotlight images over an area in Munich, Germany.Comment: 10 page

Phase-Retrieved Tomography enables imaging of a Tumor Spheroid in Mesoscopy Regime

Optical tomographic imaging of biological specimen bases its reliability on the combination of both accurate experimental measures and advanced computational techniques. In general, due to high scattering and absorption in most of the tissues, multi view geometries are required to reduce diffuse halo and blurring in the reconstructions. Scanning processes are used to acquire the data but they inevitably introduces perturbation, negating the assumption of aligned measures. Here we propose an innovative, registration free, imaging protocol implemented to image a human tumor spheroid at mesoscopic regime. The technique relies on the calculation of autocorrelation sinogram and object autocorrelation, finalizing the tomographic reconstruction via a three dimensional Gerchberg Saxton algorithm that retrieves the missing phase information. Our method is conceptually simple and focuses on single image acquisition, regardless of the specimen position in the camera plane. We demonstrate increased deep resolution abilities, not achievable with the current approaches, rendering the data alignment process obsolete.Comment: 21 pages, 5 figure

A Tensor-Based Dictionary Learning Approach to Tomographic Image Reconstruction

We consider tomographic reconstruction using priors in the form of a dictionary learned from training images. The reconstruction has two stages: first we construct a tensor dictionary prior from our training data, and then we pose the reconstruction problem in terms of recovering the expansion coefficients in that dictionary. Our approach differs from past approaches in that a) we use a third-order tensor representation for our images and b) we recast the reconstruction problem using the tensor formulation. The dictionary learning problem is presented as a non-negative tensor factorization problem with sparsity constraints. The reconstruction problem is formulated in a convex optimization framework by looking for a solution with a sparse representation in the tensor dictionary. Numerical results show that our tensor formulation leads to very sparse representations of both the training images and the reconstructions due to the ability of representing repeated features compactly in the dictionary.Comment: 29 page

A multi-level preconditioned Krylov method for the efficient solution of algebraic tomographic reconstruction problems

Classical iterative methods for tomographic reconstruction include the class of Algebraic Reconstruction Techniques (ART). Convergence of these stationary linear iterative methods is however notably slow. In this paper we propose the use of Krylov solvers for tomographic linear inversion problems. These advanced iterative methods feature fast convergence at the expense of a higher computational cost per iteration, causing them to be generally uncompetitive without the inclusion of a suitable preconditioner. Combining elements from standard multigrid (MG) solvers and the theory of wavelets, a novel wavelet-based multi-level (WMG) preconditioner is introduced, which is shown to significantly speed-up Krylov convergence. The performance of the WMG-preconditioned Krylov method is analyzed through a spectral analysis, and the approach is compared to existing methods like the classical Simultaneous Iterative Reconstruction Technique (SIRT) and unpreconditioned Krylov methods on a 2D tomographic benchmark problem. Numerical experiments are promising, showing the method to be competitive with the classical Algebraic Reconstruction Techniques in terms of convergence speed and overall performance (CPU time) as well as precision of the reconstruction.Comment: Journal of Computational and Applied Mathematics (2014), 26 pages, 13 figures, 3 table

State of the art: iterative CT reconstruction techniques

Owing to recent advances in computing power, iterative reconstruction (IR) algorithms have become a clinically viable option in computed tomographic (CT) imaging. Substantial evidence is accumulating about the advantages of IR algorithms over established analytical methods, such as filtered back projection. IR improves image quality through cyclic image processing. Although all available solutions share the common mechanism of artifact reduction and/or potential for radiation dose savings, chiefly due to image noise suppression, the magnitude of these effects depends on the specific IR algorithm. In the first section of this contribution, the technical bases of IR are briefly reviewed and the currently available algorithms released by the major CT manufacturers are described. In the second part, the current status of their clinical implementation is surveyed. Regardless of the applied IR algorithm, the available evidence attests to the substantial potential of IR algorithms for overcoming traditional limitations in CT imaging