Discrete Imaging Models for Three-Dimensional Optoacoustic Tomography using Radially Symmetric Expansion Functions

Optoacoustic tomography (OAT), also known as photoacoustic tomography, is an emerging computed biomedical imaging modality that exploits optical contrast and ultrasonic detection principles. Iterative image reconstruction algorithms that are based on discrete imaging models are actively being developed for OAT due to their ability to improve image quality by incorporating accurate models of the imaging physics, instrument response, and measurement noise. In this work, we investigate the use of discrete imaging models based on Kaiser-Bessel window functions for iterative image reconstruction in OAT. A closed-form expression for the pressure produced by a Kaiser-Bessel function is calculated, which facilitates accurate computation of the system matrix. Computer-simulation and experimental studies are employed to demonstrate the potential advantages of Kaiser-Bessel function-based iterative image reconstruction in OAT

A B-spline based and computationally performant projector for iterative reconstruction in tomography - Application to dynamic X-ray gated CT

International audienceData modelization in tomography is a key point for iterative reconstruction. The design of the projector starts with the representation of the object of interest, decomposed on a discrete basis of functions. Standard models of projector such as ray driven, or more advanced models such as distance driven, use simple cubic voxels, which result in modelization errors due to their anisotropic behaviour. Moreover approximations made at the projection step increase these errors. Long, Fessler and Balter reduce approximation errors by projecting the cubic voxels more accurately. However anisotropy errors still hold. Spherically symmetric volume elements (blobs) eradicate them, but at the cost of increased complexity. We propose a compromise between these two approaches by using B-splines as basis functions. Their quasi-isotropic behaviour allows to avoid projection inconsistencies, while conserving local influence. Small approximations transform the exact footprint (projection of the basis function) into a separable function, which does not depend on the angle of projection, and is easier and faster to integrate on detector pixels. We obtain a more accurate projector, with no additional computation cost. Such an improvement is particularly of interest in the case of dynamic gated X-ray CT, which can be considered as a tomographic reconstruction problem with very few projection data, and for which we show some preliminary results, with an original method of iterative reconstruction, using spatio-temporal regularization of the "space + time" sequence, and making no use of motion estimation

High Performance 3D PET Reconstruction Using Spherical Basis Functions on a Polar Grid

Statistical iterative methods are a widely used method of image reconstruction in emission tomography. Traditionally, the image space is modelled as a combination of cubic voxels as a matter of simplicity. After reconstruction, images are routinely filtered to reduce statistical noise at the cost of spatial resolution degradation. An alternative to produce lower noise during reconstruction is to model the image space with spherical basis functions. These basis functions overlap in space producing a significantly large number of non-zero elements in the system response matrix (SRM) to store, which additionally leads to long reconstruction times. These two problems are partly overcome by exploiting spherical symmetries, although computation time is still slower compared to non-overlapping basis functions. In this work, we have implemented the reconstruction algorithm using Graphical Processing Unit (GPU) technology for speed and a precomputed Monte-Carlo-calculated SRM for accuracy. The reconstruction time achieved using spherical basis functions on a GPU was 4.3 times faster than the Central Processing Unit (CPU) and 2.5 times faster than a CPU-multi-core parallel implementation using eight cores. Overwriting hazards are minimized by combining a random line of response ordering and constrained atomic writing. Small differences in image quality were observed between implementations

The structure of Planetary Nebulae: theory vs. practice

This paper - the first of a short series dedicated to the long-stan ding astronomical problem of de-projecting the bi-dimensional apparent morpholog y of a three-dimensional mass of gas - focuses on the density distribution in real Planetary Nebulae (and all types of expanding nebulae). We introduce some basic theoretical notions, discuss the observational methodology and develope the accurate procedure for the determination of the matter radial profile within the sharp portion of nebula in the plane of the sky identified by the zero-velocity-pixel-column (zvpc) of high-resolution spectral images. Moreover, a series of evolutive snapshots is presented, combining illustrative examples of model- and true-Planetary Nebulae. Last, the general and specific applications of the method (and some caveats) are discussed.Comment: 18 pages, 7 figures, A&A accepte

Transfer function restoration in 3D electron microscopy via iterative data refinement

Three-dimensional electron microscopy (3D-EM) is a powerful tool for visualizing complex biological systems. As with any other imaging device, the electron microscope introduces a transfer function (called in this field the contrast transfer function, CTF) into the image acquisition process that modulates the various frequencies of the signal. Thus, the 3D reconstructions performed with these CTF-affected projections are also affected by an implicit 3D transfer function. For high-resolution electron microscopy, the effect of the CTF is quite dramatic and limits severely the achievable resolution. In this work we make use of the iterative data refinement (IDR) technique to ameliorate the effect of the CTF. It is demonstrated that the approach can be successfully applied to noisy data.Partial support is acknowledged to the Comisión Interministerial de Ciencia y Tecnología of Spain through projects BIO98-0761 and BIO2001-1237 and to National Institutes of Health through grant HL70472. The work of Y. Censor was done in part at the Center for Computational Mathematics and Scientific Computation (CCMSC) at the University of Haifa and supported by Research Grant 592/00 from the Israel Science Foundation founded by the Israel Academy of Sciences and Humanities

Spline driven: high accuracy projectors for tomographic reconstruction from few projections

International audienceTomographic iterative reconstruction methods need a very thorough modeling of data. This point becomes critical when the number of available projections is limited. At the core of this issue is the projector design, i.e., the numerical model relating the representation of the object of interest to the projections on the detector. Voxel driven and ray driven projection models are widely used for their short execution time in spite of their coarse approximations. Distance driven model has an improved accuracy but makes strong approximations to project voxel basis functions. Cubic voxel basis functions are anisotropic, accurately modeling their projection is, therefore, computationally expensive. Both smoother and more isotropic basis functions better represent the continuous functions and provide simpler projectors. These considerations have led to the development of spherically symmetric volume elements, called blobs. Set apart their isotropy, blobs are often considered too computationally expensive in practice. In this paper, we consider using separable B-splines as basis functions to represent the object, and we propose to approximate the projection of these basis functions by a 2D separable model. When the degree of the B-splines increases, their isotropy improves and projections can be computed regardless of their orientation. The degree and the sampling of the B-splines can be chosen according to a tradeoff between approximation quality and computational complexity. We quantitatively measure the good accuracy of our model and compare it with other projectors, such as the distance-driven and the model proposed by Long et al. From the numerical experiments, we demonstrate that our projector with an improved accuracy better preserves the quality of the reconstruction as the number of projections decreases. Our projector with cubic B-splines requires about twice as many operations as a model based on voxel basis functions. Higher accuracy projectors can be used to improve the resolution of the existing systems, or to reduce the number of projections required to reach a given resolution, potentially reducing the dose absorbed by the patient

3D Forward and Back-Projection for X-Ray CT Using Separable Footprints

Iterative methods for 3D image reconstruction have the potential to improve image quality over conventional filtered back projection (FBP) in X-ray computed tomography (CT). However, the computation burden of 3D cone-beam forward and back-projectors is one of the greatest challenges facing practical adoption of iterative methods for X-ray CT. Moreover, projector accuracy is also important for iterative methods. This paper describes two new separable footprint (SF) projector methods that approximate the voxel footprint functions as 2D separable functions. Because of the separability of these footprint functions, calculating their integrals over a detector cell is greatly simplified and can be implemented efficiently. The SF-TR projector uses trapezoid functions in the transaxial direction and rectangular functions in the axial direction, whereas the SF-TT projector uses trapezoid functions in both directions. Simulations and experiments showed that both SF projector methods are more accurate than the distance-driven (DD) projector, which is a current state-of-the-art method in the field. The SF-TT projector is more accurate than the SF-TR projector for rays associated with large cone angles. The SF-TR projector has similar computation speed with the DD projector and the SF-TT projector is about two times slower.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/85876/1/Fessler5.pd

Exploiting symmetries for weight matrix design in CT imaging

In this paper we propose several methods of constructing the system matrix (SM) of a Computed Tomography (CT) scanner with two objectives: (1) to construct SMs in the shortest possible time and store them in an ordinary PC without losing quality, (2) to analyze the possible applications of the proposed method to 3D, taking into account SMs' sizes, computing time and reconstructed image quality. In order to build the SM, we propose two new field of view (FOV) pixellation schemes, based on a polar coordinate system (polar grid) by taking advantage of the polar rotation symmetries of CT devices. Comparisons between the SMs proposed are performed using two phantom and a real CT-simulator images. Global error, contrast, noise and homogeneity of the reconstructed images are discussed. © 2010 Elsevier Ltd.This work is partially supported by Generalitat Valenciana GVPRE/2008/303 and the Spanish M.E.C. Grant MTM2009-08587.Rodríguez-Álvarez, M.; Sánchez Martínez, F.; Soriano Asensi, A.; Iborra Carreres, A.; Mora Mora, C. (2011). Exploiting symmetries for weight matrix design in CT imaging. Mathematical and Computer Modelling. 54(7-8):1655-1664. https://doi.org/10.1016/j.mcm.2010.12.004S16551664547-