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

Iterative Tomographic Image Reconstruction Using Fourier-Based Forward and Back-Projectors

Iterative image reconstruction algorithms play an increasingly important role in modern tomographic systems, especially in emission tomography. With the fast increase of the sizes of the tomographic data, reduction of the computation demands of the reconstruction algorithms is of great importance. Fourier-based forward and back-projection methods have the potential to considerably reduce the computation time in iterative reconstruction. Additional substantial speed-up of those approaches can be obtained utilizing powerful and cheap off-the-shelf fast Fourier transform (FFT) processing hardware. The Fourier reconstruction approaches are based on the relationship between the Fourier transform of the image and Fourier transformation of the parallel-ray projections. The critical two steps are the estimations of the samples of the projection transform, on the central section through the origin of Fourier space, from the samples of the transform of the image, and vice versa for back-projection. Interpolation errors are a limitation of Fourier-based reconstruction methods. We have applied min-max optimized Kaiser-Bessel interpolation within the nonuniform FFT (NUFFT) framework and devised ways of incorporation of resolution models into the Fourier-based iterative approaches. Numerical and computer simulation results show that the min-max NUFFT approach provides substantially lower approximation errors in tomographic forward and back-projection than conventional interpolation methods. Our studies have further confirmed that Fourier-based projectors using the NUFFT approach provide accurate approximations to their space-based counterparts but with about ten times faster computation, and that they are viable candidates for fast iterative image reconstruction.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/85804/1/Fessler62.pd

Modeling and Development of Iterative Reconstruction Algorithms in Emerging X-ray Imaging Technologies

Many new promising X-ray-based biomedical imaging technologies have emerged over the last two decades. Five different novel X-ray based imaging technologies are discussed in this dissertation: differential phase-contrast tomography (DPCT), grating-based phase-contrast tomography (GB-PCT), spectral-CT (K-edge imaging), cone-beam computed tomography (CBCT), and in-line X-ray phase contrast (XPC) tomosynthesis. For each imaging modality, one or more specific problems prevent them being effectively or efficiently employed in clinical applications have been discussed. Firstly, to mitigate the long data-acquisition times and large radiation doses associated with use of analytic reconstruction methods in DPCT, we analyze the numerical and statistical properties of two classes of discrete imaging models that form the basis for iterative image reconstruction. Secondly, to improve image quality in grating-based phase-contrast tomography, we incorporate 2nd order statistical properties of the object property sinograms, including correlations between them, into the formulation of an advanced multi-channel (MC) image reconstruction algorithm, which reconstructs three object properties simultaneously. We developed an advanced algorithm based on the proximal point algorithm and the augmented Lagrangian method to rapidly solve the MC reconstruction problem. Thirdly, to mitigate image artifacts that arise from reduced-view and/or noisy decomposed sinogram data in K-edge imaging, we exploited the inherent sparseness of typical K-edge objects and incorporated the statistical properties of the decomposed sinograms to formulate two penalized weighted least square problems with a total variation (TV) penalty and a weighted sum of a TV penalty and an l1-norm penalty with a wavelet sparsifying transform. We employed a fast iterative shrinkage/thresholding algorithm (FISTA) and splitting-based FISTA algorithm to solve these two PWLS problems. Fourthly, to enable advanced iterative algorithms to obtain better diagnostic images and accurate patient positioning information in image-guided radiation therapy for CBCT in a few minutes, two accelerated variants of the FISTA for PLS-based image reconstruction are proposed. The algorithm acceleration is obtained by replacing the original gradient-descent step by a sub-problem that is solved by use of the ordered subset concept (OS-SART). In addition, we also present efficient numerical implementations of the proposed algorithms that exploit the massive data parallelism of multiple graphics processing units (GPUs). Finally, we employed our developed accelerated version of FISTA for dealing with the incomplete (and often noisy) data inherent to in-line XPC tomosynthesis which combines the concepts of tomosynthesis and in-line XPC imaging to utilize the advantages of both for biological imaging applications. We also investigate the depth resolution properties of XPC tomosynthesis and demonstrate that the z-resolution properties of XPC tomosynthesis is superior to that of conventional absorption-based tomosynthesis. To investigate all these proposed novel strategies and new algorithms in these different imaging modalities, we conducted computer simulation studies and real experimental data studies. The proposed reconstruction methods will facilitate the clinical or preclinical translation of these emerging imaging methods

High-performance blob-based iterative three-dimensional reconstruction in electron tomography using multi-GPUs

<p>Abstract</p> <p>Background</p> <p>Three-dimensional (3D) reconstruction in electron tomography (ET) has emerged as a leading technique to elucidate the molecular structures of complex biological specimens. Blob-based iterative methods are advantageous reconstruction methods for 3D reconstruction in ET, but demand huge computational costs. Multiple graphic processing units (multi-GPUs) offer an affordable platform to meet these demands. However, a synchronous communication scheme between multi-GPUs leads to idle GPU time, and a weighted matrix involved in iterative methods cannot be loaded into GPUs especially for large images due to the limited available memory of GPUs.</p> <p>Results</p> <p>In this paper we propose a multilevel parallel strategy combined with an asynchronous communication scheme and a blob-ELLR data structure to efficiently perform blob-based iterative reconstructions on multi-GPUs. The asynchronous communication scheme is used to minimize the idle GPU time so as to asynchronously overlap communications with computations. The blob-ELLR data structure only needs nearly 1/16 of the storage space in comparison with ELLPACK-R (ELLR) data structure and yields significant acceleration.</p> <p>Conclusions</p> <p>Experimental results indicate that the multilevel parallel scheme combined with the asynchronous communication scheme and the blob-ELLR data structure allows efficient implementations of 3D reconstruction in ET on multi-GPUs.</p

High-Quality Parallel-Ray x-Ray CT Back Projection Using Optimized Interpolation

We propose a new, cost-efficient method for computing back projections in parallel-ray X-ray CT. Forward and back projections are the basis of almost all X-ray CT reconstruction methods, but computing these accurately is costly. In the special case of parallel-ray geometry, it turns out that reconstruction requires back projection only. One approach to accelerate the back projection is through interpolation: fit a continuous representation to samples of the desired signal, then sample it at the required locations. Instead, we propose applying a prefilter that has the effect of orthogonally projecting the underlying signal onto the space spanned by the interpolator, which can significantly improve the quality of the interpolation. We then build on this idea by using oblique projection, which simplifies the computation while giving effectively the same improvement in quality. Our experiments on analytical phantoms show that this refinement can improve the reconstruction quality for both filtered back projection and iterative reconstruction in the high-quality regime, i.e., with low noise and many measurements

A subspace-based resolution-enhancing image reconstruction method for few-view differential phase-contrast tomography

It is well known that properly designed image reconstruction methods can facilitate reductions in imaging doses and data-acquisition times in tomographic imaging. The ability to do so is particularly important for emerging modalities, such as differential x-ray phase-contrast tomography (D-XPCT), which are currently limited by these factors. An important application of D-XPCT is high-resolution imaging of biomedical samples. However, reconstructing high-resolution images from few-view tomographic measurements remains a challenging task due to the high-frequency information loss caused by data incompleteness. In this work, a subspace-based reconstruction strategy is proposed and investigated for use in few-view D-XPCT image reconstruction. By adopting a two-step approach, the proposed method can simultaneously recover high-frequency details within a certain region of interest while suppressing noise and/or artifacts globally. The proposed method is investigated by the use of few-view experimental data acquired by an edge-illumination D-XPCT scanner

Computerized Classification of Surface Spikes in Three-Dimensional Electron Microscopic Reconstructions of Viruses

The purpose of this research is to develop computer techniques for improved three-dimensional (3D) reconstruction of viruses from electron microscopic images of them and for the subsequent improved classification of the surface spikes in the resulting reconstruction. The broader impact of such work is the following. Influenza is an infectious disease caused by rapidly-changing viruses that appear seasonally in the human population. New strains of influenza viruses appear every year, with the potential to cause a serious global pandemic. Two kinds of spikes – hemagglutinin (HA) and neuraminidase (NA) – decorate the surface of the virus particles and these proteins are primarily responsible for the antigenic changes observed in influenza viruses. Identification of the locations of the surface spikes of both kinds in a new strain of influenza virus can be of critical importance for the development of a vaccine that protects against such a virus. Two major categories of reconstruction techniques are transform methods such as weighted backprojection (WBP) and series expansion methods such as the algebraic reconstruction techniques (ART) and the simultaneous iterative reconstruction technique (SIRT). Series expansion methods aim at estimating the object to be reconstructed by a linear combination of some fixed basis functions and they typically estimate the coefficients in such an expansion by an iterative algorithm. The choice of the set of basis functions greatly influences the efficacy of the output of a series expansion method. It has been demonstrated that using spherically symmetric basis functions (blobs), instead of the more traditional voxels, results in reconstructions of superior quality. Our own research shows that, with the recommended data-processing steps performed on the projection images prior to reconstruction, ART (with its free parameters appropriately tuned) provides 3D reconstructions of viruses from tomographic tilt series that allow reliable quantification of the surface proteins and that the same is not achieved using WBP or SIRT, which are the methods that have been routinely applied by practicing electron microscopists. Image segmentation is the process of recognizing different objects in an image. Segmenting an object from a background is not a trivial task, especially when the image is corrupted by noise and/or shading. One concept that has been successfully used to achieve segmentation in such corrupted images is fuzzy connectedness. This technique assigns to each element in an image a grade of membership in an object. Classifications methods use set of relevant features to identify the objects of each class. To distinguish between HA and NA spikes in this research, discussions with biologists suggest that there may be a single feature that can be used reliably for the classification process. The result of the fuzzy connectedness technique we conducted to segment spikes from the background confirms the correctness of the biologists’ assumption. The single feature we used is the ratio of the width of the spike’s head to the width of its stem in 3D space; the ratio appears to be greater for NA than it is for HA. The proposed classifier is tested on different types of 3D reconstructions derived from simulated data. A statistical hypothesis testing based methodology allowed us to evaluate the relative suitability of reconstruction methods for the given classification task