Implementation and performance evaluation of reconstruction algorithms on graphics processors

The high-throughput needs in electron tomography and in single particle analysis have driven the parallel implementation of several reconstruction algorithms and software packages on computing clusters. Here, we report on the implementation of popular reconstruction algorithms as weighted backprojection, simultaneous iterative reconstruction technique (SIRT) and simultaneous algebraic reconstruction technique (SART) on common graphics processors (GPUs). The speed gain achieved on the GPUs is in the order of sixty (60x) to eighty (80x) times, compared to the performance of a single central processing unit (CPU), which is comparable to the acceleration achieved on a medium-range computing cluster. This acceleration of the reconstruction is caused by the highly specialized architecture of the GPU. Further, we show that the quality of the reconstruction on the GPU is comparable to the CPU. We present detailed flow-chart diagrams of the implementation. The reconstruction software does not require special hardware apart from the commercially available graphics cards and could be easily integrated in software packages like SPIDER, XMIPP, TOM-Package and others.     

Single-particle reconstruction using L(2)-gradient flow

In this paper, we present an iterative algorithm for reconstructing a three-dimensional density function from a set of two dimensional electron microscopy images. By minimizing an energy functional consisting of a fidelity term and a regularization term, an L²-gradient flow is derived. The flow is integrated by a finite element method in the spatial direction and an explicit Euler scheme in the temporal direction. Our method compares favorably with those of the weighted back projection, Fourier method, algebraic reconstruction technique and simultaneous iterative reconstruction technique.     

Fast tomographic reconstruction on multicore computers

SUMMARY: Tomo3D implements a multithreaded vectorized approach to tomographic reconstruction that takes full advantage of the computer power in modern multicore computers. Full resolution tomograms are generated at high speed on standard computers with no special system requirements. Tomo3D has the most common reconstruction methods implemented, namely weighted Back-projection (WBP) and simultaneous iterative reconstruction technique (SIRT). It proves to be competitive with current graphic processor unit solutions in terms of processing time, in the order of a few seconds with WBP or minutes with SIRT. The program is compatible with standard packages, which easily allows integration in the electron tomography workflow.     

Cone-beam breast computed tomography using ultra-fast image reconstruction with constrained,total-variation minimization for suppression of artifacts

Compressed sensing based iterative reconstruction algorithms for computed tomography such as adaptive steepest descent-projection on convex sets (ASD-POCS) are attractive due to their applicability in incomplete datasets such as sparse-view data and can reduce radiation dose to the patients while preserving image quality. Although IR algorithms reduce image noise compared to analytical Feldkamp-Davis-Kress (FDK) algorithm, they may generate artifacts, particularly along the periphery of the object. One popular solution is to use finer image-grid followed by down-sampling. This approach is computationally intensive but may be compensated by reducing the field of view. Our proposed solution is to replace the algebraic reconstruction technique within the original ASD-POCS by ordered subsets-simultaneous algebraic reconstruction technique (OS-SART) and with initialization using FDK image. We refer to this method as Fast, Iterative, TV-Regularized, Statistical reconstruction Technique (FIRST). In this study, we investigate FIRST for cone-beam dedicated breast CT with large image matrix. The signal-difference to noise ratio (SDNR), the difference of the mean value and the variance of adipose and fibroglandular tissues for both FDK and FIRST reconstructions were determined. With FDK serving as the reference, the root-mean-square error (RMSE), bias, and the full-width at half-maximum (FWHM) of microcalcifications in two orthogonal directions were also computed. Our results suggest that FIRST is competitive to the finer image-grid method with shorter reconstruction time. Images reconstructed using the FIRST do not exhibit artifacts and outperformed FDK in terms of image noise. This suggests the potential of this approach for radiation dose reduction in cone-beam breast CT.     

Transform-based backprojection for volume reconstruction of large format electron microscope tilt series

Alignment of the individual images of a tilt series is a critical step in obtaining high-quality electron microscope reconstructions. We report on general methods for producing good alignments, and utilizing the alignment data in subsequent reconstruction steps. Our alignment techniques utilize bundle adjustment. Bundle adjustment is the simultaneous calculation of the position of distinguished markers in the object space and the transforms of these markers to their positions in the observed images, along the bundle of particle trajectories along which the object is projected to each EM image. Bundle adjustment techniques are general enough to encompass the computation of linear, projective or nonlinear transforms for backprojection, and can compensate for curvilinear trajectories through the object, sample warping, and optical aberration. We will also report on new reconstruction codes and describe our results using these codes.     

The effect of overabundant projection directions on 3D reconstruction algorithms

The experimental process of collecting images from macromolecules in an electron microscope is such that it does not allow for prior specification of the angular distribution of the projection images. As a consequence, an uneven distribution of projection directions may occur. Concerns have been raised recently about the behavior of 3D reconstruction algorithms for the case of unevenly distributed projections. It has been illustrated on experimental data that in the case of a heavily uneven distribution of projection directions some algorithms tend to elongate the reconstructed volumes along the overloaded direction so much as to make a quantitative biological analysis impossible. In answer to these concerns we have developed a strategy for quantitative comparison and optimization of 3D reconstruction algorithms. We apply this strategy to quantitatively analyze algebraic reconstruction techniques (ART) with blobs, simultaneous iterative reconstruction techniques (SIRT) with voxels, and weighted backprojection (WBP). We show that the elongation artifacts that had been previously reported can be strongly reduced. With our specific choices for the free parameters of the three algorithms, WBP reconstructions tend to be inferior to those obtained with either SIRT or ART and the results obtained with ART are comparable to those with SIRT, but at a very small fraction of the computational cost of SIRT.     

Image reconstruction of optical computed tomography by using the algebraic reconstruction technique for dose readouts of polymer gel dosimeters

Optical computed tomography (optical CT) has been proven to be a useful tool for dose readouts of polymer gel dosimeters. In this study, the algebraic reconstruction technique (ART) for image reconstruction of gel dosimeters was used to improve the image quality of optical CT. Cylindrical phantoms filled with N-isopropyl-acrylamide polymer gels were irradiated using a medical linear accelerator. A circular dose distribution and a hexagonal dose distribution were produced by applying the VMAT technique and the six-field dose delivery, respectively. The phantoms were scanned using optical CT, and the images were reconstructed using the filtered back-projection (FBP) algorithm and the ART. For the circular dose distribution, the ART successfully reduced the ring artifacts and noise in the reconstructed image. For the hexagonal dose distribution, the ART reduced the hot spots at the entrances of the beams and increased the dose uniformity in the central region. Within 50% isodose line, the gamma pass rates for the 2 mm/3% criteria for the ART and FBP were 99.2% and 88.1%, respectively. The ART could be used for the reconstruction of optical CT images to improve image quality and provide accurate dose conversion for polymer gel dosimeters.     

Three-dimensional velocity field reconstruction

The problem of inter-slice magnetic resonance (MR) image reconstruction is encountered often in medical imaging applications, in such scenarios, there is a need to approximate information not captured in contiguously acquired MR images due to hardware sampling limitations. In the context of velocity field reconstruction, these data are required for visualization and computational analyses of flow fields to be effective. To provide more complete velocity information, a method has been developed for the reconstruction of flow fields based on adaptive control grid interpolation (ACGI). In this study, data for reconstruction were acquired via MRJ from in vitro models of surgically corrected pediatric cardiac vasculatures. Reconstructed velocity fields showed strong qualitative agreement with those obtained via other acquisition techniques. Quantitatively reconstruction was shown to produce data of comparable quality to accepted velocity data acquisition methods. Results indicate that ACGI-based velocity field reconstruction is capable of producing information suitable for a variety of applications demanding three-dimensional in vivo velocity data.     

Evaluation of digital tomosynthesis reconstruction algorithms used to reduce metal artifacts for arthroplasty: A phantom study

To investigate methods to reduce metal artifacts during digital tomosynthesis for arthroplasty, we evaluated five algorithms with and without metal artifact reduction (MAR)-processing tested under different radiation doses (0.54, 0.47, and 0.33 mSv): adaptive steepest descent projection onto convex sets (ASD-POCS), simultaneous algebraic reconstruction technique total variation (SART-TV), filtered back projection (FBP), maximum likelihood expectation maximization (MLEM), and SART. The algorithms were assessed by determining the artifact index (AI) and artifact spread function (ASF) on a prosthesis phantom. The AI data were statistically analyzed by two-way analysis of variance. Without MAR-processing, the greatest degree of effectiveness of the MLEM algorithm for reducing prosthetic phantom-related metal artifacts was achieved by quantification using the AI (MLEM vs. ASD-POCS, SART-TV, SART, and FBP; all P < 0.05). With MAR-processing, the greatest degree of effectiveness of the MLEM, ASD-POCS, SART-TV, and SART algorithms for reducing prosthetic phantom-related metal artifacts was achieved by quantification using the AI (MLEM, ASD-POCS, SART-TV, and SART vs. FBP; all P < 0.05). When assessed by ASF, metal artifact reduction was largest for the MLEM algorithm without MAR-processing and ASD-POCS, SART-TV, and SART algorithm with MAR-processing. In ASF, the effect of metal artifact reduction was always greater at reduced radiation doses, regardless of which reconstruction algorithm with and without MAR-processing was used. In this phantom study, the MLEM algorithm without MAR-processing and ASD-POCS, SART-TV, and SART algorithm with MAR-processing gave improved metal artifact reduction.     

Photoacoustic diagnostics of fast photochemical and photobiological processes. Analysis of inverse problem solution

Photoacoustic (PA) diagnostics is a time-resolved experimental technique that measures transient photoinduced volume changes on the nano- and microsecond time-scales. The technique has been used to study the energetics and dynamics of chemical and biochemical reactions initiated by absorption of light. The dynamics of the volume changes and associated relaxation processes can be restored from PA-waveforms by solving an ill-posed problem of deconvolution. For the systems with known relaxation kinetics scheme this problem is usually solved by an iterative approximation algorithm. In complex photoactive systems (e.g. photosynthetic samples), where information about kinetics of fast photoinduced volume changes is not available, an algorithm of direct deconvolution must be used. The implementation of one of the linear deconvolution algorithms (Tikhonov's alpha-regularization) for the PA-diagnostics is therefore considered. The problem of the optimal choice of experimental set-up, and restoration algorithm is analyzed by a numerical simulation. It is shown that the quality of PA-diagnostic experiment is mainly determined by a transfer function converting the relaxation spectrum to the spectrum of output electric signal. The analytical expressions to calculate this function (so called PA-filter) are presented. The performance of two widely used schemes of PA-diagnostics are then directly compared. The time-resolution of the PA-diagnostics in analysis of simultaneous bi-exponential decay is evaluated, and the relationship between the resolving power and parameters of the experimental set-up (signal-to-noise ratio, sampling rate, shape of the PA-filter) is found. The advantage of front face irradiation scheme with piezopolymer film detector for time-resolved measurements is demonstrated.     

An Efficient Augmented Lagrangian Method for Statistical X-Ray CT Image Reconstruction

Statistical iterative reconstruction (SIR) for X-ray computed tomography (CT) under the penalized weighted least-squares criteria can yield significant gains over conventional analytical reconstruction from the noisy measurement. However, due to the nonlinear expression of the objective function, most exiting algorithms related to the SIR unavoidably suffer from heavy computation load and slow convergence rate, especially when an edge-preserving or sparsity-based penalty or regularization is incorporated. In this work, to address abovementioned issues of the general algorithms related to the SIR, we propose an adaptive nonmonotone alternating direction algorithm in the framework of augmented Lagrangian multiplier method, which is termed as “ALM-ANAD”. The algorithm effectively combines an alternating direction technique with an adaptive nonmonotone line search to minimize the augmented Lagrangian function at each iteration. To evaluate the present ALM-ANAD algorithm, both qualitative and quantitative studies were conducted by using digital and physical phantoms. Experimental results show that the present ALM-ANAD algorithm can achieve noticeable gains over the classical nonlinear conjugate gradient algorithm and state-of-the-art split Bregman algorithm in terms of noise reduction, contrast-to-noise ratio, convergence rate, and universal quality index metrics.     

The psychological effect of mastectomy with or without breast reconstruction: a prospective,multicenter study

A multicenter, prospective study ( = 103) examined the psychological implications of women's decisions for or against breast reconstruction. Recognized measures of anxiety, depression, body image, and quality of life were completed before the operation, and 6 and 12 months later. A reduction in psychological distress over the year following the operation was evident in each surgical group (mastectomy alone or immediate or delayed reconstruction), indicating that reconstructive surgery can offer psychological benefits to some women; however, others report improved psychological functioning without this surgical procedure. In contrast to existing retrospective research, the prospective design enabled the process of adjustment during the first year after the operation to be examined. The results indicate that breast reconstruction is not a universal panacea for the emotional and psychological consequences of mastectomy. Women still reported feeling conscious of altered body image 1 year postoperatively, regardless of whether or not they had elected breast reconstruction. Health professionals should be careful of assuming that breast reconstruction necessarily confers psychological benefits compared with mastectomy alone.     

High-performance electron tomography of complex biological specimens

We have evaluated reconstruction methods using smooth basis functions in the electron tomography of complex biological specimens. In particular, we have investigated series expansion methods, with special emphasis on parallel computation. Among the methods investigated, the component averaging techniques have proven to be most efficient and have generally shown fast convergence rates. The use of smooth basis functions provides the reconstruction algorithms with an implicit regularization mechanism, very appropriate for noisy conditions. Furthermore, we have applied high-performance computing (HPC) techniques to address the computational requirements demanded by the reconstruction of large volumes. One of the standard techniques in parallel computing, domain decomposition, has yielded an effective computational algorithm which hides the latencies due to interprocessor communication. We present comparisons with weighted back-projection (WBP), one of the standard reconstruction methods in the areas of computational demand and reconstruction quality under noisy conditions. These techniques yield better results, according to objective measures of quality, than the weighted backprojection techniques after a very few iterations. As a consequence, the combination of efficient iterative algorithms and HPC techniques has proven to be well suited to the reconstruction of large biological specimens in electron tomography, yielding solutions in reasonable computation times.     

Detecting chaotic structures in noisy pulse trains based on interspike interval reconstruction

The nonlinear prediction method based on the interspike interval (ISI) reconstruction is applied to the ISI sequence of noisy pulse trains and the detection of the deterministic structure is performed. It is found that this method cannot discriminate between the noisy periodic pulse train and the noisy chaotic one when noise-induced pulses exist. When the noise-induced pulses are eliminated by the grouping of ISI sequence with the genetic algorithm, the chaotic structure of the chaotic firings becomes clear, and the noisy chaotic pulse train could be discriminated from the periodic one.     

Speech-intelligibility improvements using a binaural adaptive-scheme based conceptually on human auditory processing

A speech enhancement scheme is presented using diverse processing in sub-bands spaced according to a human-cochlear describing function. The binaural adaptive scheme decomposes the wide-band input signals into a number of band-limited signals, superficially similar to the treatment the human ears perform on incoming signals. The results of a series of intelligibility and formal listening tests are presented in which acoustic speech signals corrupted with recorded automobile noise were presented to 15 normal hearing volunteer subjects. For the experimental cases considered, the proposed binaural adaptive sub-band processing scheme delivers a statistically significant improvement in terms of both speech-intelligibility and perceived quality when compared with both the conventional wide-band processed and the noisy unprocessed case. The scheme is capable of extension to a potentially more flexible sub-band processing method based on a constrained artificial neural network (ANN).     

Processing of ND NMR spectra sampled in polar coordinates: a simple Fourier transform instead of a reconstruction

In order to reduce the acquisition time of multidimensional NMR spectra of biological macromolecules, projected spectra (or in other words, spectra sampled in polar coordinates) can be used. Their standard processing involves a regular FFT of the projections followed by a reconstruction, i.e. a non-linear process. In this communication, we show that a 2D discrete Fourier transform can be implemented in polar coordinates to obtain directly a frequency domain spectrum. Aliasing due to local violations of the Nyquist sampling theorem gives rise to base line ridges but the peak line-shapes are not distorted as in most reconstruction methods. The sampling scheme is not linear and the data points in the time domain should thus be weighted accordingly in the polar FT; however, artifacts can be reduced by additional data weighting of the undersampled regions. This processing does not require any parameter tuning and is straightforward to use. The algorithm written for polar sampling can be adapted to any sampling scheme and will permit to investigate better compromises in terms of experimental time and lack of artifacts.     

Segmental mandibulectomy and immediate free fibula osteoseptocutaneous flap reconstruction with endosteal implants: an ideal treatment method for mandibular ameloblastoma

Thirteen patients with large ameloblastomas of the mandible underwent segmental mandibulectomy and immediate reconstruction, with simultaneous placement of osseointegrated implants. All patients received palatal mucosal grafts around the dental implants 6 to 10 months after surgical treatment and received implant-supported prostheses another 1 to 2 months later. There were five female and eight male patients, with a mean age of 32 years (range, 17 to 50 years). The mean length of the mandibular defect was 8.8 cm (range, 5 to 13 cm). All free fibula flap procedures were successful, with no reexplorations or partial flap losses. There was no clinical or radiographic evidence of failure during the osseointegration process for any implant. With functional occlusal loading, the marginal bone loss around the implants was less than 1.5 mm in a mean follow-up period of 40 months (range, 18 to 70 months). There were no recurrences during that time. The technique described allows improved access to the bone at the time of reconstruction, immediate assessment of alveolar ridge relationships, and accurate fixation of the implant-fibula construct. The advantages of this procedure include a reduced risk of recurrence with segmental resection, reliable mandibular reconstruction, and reduction of the number of surgical procedures, allowing full oral rehabilitation in a shorter time. It is concluded that segmental mandibulectomy and immediate vascularized fibula osteoseptocutaneous flap reconstruction, with simultaneous placement of osseointegrated implants, represent an ideal treatment method for large ameloblastomas of the mandible.     

Noise properties of reconstructed images in a kilo-voltage on-board imaging system with iterative reconstruction techniques: A phantom study

X-ray computed tomography (CT) images obtained with a kilo-voltage (kV) on-board imaging (OBI) system improve the accuracy of patient setup and treatment planning. The use of iterative reconstruction techniques (IRTs) for CT imaging can also reduce radiation dose compared to analytic reconstruction techniques. Despite these improvements, the image quality varies with IRTs, and the noise structure of reconstructed images can be distorted by IRTs. In this study, the noise properties and spatial resolution of the images reconstructed by IRTs were evaluated in terms of conventional noise metrics, high-order statistics, noise spectral density (NSD) and modulation transfer function (MTF) at different radiation doses. A kV OBI system mounted on a Varian Trilogy machine and a CATPHAN600 phantom were used to obtain projections, and the projections were reconstructed by Feldkamp (FDK), algebraic reconstruction technique (ART), maximum-likelihood expectation–maximization (MLEM) and total variation (TV) minimization algorithms. The reconstructed images were compared according to mean, standard deviation, skewness, kurtosis, NSD and MTF at different radiation doses. The results demonstrated that the noise properties and spatial resolution of reconstructed images depend on the type of IRT and the radiation dose. The noise structures are altered by IRTs and can be characterized by high-order statistics and NSD, as well as conventional noise metrics. In conclusion, high-order statistics and NSD should be considered in order to provide detailed information for the images reconstructed by IRTs. Also, trade-off among noise properties, spatial resolution and contrast is important to optimize image quality obtained using IRTs.     

Accurate reconstruction of insertion-deletion histories by statistical phylogenetics

The Multiple Sequence Alignment (MSA) is a computational abstraction that represents a partial summary either of indel history, or of structural similarity. Taking the former view (indel history), it is possible to use formal automata theory to generalize the phylogenetic likelihood framework for finite substitution models (Dayhoff's probability matrices and Felsenstein's pruning algorithm) to arbitrary-length sequences. In this paper, we report results of a simulation-based benchmark of several methods for reconstruction of indel history. The methods tested include a relatively new algorithm for statistical marginalization of MSAs that sums over a stochastically-sampled ensemble of the most probable evolutionary histories. For mammalian evolutionary parameters on several different trees, the single most likely history sampled by our algorithm appears less biased than histories reconstructed by other MSA methods. The algorithm can also be used for alignment-free inference, where the MSA is explicitly summed out of the analysis. As an illustration of our method, we discuss reconstruction of the evolutionary histories of human protein-coding genes.