Standard Backprojection Research Articles

Buried object imaging using reflection tomography

A recent pioneering study of Steven Schock provided high-quality imaging of buried objects using the buried object sensing sonar (BOSS) system in a towed or AUV-mounted configuration [Schock, Proc. IEEE Oceans, 2005]. This paper numerically investigates the performance of compressive sensing (CS) and standard backprojection methods for imaging multiple buried objects using a sonar system similar to the BOSS. Synthetic data are generated using a 3-D pseudo-spectral model for different sediment types and geometries including synthetic aperture sonar. As compared to the standard backprojection methods, the CS-based reflection tomography provided sharper images of buried objects using smaller data sets. Based on the CS performance, several improvements on the BOSS system and data collection schemes are also presented. [Work supported by ONR.]

Measuring femoral lesions despite CT metal artefacts: a cadaveric study

ObjectiveComputed tomography is the modality of choice for measuring osteolysis but suffers from metal-induced artefacts obscuring periprosthetic tissues. Previous papers on metal artefact reduction (MAR) show qualitative improvements, but their algorithms have not found acceptance for clinical applications. We investigated to what extent metal artefacts interfere with the segmentation of lesions adjacent to a metal femoral implant and whether metal artefact reduction improves the manual segmentation of such lesions.Materials and methodsWe manually created 27 periprosthetic lesions in 10 human cadaver femora. We filled the lesions with a fibrotic interface tissue substitute. Each femur was fitted with a polished tapered cobalt-chrome prosthesis and imaged twice—once with the metal, and once with a substitute resin prosthesis inserted. Metal-affected CTs were processed using standard back-projection as well as projection interpolation (PI) MAR. Two experienced users segmented all lesions and compared segmentation accuracy.ResultsWe achieved accurate delineation of periprosthetic lesions in the metal-free images. The presence of a metal implant led us to underestimate lesion volume and introduced geometrical errors in segmentation boundaries. Although PI MAR reduced streak artefacts, it led to greater underestimation of lesion volume and greater geometrical errors than without its application.ConclusionCT metal artefacts impair image segmentation. PI MAR can improve subjective image appearance but causes loss of detail and lower image contrast adjacent to prostheses. Our experiments showed that PI MAR is counterproductive for manual segmentation of periprosthetic lesions and should be used with care.

Two dimensional characterization of skeletal muscle’s natural vibrations during voluntary contractions.

During voluntary muscular contractions, low frequency mechanical vibrations (<100 Hz) are naturally generated by skeletal muscles as a result of the muscle fiber activity and the overall change of the muscle-tendon geometry. Determining the temporal and spatial variations of muscle vibrations could reveal fundamental features of skeletal muscles’ physiology and activation mechanisms. These mechanical vibrations were recorded over a 3 × 5 grid of skin mounted accelerometers on the biceps brachii muscle for ten healthy subjects for various contraction levels during isometric elbow flexion. The spatial origin and propagation directionality of these natural muscle vibrations were characterized across frequencies using standard cross correlation techniques and back projection algorithms (akin to time-reversal imaging). Additionally cross-correlating these accelerometer recordings provided travel-time measurements of these natural muscle vibrations between multiple sensor pairs. Furthermore, travel-time tomographic inversions yielded spatial variations of their propagation velocity from which the local stiffness of the muscle could be estimated using elastography principles. This passive tomographic elastography technique could potentially lead to simpler, low-cost, and noninvasive monitoring of musculoskeletal and neuromuscular disorders, without using an external mechanical or radiation excitation as commonly required by conventional elastography techniques.

Investigation on reconstruction methods applied to 3D terahertz computed tomography

3D terahertz computed tomography has been performed using a monochromatic millimeter wave imaging system coupled with an infrared temperature sensor. Three different reconstruction methods (standard back-projection algorithm and two iterative analysis) have been compared in order to reconstruct large size 3D objects. The quality (intensity, contrast and geometric preservation) of reconstructed cross-sectional images has been discussed together with the optimization of the number of projections. Final demonstration to real-life 3D objects has been processed to illustrate the potential of the reconstruction methods for applied terahertz tomography.

Model‐based optoacoustic inversions with incomplete projection data

Optoacoustic imaging is an emerging noninvasive imaging modality that can resolve optical contrast through several millimeters to centimeters of tissue with diffraction-limited resolution of ultrasound. Yet, quantified reconstruction of tissue absorption maps requires optoacoustic signals to be collected from as many locations around the object as possible. In many tomographic imaging scenarios, however, only limited-view or partial projection data are available, which has been shown to generate image artifacts and overall loss of quantification accuracy. In this article, the recently introduced interpolated-matrix-model optoacoustic inversion method is tested in different limited-view scenarios and compared to the standard backprojection algorithm. Both direct (TGSVD) and iterative (PLSQR) regularization methods are proposed to improve the accuracy of image reconstructions with their performance tested on simulated and experimental data. While for full-view tomographic data the model-based inversion has been generally shown to attain higher reconstruction accuracy compared to backprojection algorithms, the incomplete tomographic datasets lead to ill-conditioned forward matrices and, consequently, to error-prone inversions, with strong artifacts following a distinct ripple-type pattern. The proposed regularization techniques are shown to stabilize the inversion and eliminate the artifacts. Overall, it has been determined that the regularized interpolated-matrix-model-based optoacoustic inversions show higher accuracy than reconstructions with the standard backprojection algorithm. Finally, the combination of model-based inversion with PLSQR or TGSVD regularization methods can lead to an accurate reconstruction of limited-projection angle optoacoustic data and practical systems for optoacoustic imaging in many realistic cases where the full-view dataset is unavailable.

Reconstruction of brachytherapy seed positions and orientations from cone-beam CT x-ray projections via a novel iterative forward projection matching method

To generalize and experimentally validate a novel algorithm for reconstructing the 3D pose (position and orientation) of implanted brachytherapy seeds from a set of a few measured 2D cone-beam CT (CBCT) x-ray projections. The iterative forward projection matching (IFPM) algorithm was generalized to reconstruct the 3D pose, as well as the centroid, of brachytherapy seeds from three to ten measured 2D projections. The gIFPM algorithm finds the set of seed poses that minimizes the sum-of-squared-difference of the pixel-by-pixel intensities between computed and measured autosegmented radiographic projections of the implant. Numerical simulations of clinically realistic brachytherapy seed configurations were performed to demonstrate the proof of principle. An in-house machined brachytherapy phantom, which supports precise specification of seed position and orientation at known values for simulated implant geometries, was used to experimentally validate this algorithm. The phantom was scanned on an ACUITY CBCT digital simulator over a full 660 sinogram projections. Three to ten x-ray images were selected from the full set of CBCT sinogram projections and postprocessed to create binary seed-only images. In the numerical simulations, seed reconstruction position and orientation errors were approximately 0.6 mm and 5 degrees, respectively. The physical phantom measurements demonstrated an absolute positional accuracy of (0.78 +/- 0.57) mm or less. The theta and phi angle errors were found to be (5.7 +/- 4.9) degrees and (6.0 +/- 4.1) degrees, respectively, or less when using three projections; with six projections, results were slightly better. The mean registration error was better than 1 mm/6 degrees compared to the measured seed projections. Each test trial converged in 10-20 iterations with computation time of 12-18 min/iteration on a 1 GHz processor. This work describes a novel, accurate, and completely automatic method for reconstructing seed orientations, as well as centroids, from a small number of radiographic projections, in support of intraoperative planning and adaptive replanning. Unlike standard back-projection methods, gIFPM avoids the need to match corresponding seed images on the projections. This algorithm also successfully reconstructs overlapping clustered and highly migrated seeds in the implant. The accuracy of better than 1 mm and 6 degrees demonstrates that gIFPM has the potential to support 2D Task Group 43 calculations in clinical practice.

Clinical application and validation of an iterative forward projection matching algorithm for permanent brachytherapy seed localization from conebeam‐CT x‐ray projections

To experimentally validate a new algorithm for reconstructing the 3D positions of implanted brachytherapy seeds from postoperatively acquired 2D conebeam-CT (CBCT) projection images. The iterative forward projection matching (IFPM) algorithm finds the 3D seed geometry that minimizes the sum of the squared intensity differences between computed projections of an initial estimate of the seed configuration and radiographic projections of the implant. In-house machined phantoms, containing arrays of 12 and 72 seeds, respectively, are used to validate this method. Also, four 103Pd postimplant patients are scanned using an ACUITY digital simulator. Three to ten x-ray images are selected from the CBCT projection set and processed to create binary seed-only images. To quantify IFPM accuracy, the reconstructed seed positions are forward projected and overlaid on the measured seed images to find the nearest-neighbor distance between measured and computed seed positions for each image pair. Also, the estimated 3D seed coordinates are compared to known seed positions in the phantom and clinically obtained VariSeed planning coordinates for the patient data. For the phantom study, seed localization error is (0.58 +/- 0.33) mm. For all four patient cases, the mean registration error is better than 1 mm while compared against the measured seed projections. IFPM converges in 20-28 iterations, with a computation time of about 1.9-2.8 min/ iteration on a 1 GHz processor. The IFPM algorithm avoids the need to match corresponding seeds in each projection as required by standard back-projection methods. The authors' results demonstrate approximately 1 mm accuracy in reconstructing the 3D positions of brachytherapy seeds from the measured 2D projections. This algorithm also successfully localizes overlapping clustered and highly migrated seeds in the implant.

Block matching 3D random noise filtering for absorption optical projection tomography

Absorption and emission optical projection tomography (OPT), alternatively referred to as optical computed tomography (optical-CT) and optical-emission computed tomography (optical-ECT), are recently developed three-dimensional imaging techniques with value for developmental biology and ex vivo gene expression studies. The techniques' principles are similar to the ones used for x-ray computed tomography and are based on the approximation of negligible light scattering in optically cleared samples. The optical clearing is achieved by a chemical procedure which aims at substituting the cellular fluids within the sample with a cell membranes' index matching solution. Once cleared the sample presents very low scattering and is then illuminated with a light collimated beam whose intensity is captured in transillumination mode by a CCD camera. Different projection images of the sample are subsequently obtained over a 360° full rotation, and a standard backprojection algorithm can be used in a similar fashion as for x-ray tomography in order to obtain absorption maps. Because not all biological samples present significant absorption contrast, it is not always possible to obtain projections with a good signal-to-noise ratio, a condition necessary to achieve high-quality tomographic reconstructions. Such is the case for example, for early stage's embryos. In this work we demonstrate how, through the use of a random noise removal algorithm, the image quality of the reconstructions can be considerably improved even when the noise is strongly present in the acquired projections. Specifically, we implemented a block matching 3D (BM3D) filter applying it separately on each acquired transillumination projection before performing a complete three-dimensional tomographical reconstruction. To test the efficiency of the adopted filtering scheme, a phantom and a real biological sample were processed. In both cases, the BM3D filter led to a signal-to-noise ratio increment of over 30 dB on severe noise-affected reconstructions revealing original—noise-hidden—image details. These results show the utility of the BM3D approach for OPT under typical conditions of very low light absorption, suggesting its implementation as an efficient alternative to other filtering schemes such as for example the median filter.

Adjoint-based sampling methods for electromagnetic scattering

In this paper we investigate the efficient realization of sampling methods based on solutions of certain adjoint problems. This adjoint approach does not require the explicit knowledge of the Green's function for the background medium, and allows us to sample for all points and all dipole directions simultaneously; thus, several limitations of standard sampling methods are relieved. A detailed derivation of the adjoint approach is presented for two electromagnetic model problems, but the framework can be applied to a much wider class of problems. We also discuss a relation of the adjoint sampling method to standard backprojection algorithms, and present numerical tests that illustrate the efficiency of the adjoint approach.

A very inexpensive MRI-compatible method for dichoptic visual stimulation

Here I describe a very simple, very effective, and very inexpensive method of dichoptic stimulus presentation, designed for use in a head-only MRI scanner with a standard back-projection system. The method can also be used outside of the scanner. Images are presented separately and simultaneously to the two eyes, without the use of colored lenses, with no constraints on stimulus properties (other than size: stimuli must be less than half of the width of the viewing screen), no degradation in luminance reaching the eye, and zero crosstalk between the two eyes. Simultaneous infrared eye tracking and/or pupilometry can also be performed. Components include a two-part cardboard divider (one part in the bore of the magnet, and one in the head coil) and prism lenses (readily obtainable from the local eyeglass shop) cut to fit scanner-compatible eyeglass frames. The total cost (in 2007) was approximately US$ 300.

TU-FF-A4-03: A Three-Pass Method for Metal Artifact Reduction in Computed Tomography

Purpose: A method for the reduction of metal artifacts in computed tomography(CT)images is presented. Method and Materials: The method consists of three steps. In the first step, standard CTreconstruction is used to obtain an initial image containing metal artifacts. This image is segmented using k‐means clustering in order to obtain a binary metal‐background image. The metal is forward projected to mask the metal area in the sinogram data, and the metal shadow area is bridged using interpolation. A second image is reconstructed from this sinogram using standard backprojection. Then, the k‐means clustering is applied to the second reconstruction in order to identify four image regions: air, soft tissue (low), soft tissue (high), and bone. The Hounsfield value of each region is set to the mean of each region, except for the bone region where the original values are kept. We use this model image to create a metal shadow replacement by forward projection into the original sinogram. When inserting the model data into the sinogram, we make sure that the model area connects to the borders of the metal shadow. The final image is reconstructed from the sinogram in which metal line integrals are replaced by the model line integrals (third step). Results: Artifacts, e.g. from gold seeds in the breast or prostate, hip implants, or dental fillings can be significantly reduced. In cases of large implants, the method homogenizes image intensities in the surrounding soft tissues, which is helpful for the accurate planning of radiation therapy. Conclusions: The presented three‐pass metal artifact reduction method extends a recently published method by a linear interpolation step, which improves image quality, because more accurate model images can be derived for the replacement of the corrupted metal shadow in sinograms.

Application of acoustic reflection tomography to sonar imaging

Computer-aided tomography is a technique for providing a two-dimensional cross-sectional view of a three-dimensional object through the digital processing of many one-dimensional views (or projections) taken at different look directions. In acoustic reflection tomography, insonifying the object and then recording the backscattered signal provides the projection information for a given look direction (or aspect angle). Processing the projection information for all possible aspect angles enables an image to be reconstructed that represents the two-dimensional spatial distribution of the object's acoustic reflectivity function when projected on the imaging plane. The shape of an idealized object, which is an elliptical cylinder, is reconstructed by applying standard backprojection, Radon transform inversion (using both convolution and filtered backprojections), and direct Fourier inversion to simulated projection data. The relative merits of the various reconstruction algorithms are assessed and the resulting shape estimates compared. For bandpass sonar data, however, the wave number components of the acoustic reflectivity function that are outside the passband are absent. This leads to the consideration of image reconstruction for bandpass data. Tomographic image reconstruction is applied to real data collected with an ultra-wideband sonar transducer to form high-resolution acoustic images of various underwater objects when the sonar and object are widely separated.

On intermediate view estimation in computed tomography

In many applications in computed tomography, practical limitations in data acquisition restrict the number of projections (views). The use of the standard convolution backprojection algorithm for reconstruction from an inadequate number of projections results in view aliasing artifacts. One approach to alleviating the effects of such artifacts consists of artificially increasing the number of views, by estimating a set of intermediate views. Two possible methods of estimating the intermediate views are interpolation and reprojection. In this paper, a study of the two is considered. Based on the merits and demerits of the two methods, a combination of the two methods is investigated. Specifically, a reconstruction from the available sinogram augmented by intermediate view reprojections, and the projections interpolated from the original views and the reprojections, provide an additional improvement with respect to view aliasing artifacts. The advantage of computing reprojections over smaller regions of interest is discussed. When the number of available projections is reasonably high but not adequate to produce an artifact-free reconstruction, estimating the intermediate views by interpolation provides an improvement without much additional degradation, at minimal computational cost.

Ultrawide-band synthetic aperture radar for detection of unexploded ordnance: modeling and measurements

Electromagnetic (EM) scattering from subsurface unexploded ordnance (UXO) is investigated both theoretically and experimentally. Three EM models are considered: the multilevel fast multipole algorithm (MLFMA), the method of moments (MoM), and physical optics (PO). The relative accuracy of these models is compared for several scattering scenarios. Moreover, the model results are compared to data measured by an experimental synthetic aperture radar (SAR) system, SAR images have been generated for subsurface UXO targets, in particular 155-mm shells. We compare SAR images from the measured data with theoretical images produced by the MoM and PO simulations, using a standard back-projection imaging technique. In addition to such comparisons with measurement, we consider additional buried-UXO scattering scenarios to better understand the underlying wave phenomenology.

A broadband pulsed radio frequency electron paramagnetic resonance spectrometer for biological applications

A time-domain radio frequency (rf) electron paramagnetic resonance (EPR) spectrometer/imager (EPRI) capable of detecting and imaging free radicals in biological objects is described. The magnetic field was 10 mT which corresponds to a resonance frequency of 300 MHz for paramagnetic species. Short pulses of 20–70 ns from the signal generator, with rise times of less than 4 ns, were generated using high speed gates, which after amplification to 283 Vpp, were deposited into a resonator containing the object of interest. Cylindrical resonators containing parallel loops at uniform spacing were used for imaging experiments. The resonators were maintained at the resonant frequency by tuning and matching capacitors. A parallel resistor and overcoupled circuit was used to achieve Q values in the range 20–30. The transmit and receive arms were isolated using a transmit/receive diplexer. The dead time following the trailing edge of the pulse was about 450 ns. The first stage of the receive arm contained a low noise, high gain and fast recovery amplifier, suitable for detection of spin probes with spin-spin relaxation times (T2) in the order of μs. Detection of the induction signal was carried out by mixing the signals in the receiver arm centered around 300 MHz with a local oscillator at a frequency of 350 MHz. The amplified signals were digitized and summed using a 1 GHz digitizer/summer to recover the signals and enhance the signal-to-noise ratio (SNR). The time-domain signals were transformed into frequency-domain spectra, using Fourier transformation (FT). With the resonators used, objects of size up to 5 cm3 could be studied in imaging experiments. Spatial encoding of the spins was accomplished by volume excitation of the sample in the presence of static field gradients in the range of 1.0–1.5 G/cm. The spin densities were produced in the form of plane integrals and images were reconstructed using standard back-projection methods. The image resolution of the phantom objects containing the spin probe surrounded by lossy biologic medium was better than 0.2 mm with the gradients used. To examine larger objects at local sites, surface coils were used to detect and image spin probes successfully. The results from this study indicate the potential of rf FT EPR for in vivo applications. In particular, rf FT EPR may provide a means to obtain physiologic information such as tissue oxygenation and redox status.

Tomographic image reconstruction from optical projections in light-diffusing media

The recent developments in light generation and detection techniques have opened new possibilities for optical medical imaging, tomography, and diagnosis at tissue penetration depths of ~10 cm. However, because light scattering and diffusion in biological tissue are rather strong, the reconstruction of object images from optical projections needs special attention. We describe a simple reconstruction method for diffuse optical imaging, based on a modified backprojection approach for medical tomography. Specifically, we have modified the standard backprojection method commonly used in x-ray tomographic imaging to include the effects of both the diffusion and the scattering of light and the associated nonlinearities in projection image formation. These modifications are based primarily on the deconvolution of the broadened image by a spatially variant point-spread function that is dependent on the scattering of light in tissue. The spatial dependence of the deconvolution and nonlinearity corrections for the curved propagating ray paths in heterogeneous tissue are handled semiempirically by coordinate transformations. We have applied this method to both theoretical and experimental projections taken by parallel- and fan-beam tomography geometries. The experimental objects were biomedical phantoms with multiple objects, including in vitro animal tissue. The overall results presented demonstrate that image-resolution improvements by nearly an order of magnitude can be obtained. We believe that the tomographic method presented here can provide a basis for rapid, real-time medical monitoring by the use of optical projections. It is expected that such optical tomography techniques can be combined with the optical tissue diagnosis methods based on spectroscopic molecular signatures to result in a versatile optical diagnosis and imaging technology.

Generalized fan beam reconstruction algorithm and its applications

The standard fan beam geometry is extended to a generalized geometry accounting for source, detector, and axis of rotation displacements as well as detector tilting. The standard fan beam convolution backprojection algorithm is modified so as to reconstruct from projections recorded in an arbitrary fan beam geometry. The new generalized fan beam algorithm is applied to various nonideal geometries, such as reconstruction from center-displaced projections, nonredundant single-sided projections, and partially redundant projections. It is shown that the algorithm is capable of reconstructing from truncated and partial projection data and can be applied to tomographic synthetic scanner arrays. A novel method of resolution enhancement in microtomography is presented. The generalized fan beam algorithm is shown to reconstruct from projection data recorded with a tilted detector arbitrarily stretching tiny projection images over a larger portion of the available detector range. Optimal detector use is achieved through horizontal scanner displacement compensating for the asymmetric magnification of fan beam projections onto tilted detectors. It is shown that tilted-detector microtomography possesses a number of desirable properties such as superior signal-to-noise ratio, contrast, stability, and artifact suppression in the reconstructed images. Moreover, the new algorithm substantially reduces blurring artifacts in the presence of penumbral broadening that is due to finite-size point sources. The generalized fan beam algorithm is efficiently implemented, and its run-time performance compares with that of the standard fan beam method.

RECONSTRUCTION FROM LIMITED PROJECTION DATA

An outstanding problem in reconstruction methodology is the treatment of incomplete data sets. The inexact reconstruction technique (IRT) allows a stochastic approach, carried out in real space, which provides substantial improvement in reconstruction accuracy when compared to the standard filtered backprojection algorithm. This technique relies specifically on an iterative approach to the treatment of the probability related matrix which is assumed to be proportional to the original density distribution (original object matrix). This is obtained by the summation or multiplication of the set of probability matrices generated by back-projecting the known projections after the usual reorientation to correct for the angular projection to which each corresponds. Employing a Boolean constraint, the largest value in the probability matrix is located and an `l' is placed at the same coordinates in a blank array. This point in the probability matrix is then set to zero and the matrix projections are taken at the same angular orientations followed by re-backprojection to generate a new probability matrix. This process is repeated until the probability matrix is depleted or a specified mass is reached in the reconstructed object. The algorithm requires a considerable amount of computer time due to the necessity of recreating the probability matrix after each point is taken. A compromise solution is to address a certain fraction of the probability matrix to reduce the number of iterations. It has been demonstrated that reasonable results can be obtained when the probability matrix is addressed in increments of 5% or less. In this paper we demonstrate the use of an IRT on the reconstruction of multiple grey level images using limited data sets of from four to sixteen projections.© (1992) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

Optimal Regularized Reconstruction in Computerized Tomography

We consider regularized least squares solutions for the picture reconstruction problem in computerized tomography. The choice of the regularization parameter $\rho $ is crucial, but the known methods (like cross-Validation) are expensive. This paper shows that the usual rotationally invariant geometry of tomographs greatly reduces their cost.In the case of the ${\bf L}_2 $-norm taken as the irregularity functional, this invariance was previously used to efficiently compute a solution $f_\rho $ with an a priori fixed value of $\rho $. We present an algorithm which computes first an optimal value $\rho ^ * $, then $f_{\rho ^ * } $ with only twice (four times in the Poisson noise situation) the number of operations and the same memory space as the computation of one solution with fixed $\rho $.In the case of any rotationally invariant norm and with a suitable discretization of the picture, we describe a similar algorithm which, after a first step which is roughly the standard back-projection of the data, has the same complexity as the previous one.Numerical applications show the performance of these adaptive reconstructions.