Filtered Back-projection Technique Research Articles

Multifrequency inverse obstacle scattering: the point source method and generalized filtered backprojection

We outline two methods for obstacle reconstruction from multifrequency far-field scattering data, the first built upon the point source method proposed by Potthast for solving inverse scattering problems with single frequency data in the resonance region, and the second based on filtered backprojection techniques using the physical optics approximation for high frequency scattering. Our implementation using the point source method can be viewed as a generalized filtered backprojection algorithm, the key to which is the construction of the filter used in the backprojection operator. Numerical examples illustrate that the critical factor for reconstructions in multifrequency settings is the frequency dependence of the filter.

A reconstruction algorithm for coherent scatter computed tomography based on filtered back‐projection

Coherent scatter computed tomography (CSCT) is a reconstructive x-ray imaging technique that yields the spatially resolved coherent-scatter form factor of the investigated object. Reconstruction from coherently scattered x-rays is commonly done using algebraic reconstruction techniques (ART). In this paper, we propose an alternative approach based on filtered back-projection. For the first time, a three-dimensional (3D) filtered back-projection technique using curved 3D back-projection lines is applied to two-dimensional coherent scatter projection data. The proposed algorithm is tested with simulated projection data as well as with projection data acquired with a demonstrator setup similar to a multi-line CT scanner geometry. While yielding comparable image quality as ART reconstruction, the modified 3D filtered back-projection algorithm is about two orders of magnitude faster. In contrast to iterative reconstruction schemes, it has the advantage that subfield-of-view reconstruction becomes feasible. This allows a selective reconstruction of the coherent-scatter form factor for a region of interest. The proposed modified 3D filtered back-projection algorithm is a powerful reconstruction technique to be implemented in a CSCT scanning system. This method gives coherent scatter CT the potential of becoming a competitive modality for medical imaging or nondestructive testing.

Ultrasound tomography imaging of radiation dose distributions in polymer gel dosimeters: preliminary study.

A novel imaging system for investigation of absorbed dose distributions in radiotherapy polymer gel dosimeters using ultrasound is introduced. A prototype transmission ultrasound computed tomography (UCT) imaging system is developed and evaluated. The imaging capabilities of the system are assessed through investigation of an irradiated polyacrylamide gel test phantom. Images based on transmitted signal amplitude and time of flight (TOF) of the ultrasonic signal through the phantom are reconstructed using a filtered backprojection technique. In general, the reconstruction of the square field in the TOF image was superior to the transmission image, however, transmission images displayed superior contrast to TOF images. The image quality achieved with this prototype system is promising and could be significantly enhanced through improvements, in particular through the development of more sophisticated experimental equipment. It is concluded that UCT is a viable technique for imaging absorbed dose distributions in polymer gel dosimeters and investigations are continuing to further improve the system.

Projected index computed tomography.

Projected index computed tomography (PICT) is a new imaging technique that provides a computed reconstruction of the index of refraction of a sample. PICT makes use of data from standard optical coherence tomography images taken from several view angles to determine a mapping of the refractive indices of the sample. A rectilinear propagation model is assumed, so the data are understood to be related to the line integral of the refractive index in the beam paths. These data thus provide a set of angular projections of the sample. The spatial distribution of the index of the object may then be reconstructed by use of standard filtered backprojection techniques. The resultant PICT images are free of the spatial distortion that is inherent in standard optical cross-sectional images and correspond well to the manufactured dimensions of specific samples.

Feasibility in the clinical setting of perfusion brain SPECT imaging employing a brain-dedicated gamma camera and the conjugate gradients with modified matrix reconstruction method.

In the present study, we compared Tc-99m HMPAO single photon emission computed tomography (SPECT) brain images obtained using the conventional filtered backprojection (FBP) reconstruction method with the new reconstruction method of conjugate gradients with modified matrix (CGMM). The two methods were employed to generate SPECT images of a brain perfusion study in a 41-year-old patient who had suffered from multiple embolisation of the right hemisphere. Marked improvement in spatial resolution was achieved by CGMM reconstruction as compared to FBP reconstruction; this considerably helped in defining grey matter structures and low-uptake white-matter areas, both in the normal cerebral areas and in the hemisphere that had been affected by stroke. Although the relatively long time still required by the CGMM procedure might be considered as a significant drawback to date, with the increasing diffusion of the new computer facilities the CGMM method can be proposed as a valuable alternative to the standard FBP technique in order to better recognise cerebral areas with different tracer uptake.

Direct extraction of boundaries from computed tomography scans

Presents a method, based on the filtered backprojection technique (FBP), to extract directly the boundaries of X-ray images, without previous image reconstruction. The author preprocess the raw data in order to compute directly the reconstructed values of the gradient or of the Laplacian at any location in the plane (defined with real coordinates). The reconstructed value of the gradient and of the Laplacian correspond to the exact mathematical definition of the differentials of the image. For noisy data, the author proposes also to use an extension of existing FBP techniques, adapted to the computation of the gradient and of the Laplacian. Finally, the author shows how to use the corresponding operators to perform the segmentation of a slice, without image reconstruction. Images of the reconstructed gradient, Laplacian, and segmented objects are presented.

3D acquisition and reconstruction in positron emission tomography.

3D positron emission tomography (PET) refers to an acquisition geometry and reconstruction procedure that allows all coincidence events within the solid angle of the tomograph to be recorded and subsequently reconstructed. The reconstruction algorithm must consider the angle of each coincidence event relative to the central axis of the scanner. The aim of the technique is to maximise the sensitivity of the system by utilising all events that it is possible to record from the object. Conventional cylindrical 2D PET systems typically detect approximately 0.4%-0.5% of decaying nuclei within the field of view; with a 3D system this can increase to over 3%. Reconstruction in 3D using filtered-backprojection techniques has been developed and provides results that show little degradation of physical characteristics compared with 2D systems, apart from an increased scatter event rate. 3D techniques may be used to (i) improve data quality using currently acceptable doses of radioactivity and scanning times; (ii) extend the scanning period for short-lived tracers, especially 11C-labeled ligands; or, conversely (iii) decrease injected doses of radiotracer or reduce scanning times to achieve similar results as those using current methods in 2D.

Three‐Dimensional Electron Paramagnetic Resonance Imaging Technique for Mapping Porosity in Ceramics

A three‐dimensional (3D) electron paramagnetic resonance imaging (EPRI) method was developed to probe the structure and size of pores in ceramic materials. The imaging device that was added to the EPR instrument consisted of a computer‐controlled current source and magnetic field gradient. This add‐on facility was tested using a well‐defined diphenylpicrylhydrazyl phantom sample. Pumice was then used to demonstrate the potential of the technique. This stone was immersed in a 0.5 mM15N‐substituted perdeutereted tempone water solution to fill the pores with spin labels. Images were reconstructed using a filtered backprojection technique. A two‐dimensional (2D) imaging plane was constructed by collecting 33 projection planes over 180°. A 3D image was derived from 22 planes each constructed by 22 projections. At present, the facility allows a resolution of 69 and 46μm for 2D and 3D imaging, respectively. Advancements of the imaging apparatus, software, and line width of the spin labels will be needed to enhance the resolution of this technique.

Characterization of a whole body imaging technique for PET

An investigation of rapid whole-body PET (positron emission tomography) scanning was performed with a view towards its eventual use in screening for metastatic lesions with /sup 18/F-fluoride ion or /sup 18/F-fluorodeoxyglucose. Longitudinal images of the body were formed using three techniques. Simple 2-D projection images were formed by resorting the sinogram data. The images were created for a set of angles covering a full 180 degrees to facilitate viewing in a cine format. The effects of summing over a number of angles per view and filtering to reduce noise were investigated. Limited-angle backprojection images were formed using a small range of angles and no reconstruction filter. The resulting volume was then sliced coronally to give planar images as a function of depth. Coronal images were also obtained after reconstruction with a standard filtered backprojection technique, but with no attenuation correction. All three processes provided surprisingly good images of diagnostic quality, which were obtainable in practical scan times.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Three Dimensional (3D) Electron Paramagnetic Resonance Imaging Technique For Mapping Porosity in Ceramics

ABSTRACTA three dimensional (3D) Electron Paramagnetic Resonance Imaging (EPRI) method has been developed to probe the structure and size of pores in ceramic materials. A computer control current source and magnetic field gradient coil assembly were added on the conventional EPR instrument as imaging devices. This added-on facility was tested using a phantom sample having cavities filled with DPPH (2,2-diphenyl-1-picrylhydrazyl) particles. Pumice was then used to demonstrate the feasibility of the technique. Porous pumice stone was immersed in a 0.5mM 15N-PDT-water solution to introduce the spin labels into the open volume of the sample. A two-dimensional image was reconstructed from a set of 1-D projections using a filtered back-projection technique. A three-dimensional image was derived from 22 2-D images each constructed by 22 1-D projections. At present, the facility allows a resolution of 69 and 46 μm for 2-D and 3-D imaging.

Statistical noise in three-dimensional positron tomography

The authors have derived an approximate expression for the variance at the centre of a uniform spherical source reconstructed using the 3D filtered backprojection technique. The derivation is based on the assumption that the projection data are affected only by Poisson noise, and that the projection is sufficiently finely and uniformly sampled to ensure the validity of the filtered backprojection approach. The expression for the voxel variance in a 3D reconstruction is similar to the usual 2D expression, but contains a factor dependent on the aperture of the cylindrical detector. This factor has been calculated for two different reconstruction filters and in both cases, the influence of the detector aperture on the voxel variance is small. Thus, for an isotropic source such as the uniform sphere, Poisson noise is propagated similarly by both the 2D and 3D filtered backprojection algorithms.

An experimental evaluation of the effect of time-of-flight information in image reconstructions for the Scanditronix/PETT Electronics SP-3000 positron emission tomograph-preliminary results

The effects of detector energy thresholds and time-of-flight information on image quality were investigated for the SP-3000 positron emission tomograph. Phantom studies were performed with different energy discriminator settings. A software preprocessor allowed images to be reconstructed from list mode data with different time-of-flight windows. In general, the inclusion of time-of-flight information in image reconstruction improved SNR (signal to-noise-ratio) over conventional filtered back-projection techniques. The data indicate that setting the energy discriminator level higher than the 170 keV currently used in the machine could be beneficial. The results demonstrated the need for good quality assurance testing for time-of-flight offsets and gains, and they indicate that the current look-ahead coincidence system may need to be modified. >

True three-dimensional cone-beam reconstruction (TTCR) algorithm

A true three-dimensional cone-beam reconstruction (TTCR) algorithm for direct volume image reconstruction from 2-D cone-beam projections is developed for the complete sphere geometry. The algorithm is derived from the parallel-beam true three-dimensional reconstruction (TTR) algorithm and is based on the modified filtered backprojection technique, which uses a set of 2-D space-invariant filters. The proposed algorithm proved to be superior in spatial resolution to the parallel-beam TTR algorithm and to offer better computational efficiency.

A quantitative comparison of attenuation-weighted backprojection with multiplicative and iterative postprocessing attenuation compensation in SPECT

Comparisons are made between different analytic attenuation compensation methods used in SPECT imaging. The methods include a multiplicative technique and a single-iterative technique, both applied after filtered backprojection, and two different implementations of an attenuation-weighted filtered backprojection technique (A-W FBP). The methods are compared using simple phantoms of line sources and water-filled circular and elliptical cylinders. both simulated data (without scatter) and experimental data (with scatter) are reconstructed. None of the methods is truly quantitative, even without the presence of scatter, but are potentially useful and improve quantitation. All techniques provide good peak compensation for line sources in attenuating media. The weighted backprojection methods eliminate nearly all deformation due to nonisotropic attenuation for a line source centered in an ellipse. However, the measured noise is amplified by A-W FBP, unless the method is further modified to reduce the amplification.

Inherent limitations in ectomography

Ectomography, a general tomographic method currently being implemented in nuclear medicine, is described. The object is viewed from different directions from the same projection angle, and the reconstruction process can be described as a two-dimensional filtered back-projection technique. One limitation of this limited-angle approach is that a three-dimensional Fourier representation of the acquired projections has a cone where data are missing. This empty cone can cause distortions in the tomogram by insufficient elimination of details outside the reconstructed tomographic section and by distortion of details in the section. The degree of distortion is dependent on the extension of the object in all directions and on the projection angle. Despite these limitations ectomography can be superior to single-photon-emission computed tomography for imaging sections that are close and parallel to the surface of the object, as in imaging of the hip joint or the heart.

Reconstruction of a Three-Dimensional, Transonic Rotor Flowfield from Holographic Interferograms

Holographic interferometry and computer-assisted tomography (CAT) are used to determine the transonic velocity field of a model rotor blade in hover. A pulsed ruby laser recorded 40 interferograms with a 2-ft-diam field of view near the model rotor-blade tip operating at a tip Mach number of 0.90. After digitizing the interferograms and extracting fringe-order functions, the data are transferred to a CAT code. The CAT code, based on the filtered back-projection technique, then calculates the perturbation velocity in several planes above the blade surface. The values from the holography-CAT method compare favorably with previously obtained numerical computations near the blade tip. The results demonstrate the technique's potential for threedimensional transonic rotor flow studies.

ESTIMATION OF RECONSTRUCTIONS IN COMPUTED TOMOGRAPHY

A least-squares technique is described for estimating a large number of projections from a smaller number. The technique requires a knowledge of the external size and shape of the object from which projection views are made. Reconstructions made from the estimated views are not so artifact free as those made from the same amount of measured data, but they are substantially better than reconstructions made directly from the smaller amount of data using the filtered back-projection technique. The method of estimation permits a means of controlling noise that may be varied to fit local conditions.

Estimation of reconstructions in computed tomography

A least-squares technique is described for estimating a large number of projections from a smaller number. The technique requires a knowledge of the external size and shape of the object from which projection views are made. Reconstructions made from the estimated views are not so artifact free as those made from the same amount of measured data, but they are substantially better than reconstructions made directly from the smaller amount of data using the filtered back-projection technique. The method of estimation permits a means of controlling noise that may be varied to fit local conditions.