Projection Reconstruction Method Research Articles

Projection Reconstruction Magnetic Particle Imaging

We acquire the first experimental 3-D tomographic images with magnetic particle imaging (MPI) using projection reconstruction methodology, which is similar to algorithms employed in X-ray computed tomography. The primary advantage of projection reconstruction methods is an order of magnitude increase in signal-to-noise ratio (SNR) due to averaging. We first derive the point spread function, resolution, number of projections required, and the SNR gain in projection reconstruction MPI. We then design and construct the first scanner capable of gathering the necessary data for nonaliased projection reconstruction and experimentally verify our mathematical predictions. We demonstrate that filtered backprojection in MPI is experimentally feasible and illustrate the SNR and resolution improvements with projection reconstruction. Finally, we show that MPI is capable of producing three dimensional imaging volumes in both phantoms and postmortem mice.

Two-dimensional radial sodium heart MRI using variable-rate selective excitation and retrospective electrocardiogram gating with golden angle increments

Two-dimensional projection reconstruction methods provide advantages over three-dimensional techniques because of higher flexibility regarding the resolution and shorter scan time needed. To optimize a two-dimensional radial sequence with respect to signal-to-noise ratio, variable-rate selective excitation and retrospective electrocardiogram gating is investigated. The minimal radiofrequency pulse duration is simulated in dependence of the flip angle and coil parameters using sinc waveforms with two different variable-rate selective excitation approaches and a Fermi pulse. Retrospectively electrocardiogram-gated imaging with Golden Angle incremented projections was implemented to allow for continuous data acquisition enabling the possibility of dynamic electrocardiogram-gated heart imaging. Especially for abdominal coils with high transmitter voltages required, variable-rate selective excitation strongly reduces the radiofrequency pulse duration and echo time resulting in a signal-to-noise ratio gain up to 15.5% (if the fast relaxation component of sodium is in the order of the radiofrequency pulse duration) compared with standard sinc-shaped radiofrequency pulses. Retrospective electrocardiogram gating shows higher flexibility with regard to the trigger delay enabling the trade-off between heart motion artifacts and signal-to-noise ratio. A two-dimensional radial sequence is optimized for sodium heart imaging regarding signal-to-noise ratio. Different sodium contrasts of the human heart are shown, which can give additional information on heart diseases.

Echo-based Single Point Imaging (ESPI): A novel pulsed EPR imaging modality for high spatial resolution and quantitative oximetry

A novel time-domain spectroscopic EPR imaging approach, that is a unique combination of already known techniques, is described. The first one is multi-gradient Single Point Imaging involving pure phase-encoding where the oximetry is based on T2∗. Line width derived from T2∗ is subject to susceptibility effects and therefore needs system-dependent line width calibrations. The second approach utilizes the conventional 90°–τ–180° Spin-Echo pulse sequence where the images are obtained by the filtered back-projection after FT of the echoes collected under frequency-encoding gradients. The spatially resolved oximetry information is derived from a set of T2-weighted images. The back-projection images suffer susceptibility artifacts with resolution determined by T2∗, but the oximetry based on T2 is quite reliable. The current approach combines Single Point Imaging and the Spin-Echo procedure to take advantage the enhanced spatial resolution associated with the former and the T2 dependent contrast of the latter. Pairs of images are derived choosing two time points located at identical time intervals on either side of the 180° pulse. The refocusing pulse being exactly in the middle of the two points ensures that artifacts associated with susceptibility and field inhomogeneities are eliminated. In addition, the net phase accumulated by the two time points being identical results in identical field of views, thus avoiding the zoom-in effect as a function delay in regular SPI and the associated interpolation requirements employed in T2∗-weighted oximetry. The end result is superior image resolution and reliable oximetry. In spite of the fact that projection–reconstruction methods require less number of measurements compared to SPI, the enormous advantage in SNR of the SPI procedure makes the echo-based SPI equally efficient in terms of measurement time. The Fourier reconstruction, line width independent resolution and the true T2-weighting make this novel procedure very attractive for in vivo EPR imaging of tissue oxygen quantitatively.

Structure projection reconstruction from through-focus series of high-resolution transmission electron microscopy images

A structure projection reconstruction method based on contrast transfer function correction of through-focus series of high-resolution transmission electron microscopy images is presented. In this method, defocus values are determined by evaluating phase similarities of the pixels on the Fourier transforms of the images after correction using trial defocus values. Two-fold astigmatism is also determined, by measuring focus variation along different directions. Each image in the series is corrected for the effects of contrast transfer function and then combined into a structure projection image. The method works for both crystalline and non-crystalline objects. Test results with experimental images are presented. Influences of experimental parameters for imaging and effects of crystal thickness on reconstruction are discussed.

Fenestrations accompanied by intracranial aneurysms assessed with magnetic resonance angiography

The aim of this study was to evaluate the anatomical changes and investigate the prevalence in intracranial aneurysm with fenestrations using magnetic resonance angiography (MRA). Between June 2008 and October 2010, 4652 patients (aged 23-73 years) with suspected intracranial aneurysm or other cerebrovascular diseases underwent MRA examination. MRA was performed using a three-dimensional time-of-flight technique (3D-TOF) with volume rendering (VR) and maximum intensity projection reconstruction methods. The presence and location of fenestrations and aneurysms was reviewed. When fenestrations were present in combination with aneurysms, we noted the relationship of the locations. The classification of fenestration accompanied by intracranial aneurysm was divided into three types according to the anatomical relationship as follows: Type I, aneurysm adjacent to but not on a fenestration; Type II, aneurysm located on the fenestration; type III, aneurysm located at a position remote from a fenestration. Among the 4652 patients examined, 409 patients were defined with 412 intracranial aneurysms, and the prevalence of aneurysms was 8.8%. One hundred and forty-one patients were identified with fenestrations; 24 of these patients were confirmed with intracranial aneurysms. Seven cases were classified as type I, three as type II and 14 as type III. The prevalence of intracranial aneurysm with fenestrations was 17.0%, with significant statistical difference compared with aneurysms unaccompanied with fenestrations (P=0.0064). The anatomical relationship between fenestrations and intracranial aneurysms was visualized by MRA with VR, which displayed pathologies with sufficient clarity to enable diagnosis. Furthermore, the results of this study suggest that physicians should be alerted to the occurrence of intracranial aneurysm following the detection of fenestrations by MRA.

Complete 3D Modeling from Rotational Devices

For acquisition of complete 3D models, this paper uses a rotational device to capture a set of image sequences. A direct projective reconstruction method is proposed by linear transformation, which can avoid getting corresponding points in more than two images. Actually, projective reconstructions are obtained from two neighboring images and the reconstructions are combined with the common 3D points. Finally, all reconstructions are merged into the initial one to construct a complete model. Several practical experiments have been carried out to validate the accuracy of the method.

Detecting the “Afterglow” of 13C NMR in Proteins Using Multiple Receivers

We show that the weak signal that remains after (13)C-detected experiments (the (13)C "afterglow") can still be measured with high sensitivity by proton detection. This is illustrated by the incorporation of two experiments, 2D (HA)CACO and 3D (HA)CA(CO)NNH, into a single pulse sequence that makes use of two receivers in parallel. In cases where the sensitivity is not limiting, such as applications to small proteins, the inclusion of the projection-reconstruction method permits the recording of both spectra in only 15 min. High-quality data sets for the 143 residue nuclease A inhibitor (2 °C, correlation time 17.5 ns) were obtained in 3 h, illustrating the utility of the method even in studies of moderately sized proteins.

Two‐dimensional radial acquisition technique with density adaption in sodium MRI

Conventional 2D radial projections suffer from losses in signal-to-noise ratio efficiency because of the nonuniform k-space sampling. In this study, a 2D projection reconstruction method with variable gradient amplitudes is presented to cover the k-space uniformly. The gradient is designed to keep the average sampling density constant. By this, signal-to-noise ratio is increased, and the linear form of the radial trajectory is kept. The simple gradient design and low hardware requirements in respect of slew rate allow an easy implementation at MR scanners. Measurements with the density-adapted 2D radial trajectory were compared with the conventional projection reconstruction method. It is demonstrated that the density-adapted 2D radial trajectory technique provides higher signal-to-noise ratio (up to 28% in brain tissue), less blurring, and fewer artifacts in the presence of magnetic field inhomogeneities than imaging with the conventional 2D radial trajectory scheme. The presented sequence is well-suited for electrocardiographically gated sodium heart MRI and other applications with short relaxation times.

An iterative method based on 1D subspace for projective reconstruction

AbstractHeyden et al. introduced an iterative factorization method for projective reconstruction from image sequences. In their formulation, the projective structure and motion are computed by using an iterative factorization based on 4D subspace. In this paper, the problem is reformulated based on fact that the x, y, and z coordinates of each feature in projective space are known from their projection. The projective reconstruction, i.e., the relative depths w and the 3D motion, is obtained by a simple iterative factorization based on 1D subspace. This allows the use of very fast algorithms even when using a large number of features and large number of frames. The experiments with both simulate and real data show that the method presented in the paper is efficient and has good convergency.

Projective reconstruction with occlusions

AbstractAn iteration method for projective reconstruction from uncalibrated image sequence with occlusions is presented in this paper. The reprojection points replace all the occlusions and projective reconstruction is obtained from all the points alternately, and the real positions of occlusions and the accurate projective reconstruction are finally obtained. The experiments with both synthetic and real data show that the method is effective and accurate.

Study of relative quantification of Tc-99 m with partial volume effect and spillover correction for SPECT oncology imaging

The apparent concentration of activity in structures in nuclear medicine images depends on their size relative to the system spatial resolution. This dependence is called the partial volume effect (PVE). Spillover (SO) or the blurring into a structure of counts originating in nearby structures also alters the apparent concentration of activity. In combination these effects impact the detection of lesions and quantification of activity within structures in the slices. The increased accessibility of dual-modality imaging systems makes available high-resolution anatomical information which is registered with the emission slices and can be used in correcting for the PVE and SO. In this study we investigated the use of the template projection-reconstruction method for correction of the PVE and SO. We examined the impact of correction on visual image quality and the quantification of activity in simulated spheres of varying contrast relative to a uniform background distribution of activity. Our enhancements to the template projection-reconstruction methodology included both an improvement in the matching of the blurring in the reconstructed templates of structures to the actual blurring in the reconstructed slices, and accounting for the fractional presence of structures in SPECT voxels. We determined that such corrections for the PVE and SO can dramatically improve both the visualization and quantification of activity within the source distributions we investigated.

A subspace method for projective reconstruction from multiple images with missing data

In this paper, we consider the problem of projective reconstruction based on the subspace method. Unlike existing subspace methods which require that all the points are visible in all views, we propose an algorithm to estimate projective shape, projective depths and missing data iteratively. All these estimation problems are formulated within a subspace framework in terms of the minimization of a single consistent objective function, hence ensuring the convergence of the iterative solution. Experimental results using both synthetic data and real images are provided to illustrate the performance of the proposed method.

Optimized acquisition and processing protocols for I-123 cardiac SPECT imaging

Deconvolution of septal penetration (DSP) has been developed to improve quantification so as to allow the use of low-energy high-resolution collimators for iodine 123 cardiac single photon emission computed tomography (SPECT) imaging. The purpose of this study is to optimize its acquisition and processing protocols. Planar images of a 9-compartment phantom loaded with variable radioactive concentrations were acquired to derive optimal scatter compensation scaling factors for 20% and 15% photopeak energy window configurations, respectively. A cardiac phantom, loaded with high and low heart-to-calibration ratios (HCRs), respectively, was imaged with both configurations. Repeated acquisitions were done for medium-energy all-purpose collimators for comparison. Critical frequencies for Butterworth filtering were optimized by use of defect contrast and normal short-axis uniformity as selection indices. HCRs were calculated with planar projection and different reconstruction methods, respectively, and then compared with the true HCRs. SPECT produced more accurate HCRs than planar imaging. With the optimized parameters for scatter compensation and filtering, the 2 energy window configurations yielded similar results. Iterative reconstructions with DSP yielded more accurate HCRs than other reconstructions without DSP. The optimized protocols based on DSP show promise that quantification of I-123 cardiac SPECT imaging can be achieved with the widely available low-energy high-resolution collimators.

Three-dimensional cylindrical X-band ESR imaging by a combined pulsed gradient Fourier and static gradient projection reconstruction method

Static gradient electron spin echo projection reconstruction imaging is favourable for X-band material science applications requiring temperature variation with a metal cryostat. To prevent imaging artefacts due to the high conduction electron diffusion coefficient in the preferred conduction direction of quasi-one-dimensional conductors, only pulsed gradient phase encoding for that direction can be tolerated. We present results of an appropriate cylindrical imaging scheme combining both methods. Conduction electron spin density images with 13 × 13 × 17 μm 3 volume element size or spin–lattice relaxation time images with inversion recovery sequence and 13 × 13 × 68 μm 3 volume element size are presented for fluoranthene radical cation salt single crystals of typical sizes of 0.4 × 0.4 × 1 mm 3.

Frame grouping for factorization-based reconstruction over long image sequences

For 3-D reconstruction from uncalibrated sequences, projective reconstruction is needed as a preceding step, which is classified into a merging method and factorization. Factorization-based methods generally suffer less from drift and error accumulation than sequential merging. However, they assume that most corresponding points must remain in all frames. To overcome this limitation, we present a new frame grouping method for factorization-based projective reconstruction over long image sequences. The proposed method breaks a full sequence into subsequences by considering a survival rate of the corresponding points over a sequence, the reprojection error, and the distribution of matching points on the image. All projective reconstructions in subsequences are registered into the same coordinate frame for a complete description of the scene. Experimental results demonstrate that our algorithm can recover more precise 3-D structure than the sequential merging method.

Reconstructing camera projection matrices from multiple pairwise overlapping views

In this work we address the problem of projective reconstruction from multiple views with missing data. Factorization based algorithms require point correspondences across all the views. In many applications this is an unrealistic assumption. Current methods that solve the problem of projective reconstruction with missing data require correspondence information across triplets of images. We propose a projective reconstruction method that yields a consistent camera set given the fundamental matrices between pairs of views without directly using the image correspondences. The algorithm is based on breaking the reconstruction problem into small steps. In each step, we eliminate as much uncertainty as possible.

Automated rectilinear self-gated cardiac cine imaging.

ECG-based gating in cardiac MR imaging requires additional patient preparation time, is susceptible to RF and magnetic interference, and is ineffective in a significant percentage of patients. "Wireless" or "self-gating" techniques have been described using either interleaved central k-space lines or projection reconstruction to obtain MR signals synchronous with the cardiac cycle. However, the interleaved, central line method results in a doubling of the acquisition time, while radial streak artifacts are encountered with the projection reconstruction method. In this work, a new self-gating technique is presented to overcome these limitations. A retrospectively gated TrueFISP cine sequence was modified to acquire a short second echo after the readout and phase gradients are rewound. The information obtained from this second echo was used to derive a gating signal. This technique was compared to ECG-based gating in 10 healthy volunteers and shown to have no significant difference in image quality. The results indicate that this method could serve as an alternative gating strategy without the need for external physiological signal detection.

A three-dimensional electron spin resonance microscope

An electron spin resonance (ESR) imaging system, capable of acquiring three-dimensional (3D) images with a resolution of ∼10×10×30 μm in a few minutes of acquisition, is presented. This ESR microscope employs a commercial continuous wave ESR spectrometer, working at 9.1 GHz, in conjunction with a miniature imaging probe (resonator+gradient coils), gradient current drivers, and control software. The system can acquire the image of a small (∼1.5×1.5×0.25 mm) sample either by the modulated field gradient method, the projection reconstruction method, or by a combination of the two. A short discussion regarding the resolution of the modulated field gradient method in two-dimensional (2D) and 3D imaging is given. Detailed descriptions of the various system components are provided, along with several examples of 2D and 3D images that demonstrate the capabilities of the system.

Projection-reconstruction technique for speeding up multidimensional NMR spectroscopy.

The acquisition of multidimensional NMR spectra can be speeded up by a large factor by a projection-reconstruction method related to a technique used in X-ray scanners. The information from a small number of plane projections is used to recreate the full multidimensional spectrum in the familiar format. Projections at any desired angle of incidence are obtained by Fourier transformation of time-domain signals acquired when two or more evolution intervals are incremented simultaneously at different rates. The new technique relies on an established Fourier transform theorem that relates time-domain sections to frequency-domain projections. Recent developments in NMR instrumentation, such as increased resolution and sensitivity, make fast methods for data gathering much more practical for protein and RNA research. Hypercomplex Fourier transformation generates projections in symmetrically related pairs that provide two independent "views" of the spectrum. A new reconstruction algorithm is proposed, based on the inverse Radon transform. Examples are presented of three- and four-dimensional NMR spectra of nuclease A inhibitor reconstructed by this technique with significant savings in measurement time.

2-d ESR diffusion coefficient imaging with the projection reconstruction method

The static gradient spin echo (SGSE) of the conduction electron spins in a quasi-one dimensional organic conductor is analyzed by simulation and for a microstructured (fluoranthene) 2PF 6 single crystal. It is shown that useful two-dimensional magnetic resonance images of the diffusion coefficient (mobility) D can be obtained from pixel-by-pixel analysis of the signal decay with pulse separation τ, adopting the projection reconstruction (PR) method for signal generation.