Fourier-based Reconstruction Research Articles

Compartment-based reconstruction of 3D acquisition-weighted 31 P cardiac magnetic resonance spectroscopic imaging at 7 T: A reproducibility study.

Even at 7 T, cardiac 31 P magnetic resonance spectroscopic imaging (MRSI) is fundamentally limited by low signal-to-noise ratio (SNR), leading to long scan times and poor temporal and spatial resolutions. Compartment-based reconstruction algorithms such as magnetic resonance spectroscopy with linear algebraic modeling (SLAM) and spectral localization by imaging (SLIM) may improve SNR or reduce scan time without changes to acquisition. Here, we compare the repeatability and SNR performance of these compartment-based methods, applied to three different acquisition schemes at 7 T. Twelve healthy volunteers were scanned twice. Each scan session consisted of a 6.5-min 3D acquisition-weighted (AW) cardiac 31 P phase encode-based MRSI acquisition and two 6.5-min truncated k-space acquisitions with increased averaging (4 × 4 × 4 central k-space phase encodes and fractional SLAM [fSLAM] optimized k-space phase encodes). Spectra were reconstructed using (i) AW Fourier reconstruction; (ii) AW SLAM; (iii) AW SLIM; (iv) 4 × 4 × 4 SLAM; (v) 4 × 4 × 4 SLIM; and (vi) fSLAM acquisition-reconstruction combinations. The phosphocreatine-to-adenosine triphosphate (PCr/ATP) ratio, the PCr SNR, and spatial response functions were computed, in addition to coefficients of reproducibility and variability. Using the compartment-based reconstruction algorithms with the AW 31 P acquisition resulted in a significant increase in SNR compared with previously published Fourier-based MRSI reconstruction methods while maintaining the measured PCr/ATP ratio and improving interscan reproducibility. The alternative acquisition strategies with truncated k-space performed no better than the common AW approach. Compartment-based spectroscopy approaches provide an attractive reconstruction method for cardiac 31 P spectroscopy at 7 T, improving reproducibility and SNR without the need for a dedicated k-space sampling strategy.

Accurate Range Migration for Fast Quantitative Fourier-Based Image Reconstruction With Monostatic Radar

Range migration (or range focusing) techniques are widely used in optical, acoustic, and microwave real-time image reconstruction methods. They have been successfully applied to far-field 3-D imaging where they rely on plane-wave assumptions, which ignore the data amplitude variation over the acquisition aperture. The accuracy of the plane-wave assumption, however, quickly degrades in close-range imaging, where amplitude variations are significant and where the range to the target is on the order of the range sampling step. Here, we present a range-focusing method of improved accuracy, which is applicable to both far-zone and close-range monostatic radar. It refocuses the system point-spread function (PSF) to any range location, taking into account both magnitude and phase changes. The approach can be applied with any Fourier-based imaging algorithm utilizing the Lippmann–Schwinger equation as the underlying scattering model. Here, it is validated through examples based on simulated and measured data where the images are reconstructed with quantitative microwave holography (QMH). QMH employs measured PSFs to achieve quantitative imaging in real-time. The proposed range-migration method is applicable with measured PSFs, too, leading to reduced system-calibration effort and the ability to focus an image at any desired range.

Fourier-Based Near-Field Three-Dimensional Image Reconstruction in a Multistatic Imaging Structure Using Dynamic Metasurface Antennas

Due to physical layer compression, and consequently, the failure to produce uniform radiation patterns, it is not possible to develop fast Fourier-based image reconstruction algorithms using the raw measurements collected from metasurface antennas. An effective solution in the literature is a sub-wavelength sampling of the aperture. However, this solution is currently limited to a panel-to-probe model which requires a mechanical raster scan. On the other hand, existing works are based on time-division multiplexing. This means that only a single transmit/receive channel is active in each time slot. In this paper, we introduce a panel-to-panel model in a multistatic structure. Based on this model, two pre-processing (for two different individually measured signal and combined measured signal (CMS) scenarios) are derived to convert the raw measurements into the space-frequency domain. Then, by using the output data from the pre-processing stage and according to the configuration of the introduced imaging system, the range migration algorithm is adapted. The importance of the proposed solution for the CMS scenario is that, for the first time, it demonstrates the capability of using dynamic metasurface antennas diversity to achieve simultaneous data acquisition. The performance of the proposed approach is compared with state-of-art works in terms of reconstructed image quality and computational complexity using numerical simulations and analytical discussions.

3-D Indoor Device-Free Object Detection by Passive Radio Frequency Identification

Indoor device-free object detection has many applications, such as assisted living, home security, and occupant-centered building utility control. To accommodate 3-D room layout variations and improve accuracy, multiple observation units with spatial diversity are often required, which will unavoidably cause a significant increase in the component and deployment cost if each unit needs wired power or battery. In this article, we present an indoor device-free object detection system implemented by a commercial radio frequency identification reader and many passive tags around the room. The passive tag as a dispersed observation point offers a cost-effective solution for the necessary spatial diversity. The tag backscattering phase is assembled to generate the reflectivity image inside the capture volume using Fourier-based reconstruction. A new calibration technique is proposed to compensate for multiplicative path losses and subtract the effect of background clutters, such as furniture. Noisy channels and channels with their line-of-sight blocked by the target are also filtered out during postprocessing to improve locating accuracy and mitigate ambiguity. A 1:6 room model was first used to study the effects of the indoor materials and room layout, where occupant recognition and centimeter-level locating were successfully demonstrated. Real-scale rooms were then tested, where decimeter-level 3-D location error was achieved for a single occupant, and useful information for occupant posture can also be evaluated.

Fourier Compatible Near-Field Multiple-Input Multiple-Output Terahertz Imaging With Sparse Non-Uniform Apertures

Among image reconstruction methods, Fourier transform-based techniques provide computationally better performance. However, conventional Fourier-based reconstruction techniques require uniform data sampling at the radar aperture. In this paper, a multiple-input multiple-output (MIMO) scenario for near-field (NF) terahertz imaging systems is considered. A compressive-sensing-based method compatible with efficient fast Fourier-based techniques for image reconstruction is proposed. To reduce the error due to the multistatic array topology in the NF, a multistatic-to-monostatic conversion is used. Employing the proposed method significantly reduces the number of antennas and channels. This, in addition to saving hardware resources, can improve the overall performance of the system depending on the type of channel access scheme. The results based on both numerical and electromagnetic data, presented as reconstructed images of the scene, confirm the performance of the proposed method.

Point Spread Function Formation in Plane-Wave Imaging: A Theoretical Approximation in Fourier Migration.

The point spread function (PSF) is often analyzed to determine the image quality of an ultrasound system. The formation of PSF is determined by practical factors, such as transducer aperture, element directivity, apodization, pitch, imaging position, and steering angle. Conventional numerical simulations provide an iterative approach to examine those factors' effects but cannot explain the inherent mechanism of PSF formation. This article presents a theoretical approximation of PSF formation for plane-wave imaging throughout the Fourier-based reconstruction process. Aforementioned factors are incorporated in the theory. The proposed theory is used to analyze the effects of those factors and presents a high degree of consistency with numerical simulations and experiments.

Fast Fourier-Based Implementation of Synthetic Aperture Radar Algorithm for Multistatic Imaging System

Multistatic millimeter-wave imaging structures are superior to their monostatic counterparts for imaging natural objects of sudden profile variations. Multistatic image reconstruction is conventionally performed via synthetic aperture radar (SAR)-based methods which, in spite of their high accuracy, are computationally burdensome. On the other side, the Fourier-based image reconstruction in multistatic systems also faces few challenges including multidimensional interpolation, a plane-wave approximation of spherical waves, and $k$ -space partitioning. This paper presents a fast implementation of the SAR-based image reconstruction method in case of 1-D and 2-D multistatic arrays. The proposed implementation is Fourier based across the uniform direction in $k$ -space and SAR based along the nonuniform direction. Both methods are fully parallelizable and are arranged into a vector format to maximize memory usage and minimize the computational time. The extensive validation and benchmarking have been performed with both simulation and experimental data, which proves a $256\times $ improvement in the reconstruction time for the worst case scenario compared to that of in SAR-based methods with the same image quality. Furthermore, the reconstructed image performance is around $10\times $ better than the most recent Fourier-based reconstruction method, in terms of root-mean-square error metric, and with $28\times $ less computational time.

Accelerating 2D NMR relaxation dispersion experiments using iterated maps.

NMR relaxation dispersion experiments play a central role in exploring molecular motion over an important range of timescales, and are an example of a broader class of multidimensional NMR experiments that probe important biomolecules. However, resolving the spectral features of these experiments using the Fourier transform requires sampling the full Nyquist grid of data, making these experiments very costly in time. Practitioners often reduce the experiment time by omitting 1D experiments in the indirectly observed dimensions, and reconstructing the spectra using one of a variety of post-processing algorithms. In prior work, we described a fast, Fourier-based reconstruction method using iterated maps according to the Difference Map algorithm of Veit Elser (DiffMap). Here we describe coDiffMap, a new reconstruction method that is based on DiffMap, but which exploits the strong correlations between 2D data slices in a pseudo-3D experiment. We apply coDiffMap to reconstruct dispersion curves from an [Formula: see text] relaxation dispersion experiment, and demonstrate that the method provides fast reconstructions and accurate relaxation curves down to very low numbers of sparsely-sampled data points.

Count-based imaging model for the Spectrometer/Telescope for Imaging X-rays (STIX) in Solar Orbiter

The Spectrometer/Telescope for Imaging X-rays (STIX) will study solar flares across the hard X-ray window provided by the Solar Orbiter cluster. Similarly to the Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI), STIX is a visibility-based imaging instrument that will require Fourier-based image reconstruction methods. However, in this paper we show that as for RHESSI, count-based imaging is also possible for STIX. Specifically, we introduce and illustrate a mathematical model that mimics the STIX data formation process as a projection from the incoming photon flux into a vector consisting of 120 count components. Then we test the reliability of expectation maximization for image reconstruction in the case of several simulated configurations that are typical of flare morphology.

Near-Field MIMO-SAR Millimeter-Wave Imaging With Sparsely Sampled Aperture Data

The primary challenge of a cost-effective and low-complexity near-field millimeter-wave (mmWave) imaging system is to achieve high resolution with a few antenna elements as possible. Multiple-input multiple-output (MIMO) radar using simultaneous operation of spatially diverse transmit and receive antennas is a good candidate to increase the number of available degrees of freedom. On the other hand, higher integration complexity of extremely dense transceiver electronics limits the use of MIMO only solutions within a relatively large imaging aperture. Hybrid concepts combining synthetic aperture radar (SAR) techniques and sparse MIMO arrays present a good compromise to achieve short data acquisition time and low complexity. However, compared with conventional monostatic sampling schemes, image reconstruction methods for MIMO-SAR are more complicated. In this paper, we propose a high-resolution mmWave imaging system combining 2-D MIMO arrays with SAR, along with a novel Fourier-based image reconstruction algorithm using sparsely sampled aperture data. The proposed algorithm is verified by both simulation and processing real data collected with our mmWave imager prototype utilizing commercially available 77-GHz MIMO radar sensors. The experimental results confirm that our complete solution presents a strong potential in high-resolution imaging with a significantly reduced number of antenna elements.

Simultaneous reconstruction of seismic reflections and diffractions using a global hyperbolic Radon dictionary

We have developed a new transform with basis functions that closely resemble seismic reflections and diffractions. The new transform is an extension of the classic hyperbolic Radon transform and accounts for the apex shifts of the seismic reflection hyperbolas and the asymptote shifts of the seismic diffraction hyperbolas. The adjoint and forward operators of the proposed transform are computed using Stolt operators in the frequency domain to increase the computational efficiency of the transform. This new transform is used, in conjunction with a sparse inversion algorithm, to reconstruct common-shot gathers. Our tests indicate that this new transform is an efficient tool for interpolating coarsely sampled seismic data in cases in which one cannot use small data windows to validate the linear event assumption that is often made by Fourier-based reconstruction methods.

Additive noise models for photoacoustic spatial coherence theory.

Directly displaying the spatial coherence of photoacoustic signals (i.e., coherence-based photoacoustic imaging) remarkably improves image contrast, signal-to-noise ratio (SNR), contrast-to-noise ratio (CNR), and imaging depth when compared to conventional amplitude-based reconstruction techniques (e.g., backprojection, delay-and-sum beamforming, and Fourier-based reconstruction). We recently developed photoacoustic-specific theory to describe the spatial coherence process as a function of the element spacing on a receive acoustic aperture to enable photoacoustic image optimization without requiring experiments. However, this theory lacked noise models, which contributed to significant departures in coherence measurements when compared to experimental data, particularly at higher values of element separation. In this paper, we develop and implement two models based on experimental observations of noise in photoacoustic spatial coherence measurements to improve our existing spatial coherence theory. These models were derived to describe the effects of incident fluence variations, low-energy light sources (e.g., pulsed laser diodes and light-emitting diodes), averaging multiple signals from low-energy light sources, and imaging with light sources that are > 5mm from photoacoustic targets. Results qualitatively match experimental coherence functions and provide similar contrast, SNR, and CNR to experimental SLSC images. In particular, the added noise affects image quality metrics by introducing large variations in target contrast and significantly reducing target CNR and SNR when compared to minimal-noise cases. These results provide insight into additional requirements for optimization of coherence-based photoacoustic image quality.

Fourier Accelerated Multistatic Imaging: A Fast Reconstruction Algorithm for Multiple-Input-Multiple-Output Radar Imaging

Multiple-input-multiple-output (MIMO) radar image processing presents problems difficult to address by modifying conventional monostatic radar methods as Fourier range migration. When the distance between the transmitter and receiver is comparable to the target size, the single phase center approximation is not accurate. Furthermore, if the antenna radiation pattern significantly deviates from a spherical wave, the symmetries assumed in most range migration techniques are violated. We present a rapid Fourier-based MIMO reconstruction called Fourier accelerated multistatic imaging (FAMI) suitable for massively parallel computation that accounts for frequency-dependent radiation patterns, does not require the single phase center approximation, and is able to dynamically adapt to different target support volume shapes. FAMI is especially suitable for frequency-diversity antenna systems that use spectrally modulated coded spatial radiation patterns.

Direct Fourier Inversion Reconstruction Algorithm for Computed Laminography.

Synchrotron radiation computed laminography (CL) was developed to complement the conventional computed tomography as a non-destructive 3D imaging method for the inspection of flat thin objects. Recent progress in hardware at synchrotron sources allows one to record internal evolution of specimens at the micrometer scale and sub-second range but also requires increased reconstruction speed to follow structural changes online. A 3D image of the sample interior is usually reconstructed by the well-established filtered backprojection (FBP) approach. Despite of a great success in the reduction of reconstruction time via parallel computations, the FBP algorithm still remains a time-consuming procedure. A promising way to significantly shorten computation time is to directly perform backprojection in frequency domain (a direct Fourier inversion approach). The corresponding algorithms are rarely considered in the literature because of a poor performance or inferior reconstruction quality resulted from inaccurate interpolation in Fourier domain. In this paper, we derive a Fourier-based reconstruction equation designed for the CL scanning geometry. Furthermore, we outline the translation of the continuous solution to a discrete version, which utilizes 3D sinc interpolation. A projection resampling technique allowing for the reduction of the expensive interpolation to its 1D version is proposed. A series of numerical experiments confirms that the resulting image quality is well comparable with the FBP approach while reconstruction time is drastically reduced.

Novel Fourier-based iterative reconstruction for sparse fan projection using alternating direction total variation minimization**Projected supported by the National High Technology Research and Development Program of China (Grant No. 2012AA011603) and the National Natural Science Foundation of China (Grant No. 61372172).

Sparse-view x-ray computed tomography (CT) imaging is an interesting topic in CT field and can efficiently decrease radiation dose. Compared with spatial reconstruction, a Fourier-based algorithm has advantages in reconstruction speed and memory usage. A novel Fourier-based iterative reconstruction technique that utilizes non-uniform fast Fourier transform (NUFFT) is presented in this work along with advanced total variation (TV) regularization for a fan sparse-view CT. The proposition of a selective matrix contributes to improve reconstruction quality. The new method employs the NUFFT and its adjoin to iterate back and forth between the Fourier and image space. The performance of the proposed algorithm is demonstrated through a series of digital simulations and experimental phantom studies. Results of the proposed algorithm are compared with those of existing TV-regularized techniques based on compressed sensing method, as well as basic algebraic reconstruction technique. Compared with the existing TV-regularized techniques, the proposed Fourier-based technique significantly improves convergence rate and reduces memory allocation, respectively.

NUFFT-Based Iterative Image Reconstruction via Alternating Direction Total Variation Minimization for Sparse-View CT.

Sparse-view imaging is a promising scanning method which can reduce the radiation dose in X-ray computed tomography (CT). Reconstruction algorithm for sparse-view imaging system is of significant importance. The adoption of the spatial iterative algorithm for CT image reconstruction has a low operation efficiency and high computation requirement. A novel Fourier-based iterative reconstruction technique that utilizes nonuniform fast Fourier transform is presented in this study along with the advanced total variation (TV) regularization for sparse-view CT. Combined with the alternating direction method, the proposed approach shows excellent efficiency and rapid convergence property. Numerical simulations and real data experiments are performed on a parallel beam CT. Experimental results validate that the proposed method has higher computational efficiency and better reconstruction quality than the conventional algorithms, such as simultaneous algebraic reconstruction technique using TV method and the alternating direction total variation minimization approach, with the same time duration. The proposed method appears to have extensive applications in X-ray CT imaging.

Fourier-based reconstruction via alternating direction total variation minimization in linear scan CT

In this study, we consider a novel form of computed tomography (CT), that is, linear scan CT (LCT), which applies a straight line trajectory. Furthermore, an iterative algorithm is proposed for pseudo-polar Fourier reconstruction through total variation minimization (PPF-TVM). Considering that the sampled Fourier data are distributed in pseudo-polar coordinates, the reconstruction model minimizes the TV of the image subject to the constraint that the estimated 2D Fourier data for the image are consistent with the 1D Fourier transform of the projection data. PPF-TVM employs the alternating direction method (ADM) to develop a robust and efficient iteration scheme, which ensures stable convergence provided that appropriate parameter values are given. In the ADM scheme, PPF-TVM applies the pseudo-polar fast Fourier transform and its adjoint to iterate back and forth between the image and frequency domains. Thus, there is no interpolation in the Fourier domain, which makes the algorithm both fast and accurate. PPF-TVM is particularly useful for limited angle reconstruction in LCT and it appears to be robust against artifacts. The PPF-TVM algorithm was tested with the FORBILD head phantom and real data in comparisons with state-of-the-art algorithms. Simulation studies and real data verification suggest that PPF-TVM can reconstruct higher accuracy images with lower time consumption.

Noncontact photoacoustic imaging based on all-fiber heterodyne interferometer.

We report on a noncontact photoacoustic imaging system utilizing an all-fiber-optic heterodyne interferometer as an acoustic wave detector. The acoustic wave generated by a short laser pulse via the photoacoustic effect and arriving at the sample surface could be detected with the fiber-optic heterodyne interferometer without physical contact or using an impedance matching medium. A phantom experiment was conducted to evaluate the proposed system, and the initial acoustic pressure distribution was calculated using a Fourier-based reconstruction algorithm. It is expected that the all-fiber-optic configuration of the proposed system can be applied as a minimally invasive diagnostic tool.

Low-complexity sparse reconstruction for high-resolution multi-static passive SAR imaging*

Abstract Bi-static passive synthetic aperture radar (SAR) systems using ground broadcast and wireless network signals suffer from a low spatial resolution due to the narrow bandwidths and low carrier frequencies. By exploiting multiple distributed illuminators, multi-static passive radar has the possibility of producing high-resolution SAR images. In this paper, a two-stage image formation approach, which combines the Fourier transform and sparse reconstruction strategies, is proposed to process multi-static SAR data. This method exploits the group sparsity of the sparse scene, i.e., the observations associated with different bi-static pairs share the same support of the sparse scene but correspond to aspect-dependent scattering coefficients. Such observations are described as a number of generally disjoint sub-bands in the two-dimensional spatial frequency domain. In each sub-band, the sampling satisfies the Nyquist criterion, whereas different sub-bands are sparsely distributed. In the proposed approach, Fourier-based reconstruction is applied to the sub-band data to produce the coarse-resolution images, which are then combined to produce a high-resolution image through the exploitation of sparse reconstruction techniques. The proposed approach greatly improves the imaging quality as compared to Fourier-based reconstruction, whereas it exhibits significant reduction of the computational complexity when compared to direct application of sparse reconstruction techniques. The exploitation of block sparsity-based techniques also permits practical treatment of the angle-dependent target scattering characteristics in SAR image reconstruction. The advantages of the proposed approach are delineated using analysis and simulations.

Radiation dose reduction in medical x‐ray CT via Fourier‐based iterative reconstruction

A Fourier-based iterative reconstruction technique, termed Equally Sloped Tomography (EST), is developed in conjunction with advanced mathematical regularization to investigate radiation dose reduction in x-ray CT. The method is experimentally implemented on fan-beam CT and evaluated as a function of imaging dose on a series of image quality phantoms and anonymous pediatric patient data sets. Numerical simulation experiments are also performed to explore the extension of EST to helical cone-beam geometry. EST is a Fourier based iterative algorithm, which iterates back and forth between real and Fourier space utilizing the algebraically exact pseudopolar fast Fourier transform (PPFFT). In each iteration, physical constraints and mathematical regularization are applied in real space, while the measured data are enforced in Fourier space. The algorithm is automatically terminated when a proposed termination criterion is met. Experimentally, fan-beam projections were acquired by the Siemens z-flying focal spot technology, and subsequently interleaved and rebinned to a pseudopolar grid. Image quality phantoms were scanned at systematically varied mAs settings, reconstructed by EST and conventional reconstruction methods such as filtered back projection (FBP), and quantified using metrics including resolution, signal-to-noise ratios (SNRs), and contrast-to-noise ratios (CNRs). Pediatric data sets were reconstructed at their original acquisition settings and additionally simulated to lower dose settings for comparison and evaluation of the potential for radiation dose reduction. Numerical experiments were conducted to quantify EST and other iterative methods in terms of image quality and computation time. The extension of EST to helical cone-beam CT was implemented by using the advanced single-slice rebinning (ASSR) method. Based on the phantom and pediatric patient fan-beam CT data, it is demonstrated that EST reconstructions with the lowest scanner flux setting of 39 mAs produce comparable image quality, resolution, and contrast relative to FBP with the 140 mAs flux setting. Compared to the algebraic reconstruction technique and the expectation maximization statistical reconstruction algorithm, a significant reduction in computation time is achieved with EST. Finally, numerical experiments on helical cone-beam CT data suggest that the combination of EST and ASSR produces reconstructions with higher image quality and lower noise than the Feldkamp Davis and Kress (FDK) method and the conventional ASSR approach. A Fourier-based iterative method has been applied to the reconstruction of fan-bean CT data with reduced x-ray fluence. This method incorporates advantageous features in both real and Fourier space iterative schemes: using a fast and algebraically exact method to calculate forward projection, enforcing the measured data in Fourier space, and applying physical constraints and flexible regularization in real space. Our results suggest that EST can be utilized for radiation dose reduction in x-ray CT via the readily implementable technique of lowering mAs settings. Numerical experiments further indicate that EST requires less computation time than several other iterative algorithms and can, in principle, be extended to helical cone-beam geometry in combination with the ASSR method.