Nonlinear Reconstruction Algorithm Research Articles

A New Divide-and-Conquer Method for 3-D Electrical Impedance Tomography

Electrical impedance tomography (EIT) is a patient-safe approach for imaging applications and is a promising technology for biomedical imaging. By applying a small electrical current to living tissue and measuring the electrical potential at different points of the tissue’s boundary, it is possible to solve the inverse problem and to generate a map of the tissue’s conductivities. Although it is a promising method, the reconstruction process remains a complicated task, and real-time nonlinear image reconstruction algorithms have not yet been widely adopted. Recent studies have proposed the use of artificial neural networks (ANN) to solve the EIT inverse problem. ANNs can give a nonlinear conductivity distribution. Although several studies have examined 2-D finite-element models, very little work has been done on 3-D problems. In this paper, a solution based on the divide-and-conquer method and ANNs is used to solve the nonlinear inverse problem without any linearization. The solution presented here reduces the difficulty of training large ANNs, which are commonly required to solve a 3-D EIT problem with artificial intelligence algorithms.

Compressively sampled MR image reconstruction using generalized thresholding iterative algorithm

Compressed sensing (CS) is an emerging area of interest in Magnetic Resonance Imaging (MRI). CS is used for the reconstruction of the images from a very limited number of samples in k-space. This significantly reduces the MRI data acquisition time. One important requirement for signal recovery in CS is the use of an appropriate non-linear reconstruction algorithm. It is a challenging task to choose a reconstruction algorithm that would accurately reconstruct the MR images from the under-sampled k-space data. Various algorithms have been used to solve the system of non-linear equations for better image quality and reconstruction speed in CS. In the recent past, iterative soft thresholding algorithm (ISTA) has been introduced in CS-MRI. This algorithm directly cancels the incoherent artifacts produced because of the undersampling in k-space. This paper introduces an improved iterative algorithm based on p-thresholding technique for CS-MRI image reconstruction. The use of p-thresholding function promotes sparsity in the image which is a key factor for CS based image reconstruction. The p-thresholding based iterative algorithm is a modification of ISTA, and minimizes non-convex functions. It has been shown that the proposed p-thresholding iterative algorithm can be used effectively to recover fully sampled image from the under-sampled data in MRI. The performance of the proposed method is verified using simulated and actual MRI data taken at St. Mary’s Hospital, London. The quality of the reconstructed images is measured in terms of peak signal-to-noise ratio (PSNR), artifact power (AP), and structural similarity index measure (SSIM). The proposed approach shows improved performance when compared to other iterative algorithms based on log thresholding, soft thresholding and hard thresholding techniques at different reduction factors.

The role of advanced reconstruction algorithms in cardiac CT.

Non-linear iterative reconstruction (IR) algorithms have been increasingly incorporated into clinical cardiac CT protocols at institutions around the world. Multiple IR algorithms are available commercially from various vendors. IR algorithms decrease image noise and are primarily used to enable lower radiation dose protocols. IR can also be used to improve image quality for imaging of obese patients, coronary atherosclerotic plaques, coronary stents, and myocardial perfusion. In this article, we will review the various applications of IR algorithms in cardiac imaging and evaluate how they have changed practice.

Super-resolution thermographic imaging using blind structured illumination

Using an infrared camera for thermographic imaging allows the contactless temperature measurement of many surface pixels simultaneously. From the measured surface data, the structure below the surface, embedded inside a sample or tissue, can be reconstructed and imaged, if heated by an excitation light pulse. The main drawback in active thermographic imaging is the degradation of the spatial resolution with the imaging depth, which results in blurred images for deeper lying structures. We circumvent this degradation by using blind structured illumination combined with a non-linear joint sparsity reconstruction algorithm. We demonstrate imaging of a line pattern and a star-shaped structure through a 3 mm thick steel sheet with a resolution four times better than the width of the thermal point-spread-function. The structured illumination is realized by parallel slits cut in an aluminum foil, where the excitation coming from a flashlight can penetrate. This realization of super-resolution thermographic imaging demonstrates that blind structured illumination allows thermographic imaging without high degradation of the spatial resolution for deeper lying structures. The groundbreaking concept of super-resolution can be transferred from optics to diffusive imaging by defining a thermal point-spread-function, which gives the principle resolution limit for a certain signal-to-noise ratio, similar to the Abbe limit for a certain optical wavelength. In future work, the unknown illumination pattern could be the speckle pattern generated by a short laser pulse inside a light scattering sample or tissue.

Optimal sampling recovery of mixed order Sobolev embeddings via discrete Littlewood–Paley type characterizations

In this paper we consider the L q -approximation of multivariate periodic functions f with L q -bounded mixed derivative (difference). The (possibly non-linear) reconstruction algorithm is supposed to recover the function from function values, sampled on a discrete set of n sampling nodes. The general performance is measured in terms of (non-)linear sampling widths ϱ n . We conduct a systematic analysis of Smolyak type interpolation algorithms in the framework of Besov–Lizorkin–Triebel spaces of dominating mixed smoothness based on specifically tailored discrete Littlewood–Paley type characterizations. As a consequence, we provide sharp upper bounds for the asymptotic order of the (non-)linear sampling widths in various situations and close some gaps in the existing literature. For example, in case 2 ≤ p < q < ∞ and r > 1/p the linear sampling widths ϱ lin (S W(T d ), L q (T d )) and ϱ lin (S ,∞ B(T d ), L q (T d )) show the asymptotic behavior of the corresponding Gelfand n-widths, whereas in case 1 < p < q ≤ 2 and r > 1/p the linear sampling widths match the corresponding linear widths. In the mentioned cases linear Smolyak interpolation based on univariate classical trigonometric interpolation turns out to be optimal.

Reconstruction of Kelvin probe force microscopy image with experimentally calibrated point spread function.

A Kelvin probe force microscopy (KPFM) image is sometimes difficult to interpret because it is a blurred representation of the true surface potential (SP) distribution of the materials under test. The reason for the blurring is that KPFM relies on the detection of electrostatic force, which is a long-range force compared to other surface forces. Usually, KPFM imaging model is described as the convolution of the true SP distribution of the sample with an intrinsic point spread function (PSF) of the measurement system. To restore the true SP signals from the blurred ones, the intrinsic PSF of the system is needed. In this work, we present a way to experimentally calibrate the PSF of the KPFM system. Taking the actual probe shape and experimental parameters into consideration, this calibration method leads to a more accurate PSF than the ones obtained from simulations. Moreover, a nonlinear reconstruction algorithm based on total variation (TV) regularization is applied to KPFM measurement to reverse the blurring caused by PSF during KPFM imaging process; as a result, noises are reduced and the fidelity of SP signals is improved.

13. Clinical NECR in 18F-FDG PET scans: Use for optimization purposes

The injected activity and the acquisition time per bed position for 18F-FDG PET scans are usually optimized by using metrics obtained from phantom experiments. However, optimal activity and time duration can significantly vary from a phantom set-up and from patient to patient. In this presentation, we will give an overview of the different approach used for determining optimal acquisition settings using either clinical or experimental data. We will focus next on an approach using a patient-specific noise equivalent count rate (NECR) modelling that has been previously proposed for optimizing clinical scanning protocols [1] . This methodology has been recently extended and assessed using a large population as a function of the body mass index (BMI) for deriving the optimal injected activity and acquisition duration per bed position [2] . The relationship between the NEC and the signal-to-noise ratio (SNR) was assessed both in a phantom and in a clinical setting. 491 consecutive patients were retrospectively evaluated and divided into 4 BMI subgroups. Two criteria were used to optimize the injected activity and the time per bed position was adjusted using the NECR value while keeping the total acquisition time constant. Finally, the relationship between NEC and SNR was investigated using an anthropomorphic phantom and a population of 507 other patients. While the first dose regimen suggested a unique injected activity (665 MBq) regardless of the BMI, the second dose regimen proposed a variable activity and a total acquisition time according to the BMI. The NEC improvement was around 35% as compared with the local current injection rule. Variable time per bed position was derived according to BMI and anatomical region. NEC and number of true events were found to be highly correlated with SNR for the phantom set-up and partially confirmed in the patient study for the BMI subgroup under 28 kg/m2 suggesting that for the scanner, the nonlinear reconstruction algorithm used in this study and BMI

Compressively Sampled MRI Recovery Using Modified Iterative-Reweighted Least Square Method

Magnetic resonance imaging (MRI) is a medical imaging modality used for high-resolution soft-tissue imaging of human body. In traditional MRI acquisition methods, sampling is performed at Nyquist rate to store data in k-space. The MR image is recovered using inverse Fast Fourier Transform (FFT). This approach results in slow data acquisition process, which is uncomfortable for the patients. Compressed Sensing (CS) acquisition approach offers nearly perfect recovery of MR image using non-linear reconstruction algorithms even from partial k-space data. This study presents a novel method to reconstruct MR image from highly under-sampled data using modified Iterative-Reweighted Least Square (IRLS) method with additional data consistency constraints. IRLS is an effective numerical method used in convex optimization problems. The proposed algorithm was applied on original human brain and Shepp–Logan phantom image, and the data acquired from the MRI scanner at St. Mary’s Hospital, London. The experimental results show that the proposed algorithm outperforms Projection onto Convex Sets (POCS), Separable Surrogate Functional (SSF), Iterative-Reweighted Least Squares (IRLS), Zero Filling (ZF), and Low-Resolution (LR) methods based on the parameters, e.g. Peak Signal-to-Noise Ratio (PSNR), Improved Signal-to-Noise Ratio (ISNR), Fitness, Correlation, Structural SIMilarity (SSIM) index, and Artifact Power (AP).

TU‐D‐207A‐00: Quantitative Assessment of CT Systems with Iterative Image Reconstruction Algorithms

In recent several years, motivated by the need to reduce radiation doses in CT exams, all of the major CT manufacturers have commercialized different iterative image reconstruction techniques and these innovative techniques were used in clinical routines with increasing popularity. However, due to the intrinsic nonlinearity of these new techniques, the well accepted quantitative image quality assessment metrics such as spatial resolution and contrast to noise ratio are not sufficient to provide the needed quantitative metrics for assessing image quality and for guiding the CT scan protocol optimization. This symposium aims at providing a thorough update to AAPM community on what we have understood in the past for linear CT imaging system, what are the new challenges and opportunities offered by the nonlinear iterative image reconstruction, and what would be the future directions in quantitative image quality assessment that the AAPM community can work together to address the challenges and to adapt the nonlinear image reconstruction methods to routine clinical practice to improve patient care. Three invited speakers will lead the discussions in this symposium.Dr. Ke Li from the University of Wisconsin‐Madison will be presenting the new challenges introduced in model‐based iterative reconstruction (MBIR) method with a focus on how the nonlinear nature of the MBIR reconstruction poses challenges in quantitative image quality metrics such as spatial resolution, noise power spectrum, and the limitations of CNR in protocol optimization which eventually leads to the need of task‐based detectability index as the metric.Dr. Shuai Leng from Mayo Clinic will then present how the CNR metric is insufficient for nonlinear reconstruction algorithms, and how task based model observers can be used to more accurately quantify image quality, and to optimize imaging system and scanning protocols for nonlinear iterative image reconstruction algorithms based on specific imaging task. Practical considerations regarding the application of task based image quality metrics will also be discussed.Dr. Ehsan Samei from Duke University will start the symposium by summarizing a to‐be‐released AAPM Task Group report (TG 233: Performance Evaluation of Computed Tomography Systems). He will cover what has been understood and accepted for linear CT imaging system, what are the new challenges in CT image quality assessment introduced by the nonlinear iterative reconstruction (IR) techniques, and summarize both taskneutral and task‐based metrologies developed in TG 233 to partially address these challenges, and foresee additional challenges in the future. Learning Objectives: Understand the challenges in quantitative image quality assessment introduced by nonlinear iterative reconstruction techniques Understand the challenges and methods in noise performance assessment for nonlinear iterative reconstruction techniques Understand the challenges and methods in in spatial resolution assessment for nonlinear iterative reconstruction techniques Understand the challenges and methods in in task‐based observer performance assessment for nonlinear iterative reconstruction techniquesFunding support received from NIH and DOD; Funding support received from GE Healthcare; Funding support received from Siemens AX; Patent royalties received from GE Healthcare; S. Leng, R01 EB071095; U01 EB017185; E. Samei, Research grant, Siemens; Research grant, GE; K. Li, Funding from NIH, DOD and AAPM

TU‐D‐207A‐03: Quantitative Assessment of CT Systems with Iterative Image Reconstruction Algorithms

In recent several years, motivated by the need to reduce radiation doses in CT exams, all of the major CT manufacturers have commercialized different iterative image reconstruction techniques and these innovative techniques were used in clinical routines with increasing popularity. However, due to the intrinsic nonlinearity of these new techniques, the well accepted quantitative image quality assessment metrics such as spatial resolution and contrast to noise ratio are not sufficient to provide the needed quantitative metrics for assessing image quality and for guiding the CT scan protocol optimization. This symposium aims at providing a thorough update to AAPM community on what we have understood in the past for linear CT imaging system, what are the new challenges and opportunities offered by the nonlinear iterative image reconstruction, and what would be the future directions in quantitative image quality assessment that the AAPM community can work together to address the challenges and to adapt the nonlinear image reconstruction methods to routine clinical practice to improve patient care. Three invited speakers will lead the discussions in this symposium.Dr. Ke Li from the University of Wisconsin‐Madison will be presenting the new challenges introduced in model‐based iterative reconstruction (MBIR) method with a focus on how the nonlinear nature of the MBIR reconstruction poses challenges in quantitative image quality metrics such as spatial resolution, noise power spectrum, and the limitations of CNR in protocol optimization which eventually leads to the need of task‐based detectability index as the metric.Dr. Shuai Leng from Mayo Clinic will then present how the CNR metric is insufficient for nonlinear reconstruction algorithms, and how task based model observers can be used to more accurately quantify image quality, and to optimize imaging system and scanning protocols for nonlinear iterative image reconstruction algorithms based on specific imaging task. Practical considerations regarding the application of task based image quality metrics will also be discussed.Dr. Ehsan Samei from Duke University will start the symposium by summarizing a to‐be‐released AAPM Task Group report (TG 233: Performance Evaluation of Computed Tomography Systems). He will cover what has been understood and accepted for linear CT imaging system, what are the new challenges in CT image quality assessment introduced by the nonlinear iterative reconstruction (IR) techniques, and summarize both taskneutral and task‐based metrologies developed in TG 233 to partially address these challenges, and foresee additional challenges in the future. Learning Objectives: Understand the challenges in quantitative image quality assessment introduced by nonlinear iterative reconstruction techniques Understand the challenges and methods in noise performance assessment for nonlinear iterative reconstruction techniques Understand the challenges and methods in in spatial resolution assessment for nonlinear iterative reconstruction techniques Understand the challenges and methods in in task‐based observer performance assessment for nonlinear iterative reconstruction techniquesFunding support received from NIH and DOD; Funding support received from GE Healthcare; Funding support received from Siemens AX; Patent royalties received from GE Healthcare; S. Leng, R01 EB071095; U01 EB017185; E. Samei, Research grant, Siemens; Research grant, GE; K. Li, Funding from NIH, DOD and AAPM

TU‐D‐207A‐02: Quantitative Assessment of CT Systems with Iterative Image Reconstruction Algorithms

In recent several years, motivated by the need to reduce radiation doses in CT exams, all of the major CT manufacturers have commercialized different iterative image reconstruction techniques and these innovative techniques were used in clinical routines with increasing popularity. However, due to the intrinsic nonlinearity of these new techniques, the well accepted quantitative image quality assessment metrics such as spatial resolution and contrast to noise ratio are not sufficient to provide the needed quantitative metrics for assessing image quality and for guiding the CT scan protocol optimization. This symposium aims at providing a thorough update to AAPM community on what we have understood in the past for linear CT imaging system, what are the new challenges and opportunities offered by the nonlinear iterative image reconstruction, and what would be the future directions in quantitative image quality assessment that the AAPM community can work together to address the challenges and to adapt the nonlinear image reconstruction methods to routine clinical practice to improve patient care. Three invited speakers will lead the discussions in this symposium.Dr. Ke Li from the University of Wisconsin‐Madison will be presenting the new challenges introduced in model‐based iterative reconstruction (MBIR) method with a focus on how the nonlinear nature of the MBIR reconstruction poses challenges in quantitative image quality metrics such as spatial resolution, noise power spectrum, and the limitations of CNR in protocol optimization which eventually leads to the need of task‐based detectability index as the metric.Dr. Shuai Leng from Mayo Clinic will then present how the CNR metric is insufficient for nonlinear reconstruction algorithms, and how task based model observers can be used to more accurately quantify image quality, and to optimize imaging system and scanning protocols for nonlinear iterative image reconstruction algorithms based on specific imaging task. Practical considerations regarding the application of task based image quality metrics will also be discussed.Dr. Ehsan Samei from Duke University will start the symposium by summarizing a to‐be‐released AAPM Task Group report (TG 233: Performance Evaluation of Computed Tomography Systems). He will cover what has been understood and accepted for linear CT imaging system, what are the new challenges in CT image quality assessment introduced by the nonlinear iterative reconstruction (IR) techniques, and summarize both taskneutral and task‐based metrologies developed in TG 233 to partially address these challenges, and foresee additional challenges in the future. Learning Objectives: Understand the challenges in quantitative image quality assessment introduced by nonlinear iterative reconstruction techniques Understand the challenges and methods in noise performance assessment for nonlinear iterative reconstruction techniques Understand the challenges and methods in in spatial resolution assessment for nonlinear iterative reconstruction techniques Understand the challenges and methods in in task‐based observer performance assessment for nonlinear iterative reconstruction techniquesFunding support received from NIH and DOD; Funding support received from GE Healthcare; Funding support received from Siemens AX; Patent royalties received from GE Healthcare; S. Leng, R01 EB071095; U01 EB017185; E. Samei, Research grant, Siemens; Research grant, GE; K. Li, Funding from NIH, DOD and AAPM

TU‐D‐207A‐01: Quantitative Assessment of CT Systems with Iterative Image Reconstruction Algorithms

In recent several years, motivated by the need to reduce radiation doses in CT exams, all of the major CT manufacturers have commercialized different iterative image reconstruction techniques and these innovative techniques were used in clinical routines with increasing popularity. However, due to the intrinsic nonlinearity of these new techniques, the well accepted quantitative image quality assessment metrics such as spatial resolution and contrast to noise ratio are not sufficient to provide the needed quantitative metrics for assessing image quality and for guiding the CT scan protocol optimization. This symposium aims at providing a thorough update to AAPM community on what we have understood in the past for linear CT imaging system, what are the new challenges and opportunities offered by the nonlinear iterative image reconstruction, and what would be the future directions in quantitative image quality assessment that the AAPM community can work together to address the challenges and to adapt the nonlinear image reconstruction methods to routine clinical practice to improve patient care. Three invited speakers will lead the discussions in this symposium.Dr. Ke Li from the University of Wisconsin‐Madison will be presenting the new challenges introduced in model‐based iterative reconstruction (MBIR) method with a focus on how the nonlinear nature of the MBIR reconstruction poses challenges in quantitative image quality metrics such as spatial resolution, noise power spectrum, and the limitations of CNR in protocol optimization which eventually leads to the need of task‐based detectability index as the metric.Dr. Shuai Leng from Mayo Clinic will then present how the CNR metric is insufficient for nonlinear reconstruction algorithms, and how task based model observers can be used to more accurately quantify image quality, and to optimize imaging system and scanning protocols for nonlinear iterative image reconstruction algorithms based on specific imaging task. Practical considerations regarding the application of task based image quality metrics will also be discussed.Dr. Ehsan Samei from Duke University will start the symposium by summarizing a to‐be‐released AAPM Task Group report (TG 233: Performance Evaluation of Computed Tomography Systems). He will cover what has been understood and accepted for linear CT imaging system, what are the new challenges in CT image quality assessment introduced by the nonlinear iterative reconstruction (IR) techniques, and summarize both taskneutral and task‐based metrologies developed in TG 233 to partially address these challenges, and foresee additional challenges in the future. Learning Objectives: Understand the challenges in quantitative image quality assessment introduced by nonlinear iterative reconstruction techniques Understand the challenges and methods in noise performance assessment for nonlinear iterative reconstruction techniques Understand the challenges and methods in in spatial resolution assessment for nonlinear iterative reconstruction techniques Understand the challenges and methods in in task‐based observer performance assessment for nonlinear iterative reconstruction techniquesFunding support received from NIH and DOD; Funding support received from GE Healthcare; Funding support received from Siemens AX; Patent royalties received from GE Healthcare; S. Leng, R01 EB071095; U01 EB017185; E. Samei, Research grant, Siemens; Research grant, GE; K. Li, Funding from NIH, DOD and AAPM

Compressed sensing in MRI – mathematical preliminaries and basic examples

Abstract In magnetic resonance imaging (MRI), k-space sampling, due to physical restrictions, is very time-consuming. It cannot be much improved using classical Nyquist-based sampling theory. Recent developments utilize the fact that MR images are sparse in some representations (i.e. wavelet coefficients). This new theory, created by Candès and Romberg, called compressed sensing (CS), shows that images with sparse representations can be recovered from randomly undersampled k-space data, by using nonlinear reconstruction algorithms (i.e. l 1-norm minimization). Throughout this paper, mathematical preliminaries of CS are outlined, in the form introduced by Candès. We describe the main conditions for measurement matrices and recovery algorithms and present a basic example, showing that while the method really works (reducing the time of MR examination), there are some major problems that need to be taken into consideration.

Microwave tomography for early breast cancer detection based on the alternating direction implicit finite-difference time-domain method

In microwave tomography (MWT), electric-parameter distributions of the breast can be reconstructed to detect the early-breast-cancer, which has a specific physical explanation and medical diagnostic value. In time-domain, the finite-difference time-domain (FDTD) method is usually applied to these problems. However, due to the constraint of Courant-Friedrich-Levy (CFL) stability condition, the time step should be small enough to well match the small fine cells, which begets an increasing computational cost, such as the central processing unit (CPU) time. For real-time clinical, it is very important and essential to look for efficient methods to improve the computational efficiency. The alternating-direction implicit finite-difference time-domain (ADI-FDTD) method, on the other hand, provides a larger time step than that the CFL stability condition limitation could set. In order to shorten the time of imaging and improve the detection efficiency, the ADI-FDTD method is first used for the early-breast-cancer detection in this paper. MWT for breast cancer detection requires solving nonlinear inverse scattering problems. Most nonlinear inversion algorithms require solving a number of forward scattering problems followed by an optimization procedure. Therefore, we turn the inverse scattering problem into an optimization question according to the least squares criterion. The optimization procedure aims at minimizing the error between measured scattered fields and estimated scattered fields by the forward solver. Nonlinear reconstruction algorithm is used to solve an update for the scattering object properties used in our breast model. This iteration process is repeated until the convergence between the measured and estimated data is obtained. The specific process of the iteration method is divided into two steps: the forward step, which is to solve a forward problem for a scattering object with estimated electrical properties, and the backward step, which is to solve adjoint fields by introducing the Lagrange multiplier penalty function. Both the forward and backward calculations are conducted by using the ADI-FDTD method. The algorithm is evaluated for a two-dimensional (2D) semicircle breast model with tumors. We compare the imaging results obtained by the ADI-FDTD method for various time steps with the results obtained by the conventional FDTD method and the real distribution. The results agree well, the simulation results prove that the imaging time by using this ADI-FDTD method can be reduced to 23% that by the conventional FDTD method. In addition, the simulation results suggest that the ADI-FDTD method can be more efficient if higher resolution is required, thus further enhancing the clinical applicability of MWT.

Sparse Signal Reconstruction using BasisPursuit Algorithm

Compressive Sensing acquire sparse signal significantly at very lower rate than Nyquist sampling rate. For this, a low complexity compressed sensing operation is defined and it is the combination of sampling and compression. The signals formed from compressed sensing operation are compressible signals and a set of random linear measurements accurately reconstructs compressible signals with the use of nonlinear or convex reconstruction algorithms. Basis Pursuit algorithm is one of the convex optimization algorithms to reconstruct the sparse signal. The l1 minimization theory for linear programming problems is used to formulate the compressive sensing method. Interior point method is used to solve the basis pursuit algorithm for sparse signal reconstruction. In this paper, the methodology of reconstructing sparse signal using basis pursuit algorithm is discussed.

An adaptive transpose measurement matrix algorithm for signal reconstruction in compressed sensing

Compressed sensing is a new signal sampling theory put forward in recent years. It can obtain a signal's discrete sample in the condition that the sampling rate of signal is far smaller than the Nyquist sampling rate, and then make the original signal perfectly reconstructed with nonlinear reconstruction algorithm. In this paper, three typical greedy reconstruction algorithms, i.e., orthogonal matching pursuit, regularised orthogonal matching pursuit, and subspace tracking algorithm are compared in terms of reconstruction accuracy, error rate and time of reconstruction. Furthermore, a new transpose measurement matrix reconstruction algorithm is proposed and tested through simulation. The experiments on both simulation and calculation showed that this new algorithm can effectively improve the optimisation of the signal transmission.

Clinical NECR in 18F-FDG PET scans: optimization of injected activity and variable acquisition time. Relationship with SNR

The injected activity and the acquisition time per bed position for 18F-FDG PET scans are usually optimized by using metrics obtained from phantom experiments. However, optimal activity and time duration can significantly vary from a phantom set-up and from patient to patient. An approach using a patient-specific noise equivalent count rate (NECR) modelling has been previously proposed for optimizing clinical scanning protocols. We propose using the clinical NECR on a large population as a function of the body mass index (BMI) for deriving the optimal injected activity and acquisition duration per bed position. The relationship between the NEC and the signal-to-noise ratio (SNR) was assessed both in a phantom and in a clinical setting. 491 consecutive patients were retrospectively evaluated and divided into 4 BMI subgroups. Two criteria were used to optimize the injected activity and the time per bed position was adjusted using the NECR value while keeping the total acquisition time constant. Finally, the relationship between NEC and SNR was investigated using an anthropomorphic phantom and a population of 507 other patients. While the first dose regimen suggested a unique injected activity (665 MBq) regardless of the BMI, the second dose regimen proposed a variable activity and a total acquisition time according to the BMI. The NEC improvement was around 35% as compared with the local current injection rule. Variable time per bed position was derived according to BMI and anatomical region. NEC and number of true events were found to be highly correlated with SNR for the phantom set-up and partially confirmed in the patient study for the BMI subgroup under 28 kg m−2 suggesting that for the scanner, the nonlinear reconstruction algorithm used in this study and BMI < 28 kg m−2, NEC, or the number of true events linearly correlated with SNR2.

Quantum noise properties of CT images with anatomical textured backgrounds across reconstruction algorithms: FBP and SAFIRE.

Quantum noise properties of CT images are generally assessed using simple geometric phantoms with uniform backgrounds. Such phantoms may be inadequate when assessing nonlinear reconstruction or postprocessing algorithms. The purpose of this study was to design anatomically informed textured phantoms and use the phantoms to assess quantum noise properties across two clinically available reconstruction algorithms, filtered back projection (FBP) and sinogram affirmed iterative reconstruction (SAFIRE). Two phantoms were designed to represent lung and soft-tissue textures. The lung phantom included intricate vessel-like structures along with embedded nodules (spherical, lobulated, and spiculated). The soft tissue phantom was designed based on a three-dimensional clustered lumpy background with included low-contrast lesions (spherical and anthropomorphic). The phantoms were built using rapid prototyping (3D printing) technology and, along with a uniform phantom of similar size, were imaged on a Siemens SOMATOM Definition Flash CT scanner and reconstructed with FBP and SAFIRE. Fifty repeated acquisitions were acquired for each background type and noise was assessed by estimating pixel-value statistics, such as standard deviation (i.e., noise magnitude), autocorrelation, and noise power spectrum. Noise stationarity was also assessed by examining the spatial distribution of noise magnitude. The noise properties were compared across background types and between the two reconstruction algorithms. In FBP and SAFIRE images, noise was globally nonstationary for all phantoms. In FBP images of all phantoms, and in SAFIRE images of the uniform phantom, noise appeared to be locally stationary (within a reasonably small region of interest). Noise was locally nonstationary in SAFIRE images of the textured phantoms with edge pixels showing higher noise magnitude compared to pixels in more homogenous regions. For pixels in uniform regions, noise magnitude was reduced by an average of 60% in SAFIRE images compared to FBP. However, for edge pixels, noise magnitude ranged from 20% higher to 40% lower in SAFIRE images compared to FBP. SAFIRE images of the lung phantom exhibited distinct regions with varying noise texture (i.e., noise autocorrelation/power spectra). Quantum noise properties observed in uniform phantoms may not be representative of those in actual patients for nonlinear reconstruction algorithms. Anatomical texture should be considered when evaluating the performance of CT systems that use such nonlinear algorithms.

A systematic investigation of reflectance diffuse optical tomography using nonlinear reconstruction methods and continuous wave measurements

We conducted a systematic investigation of the reflectance diffuse optical tomography using continuous wave (CW) measurements and nonlinear reconstruction algorithms. We illustrated and suggested how to fine-tune the nonlinear reconstruction methods in order to optimize target localization with depth-adaptive regularizations, reduce boundary noises in the reconstructed images using a logarithm based objective function, improve reconstruction quantification using transport models, and resolve crosstalk problems between absorption and scattering contrasts with the CW reflectance measurements. The upgraded nonlinear reconstruction algorithms were evaluated with a series of numerical and experimental tests, which show the potentials of the proposed approaches for imaging both absorption and scattering contrasts in the deep targets with enhanced image quality.

Compressed Sensing Electron tomography using adaptive dictionaries: a simulation study

Electron tomography (ET) is an increasingly important technique for examining the three-dimensional morphologies of nanostructures. ET involves the acquisition of a set of 2D projection images to be reconstructed into a volumetric image by solving an inverse problem. However, due to limitations in the acquisition process this inverse problem is considered ill-posed (i.e., no unique solution exists). Furthermore reconstruction usually suffers from missing wedge artifacts (e.g., star, fan, blurring, and elongation artifacts). Compressed sensing (CS) has recently been applied to ET and showed promising results for reducing missing wedge artifacts caused by limited angle sampling. CS uses a nonlinear reconstruction algorithm that employs image sparsity as a priori knowledge to improve the accuracy of density reconstruction from a relatively small number of projections compared to other reconstruction techniques. However, The performance of CS recovery depends heavily on the degree of sparsity of the reconstructed image in the selected transform domain. Prespecified transformations such as spatial gradients provide sparse image representation, while synthesising the sparsifying transform based on the properties of the particular specimen may give even sparser results and can extend the application of CS to specimens that can not be sparsely represented with other transforms such as Total variation (TV). In this work, we show that CS reconstruction in ET can be significantly improved by tailoring the sparsity representation using a sparse dictionary learning principle.