Nonlinear Iterative Reconstruction Research Articles

Temporal resolution and motion artifacts in single‐source and dual‐source cardiac CT

The temporal resolution of a given image in cardiac computed tomography (CT) has so far mostly been determined from the amount of CT data employed for the reconstruction of that image. The purpose of this paper is to examine the applicability of such measures to the newly introduced modality of dual-source CT as well as to methods aiming to provide improved temporal resolution by means of an advanced image reconstruction algorithm. To provide a solid base for the examinations described in this paper, an extensive review of temporal resolution in conventional single-source CT is given first. Two different measures for assessing temporal resolution with respect to the amount of data involved are introduced, namely, either taking the full width at half maximum of the respective data weighting function (FWHM-TR) or the total width of the weighting function (total TR) as a base of the assessment. Image reconstruction using both a direct fan-beam filtered backprojection with Parker weighting as well as using a parallel-beam rebinning step are considered. The theory of assessing temporal resolution by means of the data involved is then extended to dual-source CT. Finally, three different advanced iterative reconstruction methods that all use the same input data are compared with respect to the resulting motion artifact level. For brevity and simplicity, the examinations are limited to two-dimensional data acquisition and reconstruction. However, all results and conclusions presented in this paper are also directly applicable to both circular and helical cone-beam CT. While the concept of total TR can directly be applied to dual-source CT, the definition of the FWHM of a weighting function needs to be slightly extended to be applicable to this modality. The three different advanced iterative reconstruction methods examined in this paper result in significantly different images with respect to their motion artifact level, despite exactly the same amount of data being used in the reconstruction process. The concept of assessing temporal resolution by means of the data employed for reconstruction can nicely be extended from single-source to dual-source CT. However, for advanced (possibly nonlinear iterative) reconstruction algorithms the examined approach fails to deliver accurate results. New methods and measures to assess the temporal resolution of CT images need to be developed to be able to accurately compare the performance of such algorithms.

Regularization Parameter Selection for Nonlinear Iterative Image Restoration and MRI Reconstruction Using GCV and SURE-Based Methods

Regularized iterative reconstruction algorithms for imaging inverse problems require selection of appropriate regularization parameter values. We focus on the challenging problem of tuning regularization parameters for nonlinear algorithms for the case of additive (possibly complex) Gaussian noise. Generalized cross-validation (GCV) and (weighted) mean-squared error (MSE) approaches (based on Steinfs Unbiased Risk Estimate. SURE) need the Jacobian matrix of the nonlinear reconstruction operator (representative of the iterative algorithm) with respect to the data. We derive the desired Jacobian matrix for two types of nonlinear iterative algorithms: a fast variant of the standard iterative reweighted least-squares method and the contemporary split-Bregman algorithm, both of which can accommodate a wide variety of analysis- and synthesis-type regularizers. The proposed approach iteratively computes two weighted SURE-type measures: Predicted-SURE and Projected-SURE (that require knowledge of noise variance Ð2), and GCV (that does not need Ð2) for these algorithms. We apply the methods to image restoration and to magnetic resonance image (MRI) reconstruction using total variation (TV) and an analysis-type .1-regularization. We demonstrate through simulations and experiments with real data that minimizing Predicted-SURE and Projected-SURE consistently lead to near-MSE-optimal reconstructions. We also observed that minimizing GCV yields reconstruction results that are near-MSE-optimal for image restoration and slightly suboptimal for MRI. Theoretical derivations in this work related to Jacobian matrix evaluations can be extended, in principle, to other types of regularizers and reconstruction algorithms.

Accelerated and navigator-gated look-locker imaging for cardiac T1 Estimation (ANGIE) with reduced motion artifact

Background T1 mapping of the left ventricle is routinely performed using Modified Look-Locker Inversion Recovery (MOLLI) [1] in a variety of disease settings [2]. MOLLI requires relatively long breathholds, and consequently sequences of MOLLI images may be misregistered due to respiratory drift. We sought to develop a T1 mapping sequence that would not require breathholding and would not have misregistration problems. We used kspace segmentation and navigator gating to eliminate respiratory artifact, and compressed sensing [3] (CS) to accelerate image acquisition. CS utilizes undersampling in k-t space along with nonlinear iterative image reconstruction. CS is well-suited to Look-Locker imaging because these images, which vary smoothly from one inversion time to the next, exhibit time-domain sparsity.

Fast forward problem solver for image reconstruction by nonlinear optimization in electrical capacitance tomography

Electrical capacitance tomography can be used for industrial process imaging, for example multiphase flow. Image reconstruction complexity is one of the limiting factors of this technique. A custom-built method of calculating the forward problem is presented. A fast algorithm for solving the linear system with a band diagonal matrix was used. An application of the elaborated forward problem solver for nonlinear iterative image reconstruction is presented. The results of image reconstruction are presented for simulated and real objects.

THREE-DIMENSIONAL NONLINEAR INVERSION OF ELECTRICAL CAPACITANCE TOMOGRAPHY DATA USING A COMPLETE SENSOR MODEL

Electrical Capacitance Tomography (ECT) is a non- invasive and non-destructive imaging technique that uses electrical capacitance measurements at the periphery of an object to generate map of dielectric permittivity of the object. This visualization method is a relatively mature industrial process tomography technique, especially in 2D imaging mode. Volumetric ECT is a new method that poses major computational challenges in image reconstruction and new challenges in sensor design. This paper shows a nonlinear image reconstruction method for 3D ECT based on a validated forward model. The method is based on the flnite element approximation for the complete sensor model and the solution of the inverse problem with nonlinear iterative reconstruction. The nonlinear algorithm has been tested against some complicated experimental test cases, and it has been demonstrated that by using an improved forward model and nonlinear inversion method, very complex shaped samples can be reconstructed. The reconstruction of very complex geometry with objects in the shape of letters H, A, L and T is extremely promising for the applications of 3D ECT.

Performance evaluation of an iterative image reconstruction algorithm with sensitivity matrix updating based on real measurements for electrical capacitance tomography

Image reconstruction in electrical capacitance tomography requires a solution of an ill-posed inverse problem with an unknown measuring model which can be estimated during a reconstruction process. This paper presents a new version of a nonlinear iterative reconstruction similar to the Levenberg method. Only a few updates of the Jacobian are performed in contrast to modification every step in nonlinear iterative algorithms. A specialized numerical procedure was applied to speed up calculation of a sensitivity matrix. A step length factor together with a regularization parameter was used. A constraint for an estimated permittivity value was introduced. The L-curve method was applied to estimate the value of the regularization parameter. A proposed algorithm was evaluated on real objects and their numerical representations. A 16 electrode tomograph was used for real data acquisition. The elaborated algorithm achieves good quality of reconstructed images with reduced computation time.

TH-D-342-04: Advanced CT Image Reconstruction Algorithms Via Compressed Sensing

The key components of an x-ray computed tomography system are the source, detector, and image reconstruction algorithms. The introduction of multi-row detectors has enabled larger scanning coverage, higher spatial and faster complete organ scanning in the general purpose CT scanners. These improvements have enabled a variety of advanced clinical applications. The introduction of flat-panel detectors has enabled dedicated cone-beam CT in breast imaging, image-guided interventions, and image-guided radiation therapy. There is a constant interplay between the development of new and improved CT systems and advanced CT image reconstruction algorithms. New CT systems require advanced image reconstruction algorithms, and breakthroughs in image reconstruction algorithms may also enable future innovations in the future design of CT systems. The Shannon sampling theory is the foundation of conventional linear image reconstruction algorithms such as the Fourier transform and filtered backprojection methods. In these conventional image reconstruction frameworks, the violation of the Shannon sampling criterion often results in aliasing artifacts such as streaks in the reconstructed images. Recently, a new sampling theory, i.e., compressive sampling, has been formulated. It has been proven that accurate image reconstruction is possible using highly undersampled data sets provided that a nonlinear iterative image reconstruction method is utilized. This nonlinear iterative image reconstruction method is widely referred to as compressed sensing (CS). Based on the CS theory, some other generalized CS image reconstruction algorithms such as prior image constrained compressed sensing (PICCS) were recently proposed to reconstruct CT images. In this talk, we will discuss the potential impact of CS-based CT image reconstruction algorithms and their impact on current and future CT development. Educational Objectives: 1. Understand violation of sampling criterion may cause streaking artifacts in conventional linear image reconstruction algorithm. 2. Understand Compressed Sensing based image reconstruction algorithms can generate streak-free image using a highly undersampled data set. 3. Understand the potential benefit of PICCS algorithm in radiation dose reduction and improve temporal resolution using a slow gantry.

A Nonlinear Iterative Reconstruction and Analysis Approach to Shape-Based Approximate Electromagnetic Tomography

A nonlinear Helmholtz-equation-modeled electromagnetic tomographic reconstruction problem is solved for the object boundary and inhomogeneity parameters in a damped Tikhonov-regularized Gauss-Newton (DTRGN) solution framework. In this paper, the object is represented in a suitable global basis, whereas the boundary is expressed as the zero level set of a signed-distance function. For an explicit parameterized boundary-representation-based reconstruction scheme, analytical Jacobian and Hessian calculations are made to express the changes in scattered field values w.r.t. changes in the inhomogeneity parameters and the control points in a spline representation of the object boundary, via the use of a level-set representation of the object. Even though, in this paper, a homogeneous dielectric is considered and a spline representation has been used to represent the boundary, the formulation can be used for a general global basis representation of the inhomogeneity as well as arbitrary parameterizations of the boundary, and is generalizable to three dimensions. Reconstruction results are presented for test cases of landminelike dielectric objects embedded in the ground under noisy data conditions. To confirm convergence and, at times, to know which of the obtained iterates are closer to the actual unknown solution, using a perturbation theory framework, a local (Hessian-based) convergence analysis is applied to the DTRGN scheme for the reconstruction, yielding estimates of convergence rates in the residual and parameter spaces.

Unsupervised constrained radar imaging of low resolution targets

A linear spectral estimation technique, the PDFT algorithm, is used as part of a nonlinear iterative reconstruction scheme to obtain improved radar images. The iterative PDFT algorithm is used to address the limited resolution problem inherent to imaging objects buried in soil and hidden under foliage. This is achieved by subsequent application of two properties of the PDFT algorithm: the energy parameter of the PDFT algorithm is used to determine the target shape, while the shape information in turn is used to obtain super-resolved images. We describe algorithms able to exploit both properties automatically and without manual intervention. Two methods are investigated in particular, one iteratively optimizing the constraints by monitoring the energy parameter, the other method computing energy values for all points, from which a weighted prior function is determined. In addition, we discuss variants of both algorithm which provide an optimized trade-off between computation time and performance. Additional attention is given to situations, where a known target is embedded in an unknown background. Imaging results are presented for both synthetic and measured data.

Reconstruction of low-light images by use of the vector Wiener filter

Photon noise imposes severe limitations on the resolution of images detected under low-light conditions. These resolution limitations are typically more severe than those imposed by diffraction. Nonlinear iterative reconstruction techniques are available that can successfully process these images. Typical iterative methods are computationally expensive, incorporate ad hoc termination criteria, and may suffer convergence problems. The scalar Wiener filter is linear, computationally inexpensive, and noniterative. However, the scalar Wiener filter cannot improve the Fourier domain signal-to-noise ratio. We extend the vector Wiener filter to account properly for photon noise to provide a reconstruction technique that better complements nonlinear iterative methods. Our analysis confirms previous research [IEEE Trans. Signal Process.42, 156 (1994)] that showed that photon noise is correlated with respect to spatial frequency. The amount of correlation depends on the product of the mean optical transfer function (OTF) and the mean object spectrum at a difference frequency. We conduct computer simulations for a class of random Gaussian objects degraded by a known OTF. These results show the extended vector Wiener filter provides dramatic improvement in normalized mean squared error performance compared with that of the scalar Wiener filter. The vector Wiener filter can also provide a superresolution capability that is due to knowledge of the object spatial frequency statistics for frequencies beyond the OTF cutoff.