Biomedical subjects

Jeffrey A Fessler

Publications and source records attributed to Jeffrey A Fessler.

At least 19 recordsLinked to original sources

PubMed2006

Spatial domain method for the design of RF pulses in multicoil parallel excitation.

Parallel excitation has been introduced as a means of accelerating multidimensional, spatially-selective excitation using multiple transmit coils, each driven by a unique RF pulse. Previous approaches to RF pulse design in parallel excitation were either formulated in the frequency domain or restricted to echo-planar trajectories, or both. This paper presents an approach that is formulated as a quadratic optimization problem in the spatial domain and allows the use of arbitrary k-space trajectories. Compared to frequency domain approaches, the new design method has some important advantages. It allows for the specification of a region of interest (ROI), which improves excitation accuracy at high speedup factors. It allows for magnetic field inhomogeneity compensation during excitation. Regularization may be used to control integrated and peak pulse power. The effects of Bloch equation nonlinearity on the large-tip-angle excitation error of RF pulses designed with the method are investigated, and the utility of Tikhonov regularization in mitigating this error is demonstrated.

Algorithms↗

PubMed2006

Advanced three-dimensional tailored RF pulse for signal recovery in T2*-weighted functional magnetic resonance imaging.

T(2) (*)-weighted functional MR images are plagued by signal loss artifacts caused by susceptibility-induced through-plane dephasing. We present major advances to the original three-dimensional tailored RF (3DTRF) pulse method that pre-compensates the dephasing using three-dimensional selective excitation. The proposed 3DTRF pulses are designed iteratively with off-resonance incorporation and with a novel echo-volumar trajectory that frequency-encodes in z and phase-encodes in x,y. We also propose a computational scheme to accelerate the pulse design process. We demonstrate effective signal recovery in a 5-mm slice in both phantom and inferior brain, using 3DTRF pulses that are only 15.4 ms long. Compared to the original method, the new approach leads to significantly reduced pulse length and enhancement in slice selectivity. 3D images of the slice volume confirm fidelity of the excited phase pattern and slice profile.

Algorithms↗

PubMed2006

Analysis of observer performance in known-location tasks for tomographic image reconstruction.

We consider the task of detecting a statistically varying signal of known location on a statistically varying background in a reconstructed tomographic image. We analyze the performance of linear observer models in this task. We show that, if one chooses a suitable reconstruction method, a broad family of linear observers can exactly achieve the optimal detection performance attainable with any combination of a linear observer and linear reconstructor. This conclusion encompasses several well-known observer models from the literature, including models with a frequency-selective channel mechanism and certain types of internal noise. Interestingly, the "optimal" reconstruction methods are unregularized and in some cases quite unconventional. These results suggest that, for the purposes of designing regularized reconstruction methods that optimize lesion detectability, known-location tasks are of limited use.

Algorithms↗

PubMed2006

Convergent incremental optimization transfer algorithms: application to tomography.

No convergent ordered subsets (OS) type image reconstruction algorithms for transmission tomography have been proposed to date. In contrast, in emission tomography, there are two known families of convergent OS algorithms: methods that use relaxation parameters, and methods based on the incremental expectation-maximization (EM) approach. This paper generalizes the incremental EM approach by introducing a general framework, "incremental optimization transfer." The proposed algorithms accelerate convergence speeds and ensure global convergence without requiring relaxation parameters. The general optimization transfer framework allows the use of a very broad family of surrogate functions, enabling the development of new algorithms. This paper provides the first convergent OS-type algorithm for (nonconcave) penalized-likelihood (PL) transmission image reconstruction by using separable paraboloidal surrogates (SPS) which yield closed-form maximization steps. We found it is very effective to achieve fast convergence rates by starting with an OS algorithm with a large number of subsets and switching to the new "transmission incremental optimization transfer (TRIOT)" algorithm. Results show that TRIOT is faster in increasing the PL objective than nonincremental ordinary SPS and even OS-SPS yet is convergent.

Algorithms↗

PubMed2006

Fourier-based forward and back-projectors in iterative fan-beam tomographic image reconstruction.

Fourier-based forward and back-projection methods can reduce computation in iterative tomographic image reconstruction. Recently, an optimized nonuniform fast Fourier transform (NUFFT) approach was shown to yield accurate parallel-beam projections. In this paper, we extend the NUFFT approach to describe an O (N2 log N) projector/backprojector pair for fan-beam transmission tomography. Simulations and experiments with real CT data show that fan-beam Fourier-based forward and back-projection methods can reduce computation for iterative reconstruction while still providing accuracy comparable to their O (N3) space-based counterparts.

Algorithms↗

PubMed2006

Incorporation of system resolution compensation (RC) in the ordered-subset transmission (OSTR) algorithm for transmission imaging in SPECT.

In order to reconstruct attenuation maps with improved spatial resolution and quantitative accuracy, we developed an approximate method of incorporating system resolution compensation (RC) in the ordered-subset transmission (OSTR) algorithm for transmission reconstruction. Our method approximately models the blur caused by the finite intrinsic detector resolution, the nonideal source collimation and detector collimation. We derived the formulation using the optimization transfer principle as in the derivation of the OSTR algorithm. The formulation includes one forward-blur step and one back-blur step, which do not severely slow down reconstruction. The formulation could be applicable to various transmission geometries, such as point-source, line-source, and sheet-source systems. Through computer simulations of the MCAT phantom and transmission measurements of the air-filled Data Spectrum Deluxe single photo emission computed tomography (SPECT) Phantom on a system which employed a cone-beam geometry and a system which employed a scanning-line-source geometry, we showed that incorporation of RC increased spatial resolution and improved the quantitative accuracy of reconstruction. In simulation studies, attenuation maps reconstructed with RC correction improved the quantitative accuracy of emission reconstruction.

Algorithms↗

PubMed2006

Exploring breathing pattern irregularity with projection-based method.

Accurate descriptions of organ motion due to breathing are highly desirable for radiation treatment planning. This paper proposes an index that quantifies the irregularity of a signal related to respiratory motion. The method works by finding the periodic band-limited signal that best fits the signal samples, and then computing the root mean squared (RMS) residual error. The fitted signal itself may be useful for treatment planning. Using clinical data describing amplitude-time relationships (RPM, Varian) from twelve patients, we correlated the proposed index against relevant metrics from various treatment planning schemes. Simulation results demonstrate a reasonable match with all treatment methods considered, suggesting that the proposed irregularity index is suitable for a variety of treatment methods. Compared to the modified cosine function, which was investigated previously for breathing pattern models, the proposed approach is more representative, flexible, and computationally efficient.

Algorithms↗

PubMed2005

Iterative RF pulse design for multidimensional, small-tip-angle selective excitation.

The excitation k-space perspective on small-tip-angle selective excitation has facilitated RF pulse designs in a range of MR applications. In this paper, k-space-based design of multidimensional RF pulses is formulated as a quadratic optimization problem, and solved efficiently by the iterative conjugate-gradient (CG) algorithm. Compared to conventional design approaches, such as the conjugate-phase (CP) method, the new design approach is beneficial in several regards. It generally produces more accurate excitation patterns. The improvement is particularly significant when k-space is undersampled, and it can potentially shorten pulse lengths. A prominent improvement in accuracy is also observed when large off-resonance gradients are present. A further boost in excitation accuracy can be accomplished in regions of interest (ROIs) if they are specified together with "don't-care" regions. The density compensation function (DCF) is no longer required. In addition, regularization techniques allow control over integrated and peak pulse power.

Algorithms↗

PubMed2005

Conjugate phase MRI reconstruction with spatially variant sample density correction.

A new image reconstruction method to correct for the effects of magnetic field inhomogeneity in non-Cartesian sampled magnetic resonance imaging (MRI) is proposed. The conjugate phase reconstruction method, which corrects for phase accumulation due to applied gradients and magnetic field inhomogeneity, has been commonly used for this case. This can lead to incomplete correction, in part, due to the presence of gradients in the field inhomogeneity function. Based on local distortions to the k-space trajectory from these gradients, a spatially variant sample density compensation function is introduced as part of the conjugate phase reconstruction. This method was applied to both simulated and experimental spiral imaging data and shown to produce more accurate image reconstructions. Two approaches for fast implementation that allow the use of fast Fourier transforms are also described. The proposed method is shown to produce fast and accurate image reconstructions for spiral sampled MRI.

Algorithms↗

PubMed2005

Respiratory motion estimation from slowly rotating x-ray projections: theory and simulation.

Understanding the movement of tumors caused by respiratory motion is very important for conformal radiatherapy. However, respiratory motion is very difficult to study by conventional x-ray CT imaging since object motion causes inconsistent projection views, leading to artifacts in reconstructed images. We propose to estimate the parameters of a nonrigid, free breathing motion model from a set of projection views of the thorax that are acquired using a slowly rotating cone-beam CT scanner. This approach involves deforming a motion-free reference thorax volume according to the estimated parameters and comparing its projections to the corresponding measured projection views. The parameters are optimized by minimizing a regularized squared error cost function. Simulation results with a fan-beam geometry show good agreement between the estimated motion and the true motion, which supports the potential of this approach for estimating four-dimensional (three-dimensional spatial + temporal) respiratory motion.

Algorithms↗

PubMed2004

Pragmatic fully 3D image reconstruction for the MiCES mouse imaging PET scanner.

We present a pragmatic approach to image reconstruction for data from the micro crystal elements system (MiCES) fully 3D mouse imaging positron emission tomography (PET) scanner under construction at the University of Washington. Our approach is modelled on fully 3D image reconstruction used in clinical PET scanners, which is based on Fourier rebinning (FORE) followed by 2D iterative image reconstruction using ordered-subsets expectation-maximization (OSEM). The use of iterative methods allows modelling of physical effects (e.g., statistical noise, detector blurring, attenuation, etc), while FORE accelerates the reconstruction process by reducing the fully 3D data to a stacked set of independent 2D sinograms. Previous investigations have indicated that non-stationary detector point-spread response effects, which are typically ignored for clinical imaging, significantly impact image quality for the MiCES scanner geometry. To model the effect of non-stationary detector blurring (DB) in the FORE+OSEM(DB) algorithm, we have added a factorized system matrix to the ASPIRE reconstruction library. Initial results indicate that the proposed approach produces an improvement in resolution without an undue increase in noise and without a significant increase in the computational burden. The impact on task performance, however, remains to be evaluated.

Animals↗

PubMed2004

Dynamic field map estimation using a spiral-in/spiral-out acquisition.

The long readout times of single-shot acquisitions and the high field strengths desired for functional MRI (fMRI) using blood oxygenation level-dependent (BOLD) contrast make functional scans sensitive to magnetic field inhomogeneity. If it is not corrected during image reconstruction, field inhomogeneity can cause geometric distortions in the images when Cartesian k-space trajectories are used or blurring with spiral acquisitions. Many traditional methods to correct for field inhomogeneity distortions rely on a static field map measured with the use of images that are themselves distorted. In this work, we employ a regularized least-squares approach to jointly estimate both the undistorted image and field map at each acquisition using a spiral-in/spiral-out pulse sequence. Simulation and phantom studies show that this method is accurate and stable over a time series. Human functional studies show that the jointly estimated field map may be more accurate than standard field map estimates in the presence of respiration-induced phase oscillations, leading to better detection of functional activation. The proposed method measures a dynamic field map that accurately tracks magnetic field drift and respiration-induced phase oscillations during the course of a functional study.

Brain↗

PubMed2004

Compensation for nonuniform resolution using penalized-likelihood reconstruction in space-variant imaging systems.

Imaging systems that form estimates using a statistical approach generally yield images with nonuniform resolution properties. That is, the reconstructed images possess resolution properties marked by space-variant and/or anisotropic responses. We have previously developed a space-variant penalty for penalized-likelihood (PL) reconstruction that yields nearly uniform resolution properties. We demonstrated how to calculate this penalty efficiently and apply it to an idealized positron emission tomography (PET) system whose geometric response is space-invariant. In this paper, we demonstrate the efficient calculation and application of this penalty to space-variant systems. (The method is most appropriate when the system matrix has been precalculated.) We apply the penalty to a large field of view PET system where crystal penetration effects make the geometric response space-variant, and to a two-dimensional single photon emission computed tomography system whose detector responses are modeled by a depth-dependent Gaussian with linearly varying full-width at half-maximum. We perform a simulation study comparing reconstructions using our proposed PL approach with other reconstruction methods and demonstrate the relative resolution uniformity, and discuss tradeoffs among estimators that yield nearly uniform resolution. We observe similar noise performance for the PL and post-smoothed maximum-likelihood (ML) approaches with carefully matched resolution, so choosing one estimator over another should be made on other factors like computational complexity and convergence rates of the iterative reconstruction. Additionally, because the postsmoothed ML and the proposed PL approach can outperform one another in terms of resolution uniformity depending on the desired reconstruction resolution, we present and discuss a hybrid approach adopting both a penalty and post-smoothing.

Algorithms↗

PubMed2004

Iterative tomographic image reconstruction using Fourier-based forward and back-projectors.

Iterative image reconstruction algorithms play an increasingly important role in modern tomographic systems, especially in emission tomography. With the fast increase of the sizes of the tomographic data, reduction of the computation demands of the reconstruction algorithms is of great importance. Fourier-based forward and back-projection methods have the potential to considerably reduce the computation time in iterative reconstruction. Additional substantial speed-up of those approaches can be obtained utilizing powerful and cheap off-the-shelf fast Fourier transform (FFT) processing hardware. The Fourier reconstruction approaches are based on the relationship between the Fourier transform of the image and Fourier transformation of the parallel-ray projections. The critical two steps are the estimations of the samples of the projection transform, on the central section through the origin of Fourier space, from the samples of the transform of the image, and vice versa for back-projection. Interpolation errors are a limitation of Fourier-based reconstruction methods. We have applied min-max optimized Kaiser-Bessel interpolation within the nonuniform FFT (NUFFT) framework and devised ways of incorporation of resolution models into the Fourier-based iterative approaches. Numerical and computer simulation results show that the min-max NUFFT approach provides substantially lower approximation errors in tomographic forward and back-projection than conventional interpolation methods. Our studies have further confirmed that Fourier-based projectors using the NUFFT approach provide accurate approximations to their space-based counterparts but with about ten times faster computation, and that they are viable candidates for fast iterative image reconstruction.

Algorithms↗

PubMed2004

Emission image reconstruction for randoms-precorrected PET allowing negative sinogram values.

Most positron emission tomography (PET) emission scans are corrected for accidental coincidence (AC) events by real-time subtraction of delayed-window coincidences, leaving only the randoms-precorrected data available for image reconstruction. The real-time randoms precorrection compensates in mean for AC events but destroys the Poisson statistics. The exact log-likelihood for randoms-precorrected data is inconvenient, so practical approximations are needed for maximum likelihood or penalized-likelihood image reconstruction. Conventional approximations involve setting negative sinogram values to zero, which can induce positive systematic biases, particularly for scans with low counts per ray. We propose new likelihood approximations that allow negative sinogram values without requiring zero-thresholding. With negative sinogram values, the log-likelihood functions can be nonconcave, complicating maximization; nevertheless, we develop monotonic algorithms for the new models by modifying the separable paraboloidal surrogates and the maximum-likelihood expectation-maximization (ML-EM) methods. These algorithms ascend to local maximizers of the objective function. Analysis and simulation results show that the new shifted Poisson (SP) model is nearly free of systematic bias yet keeps low variance. Despite its simpler implementation, the new SP performs comparably to the saddle-point model which has shown the best performance (as to systematic bias and variance) in randoms-precorrected PET emission reconstruction.

Algorithms↗

PubMed2004

Intensity-based image registration using robust correlation coefficients.

The ordinary sample correlation coefficient is a popular similarity measure for aligning images from the same or similar modalities. However, this measure can be sensitive to the presence of "outlier" objects that appear in one image but not the other, such as surgical instruments, the patient table, etc., which can lead to biased registrations. This paper describes an intensity-based image registration technique that uses a robust correlation coefficient as a similarity measure. Relative to the ordinary sample correlation coefficient, the proposed similarity measure reduces the influence of outliers. We also compared the performance of the proposed method with the mutual information-based method. The robust correlation-based method should be useful for image registration in radiotherapy (KeV to MeV X-ray images) and image-guided surgery applications. We have investigated the properties of the proposed method by theoretical analysis, computer simulations, a phantom experiment, and with functional magnetic resonance imaging data.

Algorithms↗

PubMed2004

Efficient calculation of resolution and covariance for penalized-likelihood reconstruction in fully 3-D SPECT.

Resolution and covariance predictors have been derived previously for penalized-likelihood estimators. These predictors can provide accurate approximations to the local resolution properties and covariance functions for tomographic systems given a good estimate of the mean measurements. Although these predictors may be evaluated iteratively, circulant approximations are often made for practical computation times. However, when numerous evaluations are made repeatedly (as in penalty design or calculation of variance images), these predictors still require large amounts of computing time. In Stayman and Fessler (2000), we discussed methods for precomputing a large portion of the predictor for shift-invariant system geometries. In this paper, we generalize the efficient procedure discussed in Stayman and Fessler (2000) to shift-variant single photon emission computed tomography (SPECT) systems. This generalization relies on a new attenuation approximation and several observations on the symmetries in SPECT systems. These new general procedures apply to both two-dimensional and fully three-dimensional (3-D) SPECT models, that may be either precomputed and stored, or written in procedural form. We demonstrate the high accuracy of the predictions based on these methods using a simulated anthropomorphic phantom and fully 3-D SPECT system. The evaluation of these predictors requires significantly less computation time than traditional prediction techniques, once the system geometry specific precomputations have been made.

Abdomen↗

PubMed2004

Penalized-likelihood image reconstruction for digital holography.

Conventional numerical reconstruction for digital holography using a filter applied in the spatial-frequency domain to extract the primary image may yield suboptimal image quality because of the loss in high-frequency components and interference from other undesirable terms of a hologram. We propose a new numerical reconstruction approach using a statistical technique. This approach reconstructs the complex field of the object from the real-valued hologram intensity data. Because holographic image reconstruction is an ill-posed problem, our statistical technique is based on penalized-likelihood estimation. We develop a Poisson statistical model for this problem and derive an optimization transfer algorithm that monotonically decreases the cost function at each iteration. Simulation results show that our statistical technique has the potential to improve image quality in digital holography relative to conventional reconstruction techniques.

Journal Article↗