Idris A. Elbakri

Statistical image reconstruction for polyenergetic X-ray computed tomography

This paper describes a statistical image reconstruction method for X-ray computed tomography (CT) that is based on a physical model that accounts for the polyenergetic X-ray source spectrum and the measurement nonlinearities caused by energy-dependent attenuation. We assume that the object consists of a given number of nonoverlapping materials, such as soft tissue and bone. The attenuation coefficient of each voxel is the product of its unknown density and a known energy-dependent mass attenuation coefficient. We formulate a penalized-likelihood function for this polyenergetic model and develop an ordered-subsets iterative algorithm for estimating the unknown densities in each voxel. The algorithm monotonically decreases the cost function at each iteration when one subset is used. Applying this method to simulated X-ray CT measurements of objects containing both bone and soft tissue yields images with significantly reduced beam hardening artifacts.

Segmentation-free statistical image reconstruction for polyenergetic x-ray computed tomography with experimental validation

This paper describes a statistical image reconstruction method for x-ray CT that is based on a physical model that accounts for the polyenergetic x-ray source spectrum and the measurement nonlinearities caused by energy-dependent attenuation. Unlike our earlier work, the proposed algorithm does not require pre-segmentation of the object into the various tissue classes (e.g., bone and soft tissue) and allows mixed pixels. The attenuation coefficient of each voxel is modelled as the product of its unknown density and a weighted sum of energy-dependent mass attenuation coefficients. We formulate a penalized-likelihood function for this polyenergetic model and develop an iterative algorithm for estimating the unknown density of each voxel. Applying this method to simulated x-ray CT measurements of objects containing both bone and soft tissue yields images with significantly reduced beam hardening artefacts relative to conventional beam hardening correction methods. We also apply the method to real data acquired from a phantom containing various concentrations of potassium phosphate solution. The algorithm reconstructs an image with accurate density values for the different concentrations, demonstrating its potential for quantitative CT applications.

Efficient and accurate likelihood for iterative image reconstruction in x-ray computed tomography

We report a novel approach for statistical image reconstruction in X-ray CT. Statistical image reconstruction depends on maximizing a likelihood derived from a statistical model for the measurements. Traditionally, the measurements are assumed to be statistically Poisson, but more recent work has argued that CT measurements actually follow a compound Poisson distribution due to the polyenergetic nature of the X-ray source. Unlike the Poisson distribution, compound Poisson statistics have a complicated likelihood that impedes direct use of statistical reconstruction. Using a generalization of the saddle-point integration method, we derive an approximate likelihood for use with iterative algorithms. In its most realistic form, the approximate likelihood we derive accounts for polyenergetic X-rays and poisson light statistics in the detector scintillator, and can be extended to account for electronic additive noise. The approximate likelihood is closer to the exact likelihood than is the conventional Poisson likelihood, and carries the promise of more accurate reconstruction, especially in low X-ray dose situations.

Statistical x-ray-computed tomography image reconstruction with beam- hardening correction

This paper describes two statistical iterative reconstruction methods for X-ray CT. The first method assumes a mono-energetic model for X-ray attenuation. We approximate the transmission Poisson likelihood by a quadratic cost function and exploit its convexity to derive a separable quadratic surrogate function that is easily minimized using parallelizable algorithms. Ordered subsets are used to accelerate convergence. We apply this mono-energetic algorithm (with edge-preserving regularization) to simulated thorax X-ray CT scans. A few iterations produce reconstructed images with lower noise than conventional FBP images at equivalent resolutions. The second method generalizes the physical model and accounts for the poly-energetic X-ray source spectrum and the measurement nonlinearities caused by energy-dependent attenuation. We assume the object consists of a given number of non-overlapping tissue types. The attenuation coefficient of each tissue is the product of its unknown density and a known energy-dependent mass attenuation coefficient. We formulate a penalized-likelihood function for this poly-energetic model and develop an iterative algorithm for estimating the unknown densities in each voxel. Applying this method to simulated X-ray CT measurements of a phantom containing both bone and soft tissue yields images with significantly reduced beam hardening artifacts.

Combined ultrasound image guidance and therapy using a therapeutic phased array

Ultrasonic imaging has been suggested for guidance of high intensity focused ultrasound therapy. This is typically implemented using two different ultrasonic transducer systems. However the need for two transducers may pose practical difficulties such as alignment and different coordinate systems. In this paper we investigate the possibility of using the same physical transducer array for performing both therapy and imaging. A spherically shaped 1D 64-element high intensity focused ultrasound transducer capable of operating in therapeutic and imaging modes was designed and fabricated. In vitro experiments were conducted to show that this transducer is capable of creating well defined lesions 30-50 mm deep into bovine muscle samples. Furthermore, an experimental pulse-echo system was designed to collect full synthetic aperture data using this transducer. Images of multiple-wire and speckle-generating phantoms are shown to illustrate the imaging capability of this transducer. Although the image quality achieved with this array is inferior to that obtained by conventional diagnostic imaging transducers, it is sufficiently high to produce image features suitable for guidance.

Segmentation-free statistical image reconstruction for polyenergetic X-ray computed tomography

This paper describes a statistical iterative reconstruction method for X-ray CT based on a physical model that accounts for the polyenergetic X-ray source spectrum and the measurement nonlinearities caused by energy-dependent attenuation. The algorithm accommodates mixtures of tissues with known mass attenuation coefficients but unknown densities. We formulate a penalized-likelihood approach for this polyenergetic model based on Poisson statistics.

A filter‐based pulse‐echo coded‐excitation system for real‐time cardiac imaging

A new filter‐based approach to pulse‐echo imaging capable of parallel processing of multiple image lines has been developed. A major application of this approach is in true real‐time 3D imaging, e.g., in cardiac imaging. The new approach utilizes a set of coded waveforms on transmit and conventional beamforming on receive. The transmitted codes produce a coded wavefront in the region of interest (ROI) and the receive beam is designed to be wide enough to allow echoes from the ROI to be received while rejecting echoes from outside the ROI. Image formation is achieved using a filter bank structure (post‐beamforming) with every filter designed to extract echoes from a given direction in the ROI. The filter bank is derived from a regularized pseudoinverse operator of the (discretized) propagation operator from the ROI to the receiving array. Image reconstructions from speckle‐generating phantoms using the new approach demonstrate its robustness and its potential in medical imaging applications. A complete description of the algorithm and its fundamental spatial and contrast resolution limits will be presented with illustrative experimental data. System architectures for robust real‐time implementation will be discussed. [Work funded by NIH Grant HL57167.]