Kwang Eun Jang

Fully iterative scatter corrected digital breast tomosynthesis using GPU-based fast Monte Carlo simulation and composition ratio update.

PURPOSE In digital breast tomosynthesis (DBT), scatter correction is highly desirable, as it improves image quality at low doses. Because the DBT detector panel is typically stationary during the source rotation, antiscatter grids are not generally compatible with DBT; thus, a software-based scatter correction is required. This work proposes a fully iterative scatter correction method that uses a novel fast Monte Carlo simulation (MCS) with a tissue-composition ratio estimation technique for DBT imaging. METHODS To apply MCS to scatter estimation, the material composition in each voxel should be known. To overcome the lack of prior accurate knowledge of tissue composition for DBT, a tissue-composition ratio is estimated based on the observation that the breast tissues are principally composed of adipose and glandular tissues. Using this approximation, the composition ratio can be estimated from the reconstructed attenuation coefficients, and the scatter distribution can then be estimated by MCS using the composition ratio. The scatter estimation and image reconstruction procedures can be performed iteratively until an acceptable accuracy is achieved. For practical use, (i) the authors have implemented a fast MCS using a graphics processing unit (GPU), (ii) the MCS is simplified to transport only x-rays in the energy range of 10-50 keV, modeling Rayleigh and Compton scattering and the photoelectric effect using the tissue-composition ratio of adipose and glandular tissues, and (iii) downsampling is used because the scatter distribution varies rather smoothly. RESULTS The authors have demonstrated that the proposed method can accurately estimate the scatter distribution, and that the contrast-to-noise ratio of the final reconstructed image is significantly improved. The authors validated the performance of the MCS by changing the tissue thickness, composition ratio, and x-ray energy. The authors confirmed that the tissue-composition ratio estimation was quite accurate under a variety of conditions. Our GPU-based fast MCS implementation took approximately 3 s to generate each angular projection for a 6 cm thick breast, which is believed to make this process acceptable for clinical applications. In addition, the clinical preferences of three radiologists were evaluated; the preference for the proposed method compared to the preference for the convolution-based method was statistically meaningful (p < 0.05, McNemar test). CONCLUSIONS The proposed fully iterative scatter correction method and the GPU-based fast MCS using tissue-composition ratio estimation successfully improved the image quality within a reasonable computational time, which may potentially increase the clinical utility of DBT.

Statistical reconstruction using dual formulation of subband-wise total variation regularization (SDST) for limited angle tomography

In this paper, a novel reconstruction algorithm for limited angle tomography using total variation (TV) regularization is presented. Inspired by duality-based TV minimization in denoising and deblurring applications, we derived a TV regularized statistical reconstruction algorithm composed of relatively simple and structured operations such as discrete gradient and divergence calculations, which presents an effective way to introduce TV regularization to the statistical reconstruction. In initial tests with real data from a digital breast tomosynthesis system, the proposed algorithm showed reliable reconstructions for low dose conditions.

Information theoretic discrepancy-based iterative reconstruction (IDIR) algorithm for limited angle tomography

The X-ray tomosynthesis that measures several low dose projections over a limited angular range has been investigated as an alternative method of X-ray mammography for breast cancer screening. An extension of the scan coverage increases the vertical resolution by mitigating the interplane blurring. The implementation of a wide angle tomosynthesis equipment, however, may not be straightforward, mainly due to the image deterioration from the statistical noise in exterior projections. In this paper, we adopt the voltage modulation scheme to enlarge the coverage of the tomosynthesis scan. The higher tube voltages are used for outer angles, which offers the sufficient penetrating power for outlying frames in which the pathway of X-ray photons is elongated. To reconstruct 3D information from voltage modulated projections, we propose a novel algorithm, named information theoretic discrepancy based iterative reconstruction (IDIR) algorithm, which allows to account for the polychromatic acquisition model. The generalized information theoretic discrepancy (GID) is newly employed as the objective function. Using particular features of the GID, the cost function is derived in terms of imaginary variables with energy dependency, which leads to a tractable optimization problem without using the monochromatic approximation. In preliminary experiments using simulated and experimental equipment, the proposed imaging architecture and IDIR algorithm showed superior performances over conventional approaches.

A novel material decomposition algorithm for multienergy X-ray radiography systems

A novel algorithm for multienergy X-ray radiography systems that simultaneously estimate multiple measurements with energy diversity is presented. In contrast to conventional dual source X-ray radiography which utilizes simple weighted subtractions, the proposed algorithm aims for an accurate material decomposition of more than two materials. The numerical simulation as well as the real experiment using an energy discriminating detector confirmed our finding.

Information theoretic discrepancy based iterative reconstruction for transmission tomography

The monochromatic approximation, which postulates that a source emits monochromatic radiation, has been widely used in the transmission tomography. However, due to the ignorance of energy dependency, image degradations such as beam hardening artifact are often occurred. In this paper, we present novel reconstruction algorithms to reflect the exact polychromatic model. Departing from the conventional algebraic and statistical reconstructions, the generalized information theoretic discrepancy (GID) is employed as the new data fidelity metric. By using the particular features of the GID, the cost function is derived in terms of imaginary variables, which incorporates energy dependency and leads to a tractable optimization problem even without the monochromatic approximation. In preliminary experiments with a simulated dual energy CT and a real experimental tomosyn-thesis, the proposed information theoretic discrepancy based iterative reconstruction (IDIR) algorithm showed superior performances over conventional reconstruction schemes.

Regularized polychromatic reconstruction for transmission tomography

A polychromatic reconstruction algorithm that accounts for the exact physical model of transmission tomography is presented. Based on the equivalence between the Poisson log-likelihood function and the I-divergence, we derived a fast convergencing algorithm with a pixel-wise updating scheme, which is an extended version of the AM-ICD algorithm. The objective function in each iteration consists of approximated I-divergence and the generalized Gaussian Markov random field (GGMRF) model based regularization term for preventing diverging due to additive noise and the approximation of I-divergence. In a simulation study, we observed that the beam hardening artifact was significantly reduced in the extended AM-ICD algorithm with the use of a reasonable number of iterations. In addition, the proposed algorithm also showed reliable reconstruction results even for low dose conditions.

Comparative studies on exposure conditions and reconstruction algorithms in limited angle tomography

Digital breast tomosynthesis (DBT) has been investigated as a promising alternative to conventional X-ray mammography for breast cancer screening. By reconstructing 3D volumetric images from multiple 2D projections measured over a limited angular range, it can offer depth-directional information and improve both sensitivity and specificity of cancer detection in dense breasts. The diagnostic performance of DBT can be affected by a number of imaging parameters. The angular range of scan orbit is one of the most crucial factors, since it determines the depth-directional resolution. Recently, we proposed the wide angle tomosynthesis based on voltage modulations of X-ray source. By using X-rays with large penetration power on exterior positions, it can acquire high-SNR projections over a wide angular range. In this paper, we present comparative studies on exposure conditions in DBT, including narrow and wide angle scan using an invariant tube voltage of X-ray source, and wide angle scan with the voltage modulation technique. In addition, we compared the conventional reconstruction methods with recently proposed IDIR algorithms. In preliminary studies, the wide-angle scheme with proposed IDIR algorithm showed superior performances in detecting abnormal lesions over conventional approaches.

Information theoretic discrepancy based iterative reconstruction (IDIR) algorithm for dual energy x-ray systems

In dual energy computed tomography (DECT), two sets of projection data are acquired using a couple of independent X-ray spectra. Since the attenuation characteristic of a material without a K-edge in a typical medical X-ray spectrum range is accurately described by the linear combination of two phenomena, which are the photoelectric attenuation and the Compton scatter, the DECT is theoretically capable of separating one material from another. However, the material decomposition (MD) is still a challenging problem in DECT, since two sets of sinograms from distinct X-ray spectra are not spatially aligned in practices. To avoid this problem, the MD is often achieved by a weighted summation of two reconstructed volumes that correspond to a couple of sets of projection data, which the monochromatic approximation is generally used in the reconstruction procedure. The accuracy of the MD, therefore, can be limited due to the erroneous ignorance of the energy dependency of the acquisition model. In this paper, we propose a novel algorithm, named information theoretic discrepancy based iterative reconstruction (IDIR) algorithm, for an accurate MD in dual energy X-ray systems. The generalized information theoretic discrepancy (GID) measure is newly employed as the objective value. Using particular features of the GID, a tractable objective function for the material-selective reconstruction is derived, which accounts the exact polychromatic model of transmission tomography. Since the spectral model of measured data is explicitly considered, the accurate MD is possible even for misaligned projections. In numerical experiments, the proposed method showed superior reconstruction performance over the conventional approach.

Iterative scatter correction for digital tomosynthesis using composition ratio update and GPU based Monte Carlo simulation

In digital tomosynthesis (DTS), accurate scatter correction is often necessary for quantitative analysis. This is especially important because low energy x-ray of 10-40 keV, which is widely used for the breast imaging to enhance the contrast between adipose and glandular, results in high scatter fraction. In this paper, we propose an iterative scatter correction for digital tomopsynthesis using composition ratio update and GPU based Monte Carlo simulation (MCS). One of the technical difficulty in scatter estimation using MCS for tomosynthesis is that accurate segmentation of 3D volume is very difficult due to the low resolution of the reconstruction object. Thus, an intermediate surrogate object is introduced to represent composition ratio between adipose and glandular. We show that the composition ratio can be calculated using average attenuation coefficients. Another technical challenge is extremely high computational cost of MCS. We overcome this using GPU based ultra-fast MCS. Our results demonstrate that our iterative scatter correction using composition ratio update is indeed effective in improving the quality of the reconstruction object in a reasonable time frame.

Limited Data Tomographic Image Reconstruction via Dual Formulation of Total Variation Minimization

The X-ray mammography is the primary imaging modality for breast cancer screening. For the dense breast, however, the mammogram is usually difficult to read due to tissue overlap problem caused by the superposition of normal tissues. The digital breast tomosynthesis (DBT) that measures several low dose projections over a limited angle range may be an alternative modality for breast imaging, since it allows the visualization of the cross-sectional information of breast. The DBT, however, may suffer from the aliasing artifact and the severe noise corruption. To overcome these problems, a total variation (TV) regularized statistical reconstruction algorithm is presented. Inspired by the dual formulation of TV minimization in denoising and deblurring problems, we derived a gradient-type algorithm based on statistical model of X-ray tomography. The objective function is comprised of a data fidelity term derived from the statistical model and a TV regularization term. The gradient of the objective function can be easily calculated using simple operations in terms of auxiliary variables. After a descending step, the data fidelity term is renewed in each iteration. Since the proposed algorithm can be implemented without sophisticated operations such as matrix inverse, it provides an efficient way to include the TV regularization in the statistical reconstruction method, which results in a fast and robust estimation for low dose projections over the limited angle range. Initial tests with an experimental DBT system confirmed our finding.