Kedar Bhalchandra Khare

Accelerated diffusion spectrum imaging in the human brain using compressed sensing

We developed a novel method to accelerate diffusion spectrum imaging using compressed sensing. The method can be applied to either reduce acquisition time of diffusion spectrum imaging acquisition without losing critical information or to improve the resolution in diffusion space without increasing scan time. Unlike parallel imaging, compressed sensing can be applied to reconstruct a sub‐Nyquist sampled dataset in domains other than the spatial one. Simulations of fiber crossings in 2D and 3D were performed to systematically evaluate the effect of compressed sensing reconstruction with different types of undersampling patterns (random, gaussian, Poisson disk) and different acceleration factors on radial and axial diffusion information. Experiments in brains of healthy volunteers were performed, where diffusion space was undersampled with different sampling patterns and reconstructed using compressed sensing. Essential information on diffusion properties, such as orientation distribution function, diffusion coefficient, and kurtosis is preserved up to an acceleration factor of R = 4. Magn Reson Med, 2011.

Accelerated MR imaging using compressive sensing with no free parameters

We describe and evaluate a robust method for compressive sensing MRI reconstruction using an iterative soft thresholding framework that is data‐driven, so that no tuning of free parameters is required. The approach described here combines a Nesterov type optimal gradient scheme for iterative update along with standard wavelet‐based adaptive denoising methods, resulting in a leaner implementation compared with the nonlinear conjugate gradient method. Tests with T2 weighted brain data and vascular 3D phase contrast data show that the image quality of reconstructions is comparable with those from an empirically tuned nonlinear conjugate gradient approach. Statistical analysis of image quality scores for multiple datasets indicates that the iterative soft thresholding approach as presented here may improve the robustness of the reconstruction and the image quality, when compared with nonlinear conjugate gradient that requires manual tuning for each dataset. A data‐driven approach as illustrated in this article should improve future clinical applicability of compressive sensing image reconstruction. Magn Reson Med, 2012.

Inverse geometry CT: The next-generation CT architecture?

We present a new system architecture for X-ray computed tomography (CT). A multi-source inverse-geometry CT scanner is composed of a large distributed X-ray source with an array of discrete electron emitters and focal spots, and a high frame-rate flat-panel X-ray detector. In this work we study the advantages and the challenges of this new architecture. We predict potential breakthroughs in volumetric coverage, dose efficiency, and spatial resolution. We also present experimental results obtained with a universal benchtop system.

Parametric boundary reconstruction algorithm for industrial CT metrology application

High-energy X-ray computed tomography (CT) systems have been recently used to produce high-resolution images in various nondestructive testing and evaluation (NDT/NDE) applications. The accuracy of the dimensional information extracted from CT images is rapidly approaching the accuracy achieved with a coordinate measuring machine (CMM), the conventional approach to acquire the metrology information directly. On the other hand, CT systems generate the sinogram which is transformed mathematically to the pixel-based images. The dimensional information of the scanned object is extracted later by performing edge detection on reconstructed CT images. The dimensional accuracy of this approach is limited by the grid size of the pixel-based representation of CT images since the edge detection is performed on the pixel grid. Moreover, reconstructed CT images usually display various artifacts due to the underlying physical process and resulting object boundaries from the edge detection fail to represent the true boundaries of the scanned object. In this paper, a novel algorithm to reconstruct the boundaries of an object with uniform material composition and uniform density is presented. There are three major benefits in the proposed approach. First, since the boundary parameters are reconstructed instead of image pixels, the complexity of the reconstruction algorithm is significantly reduced. The iterative approach, which can be computationally intensive, will be practical with the parametric boundary reconstruction. Second, the object of interest in metrology can be represented more directly and accurately by the boundary parameters instead of the image pixels. By eliminating the extra edge detection step, the overall dimensional accuracy and process time can be improved. Third, since the parametric reconstruction approach shares the boundary representation with other conventional metrology modalities such as CMM, boundary information from other modalities can be directly incorporated as prior knowledge to improve the convergence of an iterative approach. In this paper, the feasibility of parametric boundary reconstruction algorithm is demonstrated with both simple and complex simulated objects. Finally, the proposed algorithm is applied to the experimental industrial CT system data.

A 3D study comparing filtered backprojection, weighted least squares, and penalized weighted least squares for CT reconstruction

We have extended 2D weighted least squares and penalized weighted least squares transmission reconstruction methods (WLSTR and PWLSTR respectively) to 3D to explore their impact on image noise and spatial resolution. 3D sinograms of circular and elliptical water cylinders were simulated using a conventional third generation CT system geometry. Data were generated using the realistic CT simulation software CATSIM. Resolution-Noise curves demonstrated that for high contrast wires the in-plane resolution can be improved using PWLS with a Huber-like prior compared to the resolution of the respective FBP image, maintaining the noise, or the noise can be reduced matching the resolution. The achieved noise reduction is greater for the elliptical cylinder than for the circular cylinder. For both phantoms we observed modest degradation in the xz-resolution compared to the in-plane resolution (for equal noise levels). Although in the case of the circular cylinder, improved resolution in the xz-plane is still achievable when compared to the respective resolution in the xz-plane observed in the FBP images (for equal noise levels), the resolution in the xz-plane for the elliptical cylinder is worse than the respective resolution of the FBP images. We present a method and results for resolution recovery in the latter case. Similarly to the previous 2D results, the Huber- like prior resulted in better resolution-noise curves than the quadratic. Furthermore, the use of priors reduces image noise significantly compared to the results generated without a prior.

Sampling theorem, bandlimited integral kernels and inverse problems

We describe a novel approach based on the sampling theorem for studying eigenvalue problems associated with bandlimited integral kernels of convolution type. Two sets of functions biorthogonal to the eigenfunctions, one over the infinite interval and the other over a finite interval, are constructed and several identities satisfied by them are derived. The sampling theorem-based approach to the eigenvalue problem is further extended to construct the singular functions associated with the integral operator. It is shown that for the special case of the sinc-kernel, the eigenfunctions, the two biorthogonal sets and the singular functions reduce to the angular prolate spheroidal functions (or Slepian functions). Two methods are discussed for treating the inverse problem associated with bandlimited kernels—one employing the eigenfunctions and the biorthogonal sets and the other employing the singular functions. Numerical examples are included to illustrate the computation of eigenfunctions, biorthogonal sets and the singular functions and their application to the estimation of inverse solution.

Tomosynthesis imaging with 2D scanning trajectories

Tomosynthesis imaging in chest radiography provides volumetric information with the potential for improved diagnostic value when compared to the standard AP or LAT projections. In this paper we explore the image quality benefits of 2D scanning trajectories when coupled with advanced image reconstruction approaches. It is intuitively clear that 2D trajectories provide projection data that is more complete in terms of Radon space filling, when compared with conventional tomosynthesis using a linearly scanned source. Incorporating this additional information for obtaining improved image quality is, however, not a straightforward problem. The typical tomosynthesis reconstruction algorithms are based on direct inversion methods e.g. Filtered Backprojection (FBP) or iterative algorithms that are variants of the Algebraic Reconstruction Technique (ART). The FBP approach is fast and provides high frequency details in the image but at the same time introduces streaking artifacts degrading the image quality. The iterative methods can reduce the image artifacts by using image priors but suffer from a slow convergence rate, thereby producing images lacking high frequency details. In this paper we propose using a fast converging optimal gradient iterative scheme that has advantages of both the FBP and iterative methods in that it produces images with high frequency details while reducing the image artifacts. We show that using favorable 2D scanning trajectories along with the proposed reconstruction method has the advantage of providing improved depth information for structures such as the spine and potentially producing images with more isotropic resolution.