Compressed-sensing-based content-driven hierarchical reconstruction: Theory and application to C-arm cone-beam tomography

Magnification-driven B-spline interpolation for cone-beam projection and backprojection

PURPOSE

Discretizing tomographic forward and backward operations is a crucial step in the design of model-based reconstruction algorithms. Standard projectors rely on linear interpolation, whose adjoint introduces discretization errors during backprojection. More advanced techniques are obtained through geometric footprint models that may present a high computational cost and an inner logic that is not suitable for implementation on massively parallel computing architectures. In this work, we take a fresh look at the discretization of resampling transforms and focus on the issue of magnification-induced local sampling variations by introducing a new magnification-driven interpolation approach for tomography.

METHODS

Starting from the existing literature on spline interpolation for magnification purposes, we provide a mathematical formulation for discretizing a one-dimensional homography. We then extend our approach to two-dimensional representations in order to account for the geometry of cone-beam computed tomography with a flat panel detector. Our new method relies on the decomposition of signals onto a space generated by nonuniform B-splines so as to capture the spatially varying magnification that locally affects sampling. We propose various degrees of approximations for a rapid implementation of the proposed approach. Our framework allows us to define a novel family of projector/backprojector pairs parameterized by the order of the employed B-splines. The state-of-the-art distance-driven interpolation appears to fit into this family thus providing new insight and computational layout for this scheme. The question of data resampling at the detector level is handled and integrated with reconstruction in a single framework.

RESULTS

Results on both synthetic data and real data using a quality assurance phantom, were performed to validate our approach. We show experimentally that our approximate implementations are associated with reduced complexity while achieving a near-optimal performance. In contrast with linear interpolation, B-splines guarantee full usage of all data samples, and thus the X-ray dose, leading to more uniform noise properties. In addition, higher-order B-splines allow analytical and iterative reconstruction to reach higher resolution. These benefits appear more significant when downsampling frames acquired by X-ray flat-panel detectors with small pixels.

CONCLUSIONS

Magnification-driven B-spline interpolation is shown to provide high-accuracy projection operators with good-quality adjoints for iterative reconstruction. It equally applies to backprojection for analytical reconstruction and detector data downsampling.

Dual-rotation C-arm cone-beam computed tomography to increase low-contrast detection

PURPOSE

This paper investigates the capabilities of a dual-rotation C-arm cone-beam computed tomography (CBCT) framework to improve non-contrast-enhanced low-contrast detection for full volume or volume-of-interest (VOI) brain imaging.

METHOD

The idea is to associate two C-arm short-scan rotational acquisitions (spins): one over the full detector field of view (FOV) at low dose, and one collimated to deliver a higher dose to the central densest parts of the head. The angular sampling performed by each spin is allowed to vary in terms of number of views and angular positions. Collimated data is truncated and does not contain measurement of the incoming X-ray intensities in air (air calibration). When targeting full volume reconstruction, the method is intended to act as a virtual bow-tie. When targeting VOI imaging, the method is intended to provide the minimum full detector FOV data that sufficiently corrects for truncation artifacts. A single dedicated iterative algorithm is described that handles all proposed sampling configurations despite truncation and absence of air calibration.

RESULTS

Full volume reconstruction of dual-rotation simulations and phantom acquisitions are shown to have increased low-contrast detection for less dose, with respect to a single-rotation acquisition. High CNR values were obtained on 1% inserts of the Catphan® 515 module in 0.94 mm thick slices. Image quality for VOI imaging was preserved from truncation artifacts even with less than 10 non-truncated views, without using the sparsity a priori common to such context.

CONCLUSION

A flexible dual-rotation acquisition and reconstruction framework is proposed that has the potential to improve low-contrast detection in clinical C-arm brain soft-tissue imaging.

A review of GPU-based medical image reconstruction

Tomographic image reconstruction is a computationally demanding task, even more so when advanced models are used to describe a more complete and accurate picture of the image formation process. Such advanced modeling and reconstruction algorithms can lead to better images, often with less dose, but at the price of long calculation times that are hardly compatible with clinical workflows. Fortunately, reconstruction tasks can often be executed advantageously on Graphics Processing Units (GPUs), which are exploited as massively parallel computational engines. This review paper focuses on recent developments made in GPU-based medical image reconstruction, from a CT, PET, SPECT, MRI and US perspective. Strategies and approaches to get the most out of GPUs in image reconstruction are presented as well as innovative applications arising from an increased computing capacity. The future of GPU-based image reconstruction is also envisioned, based on current trends in high-performance computing.

Optimization-based image reconstruction with artifact reduction in C-arm CBCT

We investigate an optimization-based reconstruction, with an emphasis on image-artifact reduction, from data collected in C-arm cone-beam computed tomography (CBCT) employed in image-guided interventional procedures. In the study, an image to be reconstructed is formulated as a solution to a convex optimization program in which a weighted data divergence is minimized subject to a constraint on the image total variation (TV); a data-derivative fidelity is introduced in the program specifically for effectively suppressing dominant, low-frequency data artifact caused by, e.g. data truncation; and the Chambolle-Pock (CP) algorithm is tailored to reconstruct an image through solving the program. Like any other reconstructions, the optimization-based reconstruction considered depends upon numerous parameters. We elucidate the parameters, illustrate their determination, and demonstrate their impact on the reconstruction. The optimization-based reconstruction, when applied to data collected from swine and patient subjects, yields images with visibly reduced artifacts in contrast to the reference reconstruction, and it also appears to exhibit a high degree of robustness against distinctively different anatomies of imaged subjects and scanning conditions of clinical significance. Knowledge and insights gained in the study may be exploited for aiding in the design of practical reconstructions of truly clinical-application utility.