A compressed sensing based reconstruction algorithm for synchrotron source propagation-based X-ray phase contrast computed tomography

Abstract

Synchrotron source propagation-based X-ray phase contrast computed tomography is increasingly used in pre-clinical imaging. However, it typically requires a large number of projections, and subsequently a large radiation dose, to produce high quality images. To improve the applicability of this imaging technique, reconstruction algorithms that can reduce the radiation dose and acquisition time without degrading image quality are needed. The proposed research focused on using a novel combination of Douglas–Rachford splitting and randomized Kaczmarz algorithms to solve large-scale total variation based optimization in a compressed sensing framework to reconstruct 2D images from a reduced number of projections. Visual assessment and quantitative performance evaluations of a synthetic abdomen phantom and real reconstructed image of an ex-vivo slice of canine prostate tissue demonstrate that the proposed algorithm is competitive in reconstruction process compared with other well-known algorithms. An additional potential benefit of reducing the number of projections would be reduction of time for motion artifact to occur if the sample moves during image acquisition. Use of this reconstruction algorithm to reduce the required number of projections in synchrotron source propagation-based X-ray phase contrast computed tomography is an effective form of dose reduction that may pave the way for imaging of in-vivo samples.

Introduction

One limitation of conventional X-ray computed tomography (CT) is that the tissue attenuation of soft tissue structures are similar in hard X-rays and these tissues cannot be examined without using iodine. For example, conventional X-ray CT cannot discriminate minor differences in tissue density/variation which occurs in the early stages of prostate cancer [1]. To address this issue, X-ray phase contrast computed tomography (XPC-CT) [2], [3] has been utilizing the change in phase of X-ray beams as they pass through a sample rather than solely relying on the amplitude attenuation, as is the case with conventional X-ray CT. The phase sensitivity to mild density variation in the soft tissues is three orders of magnitude higher than the amplitude sensitivity at 10-100 keV range [4]. Therefore, XPC-CT has an improved ability to differentiate amongst different soft tissue structures without need for exogenous contrast.

There are several experimental setups available to generate X-ray phase contrast images. Among them, propagation-based XPC-CT (also known as “in-line holography”) has a simple setup with high spatial resolution (a few tens of microns) and low dose capability. Some encouraging results have been reported for the application of this technique in clinical experiments [5]. Phase-contrast images can be generated with this technique when the X-ray source provides a spatially coherent illumination [6]. Propagation-based XPC-CT techniques have been developed with synchrotrons sources as they provides spatially coherent high brilliance radiation [7], [8]. The experimental setup of this synchrotron based technique is like the setup used in radiography i.e. synchrotron X-ray source, the sample and the detector are inline, without any optical element between the sample and the detector. Instead of placing the detector directly behind the sample, which is convenient in radiography, it is placed in some distance from the sample (often called propagation distance). As a result, the X-rays that are refracted by different tissues due to different refractive indices inside the sample can interfere with unaffected beam on the detector [9]. The phase contrast image formed in the detector is sensitive to abrupt variations of refractive indices; so the structural boundaries between different tissues inside the sample are enhanced in this technique [10].

With this capability, the synchrotron-based propagation-based XPC-CT can provide higher tissue contrast and spatial resolution of prostate images compared with conventional X-ray CT [11]. To achieve the requisite spatial resolution, a large number of projection views (>1000) is necessary to discriminate fine details of small structures in the sample field of view [12], [13], [14]. This exposes the specimen to high radiation that would be detrimental when imaging a live patient or animal in-vivo. One approach to decrease total X-ray dose and imaging time is to reduce exposure time per projection which is the only parameter that can be used to control the amount of X-ray dose in each projection since the photon brightness of synchrotron X-ray is fixed [15]. However, the minimum exposure time is limited by detector sensitivity and readout speed. Also, low exposure time generally results in lower projection signal to noise and accordingly lower quality of reconstructed image [16]. Sparse-view imaging technique is another approach which can reduce the number of projections and consequently the total X-ray dose and imaging time, while maintaining acceptable diagnostic image quality.

Analytical algorithms such as Filtered Back Projection (FBP) remains the standard reconstruction algorithm for most commercial CT scanners. When sparse-view imaging technique is used with this algorithm, serious aliasing artifacts, such as sharp streaks, can be observed in the reconstructed images [17]. Unlike analytical algorithms, iterative algorithms are increasingly used for reconstruction of images when noisy and incomplete projection data are available [18]. Iterative algorithms are based on solving a system of linear equations subject to the constraints that are obtained from prior information about the reconstructed image. A number of well-known iterative algorithms include: Projection onto Convex Sets (POCS) [19], Maximum Likelihood Expectation Maximization (MLEM) [20] and Adaptive Steepest Descent – Projection onto Convex Sets (ASD-POCS) [21]. POCS, also known as the alternating projection algorithm, has relatively low computational complexity and is utilized to find the intersection point of two or more closed convex sets to solve a system of linear equations. The MLEM algorithm attempts to solve a system of linear equations which have non-negative coefficients in both the system matrix and observation vector. The ASD-POCS algorithm attempts to reconstruct the assumed non-negative images by minimizing the total variation seminorm in the image, subject to the constraint that the estimated projected data should be within a known tolerance of the acquired data.

Recently, compressed sensing (CS) theory has attracted huge attention in the imaging community because of its ability to formulate the principles for exact recovery of signal from highly incomplete frequency information [22], [23]. This theory is applicable to images that are compressible in a predefined basis/frame such as wavelet, gradient, Fourier i.e. most of the transformed image pixels should be approximately zero. Use of the gradient basis such as total variation (TV) has proven advantageous for tomographic images as they have uniform tissues with only abrupt changes at boundaries [24]. It motivates us to propose a CS-based algorithm to reconstruct large-scale high resolution images from significantly reduced projection data.

The algorithm proposed in this paper aims to recover the image from sparse-view synchrotron source propagation-based phase contrast data using a combination of Douglas–Rachford splitting (DRS) and randomized Kaczmarz algorithms. These algorithms are used to solve a large-scale TV based optimization problem in the compressed sensing framework. The DRS algorithm was first formulated in [25] and is applicable to convex programming in which a large problem can be divided into smaller and easier to solve problems. The randomized Kaczmarz algorithm is an iterative algorithm that can be used to solve linear equations. One application of this algorithm in solving linear equations is illustrated by reconstruction of a band-limited function from non-uniform spaced sampling values in [26]. We hypothesize that the proposed algorithm is able to reconstruct smooth image regions while preserving prominent edges at the borders of different regions better than existing reconstruction algorithms.

Our proposed algorithm may also be applicable to other synchrotron-based medical imaging technologies including micro computed tomography (micro-CT) [27], K-edge subtraction computed tomography (KES-CT) [28] and computed tomography of diffraction enhanced imaging (DEI-CT) [29] to reduce radiation dose and imaging time.