A Patch-based CBCT Scatter Artifact Correction Using Prior CT

Abstract

We have developed a novel patch-based cone beam CT (CBCT) artifact correction method based on prior CT images. First, we used the image registration to align the planning CT with the CBCT to reduce the geometry difference between the two images. Then, we brought the planning CT-based prior information into the Bayesian deconvolution framework to perform the CBCT scatter artifact correction based on patch-wise nonlocal mean strategy. We evaluated the proposed correction method using a Catphan phantom with multiple inserts based on contrast-to-noise ratios (CNR) and signal-to-noise ratios (SNR), and the image spatial non-uniformity (ISN). All values of CNR SNR and ISN in the corrected CBCT image were much closer to those in the planning CT images. The results demonstrated that the proposed CT-guided correction method could significantly reduce scatter artifacts and improve the image quality. This method has great potential to correct CBCT images allowing its use in adaptive radiotherapy.

1. INTRODUCTION

Quantitative cone-beam CT (CBCT) imaging is on increasing demand for precise image guided radiation therapy since it provides a foundation for advanced image-guidance techniques, including accurate treatment setup, online tumor delineation and patient dose calculation [1, 2]. With more precise treatment monitoring from accurate CBCT images, dose delivery errors can be significantly reduced in each fraction and further compensated for in subsequent fractions using adaptive radiation therapy. However, the current CBCT imaging has severe artifacts mainly due to scatter contamination and its current clinical application is therefore limited to patient setup based on only bony structures [3, 4]. Artifacts assumed to be associated with scatter, such as cupping and streaking, can easily be observed from reconstructed patient images in clinical studies [4, 5]. Various scatter correction methods have been developed and can be categorized into two general types: scatter suppression and scatter estimation [6, 7]. Scatter suppression techniques, such as using anti-scatter grids and increasing the air gap, attempt to reduce the number of scatter photons that reach the detector array [8, 9]. Scatter estimation techniques attempt to remove the scatter photons from the acquired projection images using analytical or empirical predictions of scatter distribution, such as deconvolution [6, 10], offline calibration [7], Monte Carlo [11] and hybrid techniques [12, 13].

X-ray scatter can be approximated as a convolution of the primary signal by a blurring kernel [14], and thereafter it can be estimated and removed by deconvolution methods. Deconvolution methods are relatively easy to implement; usually, no additional hardware or acquisition time is required and no additional dose is given to the patient [15]. We proposed a scatter artifact correction method using a patch-based Bayesian deconvolution framework to improve the CBCT image quality. In the current radiotherapy workflow, a planning CT is usually required to acquire before radiotherapy to generate treatment plans. We utilized the acquired planning CT to provide the prior knowledge of true objects for Bayesian framework to iteratively perform scatter artifact correction for CBCT mages. This proposed approach has 2 distinctive strengths: 1) Instead of suffering from the accuracy of anatomical image segmentation, the proposed method introduced a patch-based nonlocal mean strategy to capture the prior information from planning CT to guide the scatter correction of CBCT images; 2) Contrary to classical Bayesian framework, the proposed method is derived in a Bayesian framework with an Markov Random Field (MRF) model for prior information regularization.

2. METHODS

In the proposed method, image registration is firstly used to reduce the geometry difference between the two images. The planning CT-based prior information using patch-based nonlocal mean strategy is added into Bayesian deconvolution framework to iteratively perform scatter artifact correction for CBCT mages. The three major steps are briefly described below.

2.1. Bayesian-based Deconvolution Framework

Assume i(r) is the CBCT image after scanning a true spatial distribution of point object o(r) by a CBCT scanner with a 3D point spread function ofh(r) [16]. r is the 3D coordinate of an image voxel. Under these conditions, CBCT imaging is a convolution process and is modeled as

$$i(r)=o(r)\otimes h(r)+n(r)$$ (1)

where r is a 3D vector ([x,y,z]^T) representing a point in a 3D space or a 2D vector ([x,y]^T) in 2D. n(r) is a spatial independent Gaussian distributed noise, and the operator ⊗ denotes a convolution. The goal of correction is to restore the true object o(r) by deconvolution of the observed CBCT i(r). It becomes a least square minimization denoted as

$$E^{Deconvolution}=\sum _r(i(r)-o(r)\otimes h(r){)}^2$$ (2)

Solving o(r) by minimization of E usually leads to noise amplification and severe ring artifacts. In order to find a unique and stable solution for E, prior knowledge about o(r) is required to regularize the minimization.

Viewing x-ray CBCT as a probabilistic mapping of the objects’ interaction with x-rays, scatter correction can be considered as maximization of a posteriori probability to obtain the true object o providing the observed image i, point spread function (PSF), and prior information about object o. According to Bayesian’ theorem, a posteriori probability can be expressed as

$$p(o\mid i)=p(i\mid o)p(o)∕p(i)$$ (3)

p(o ∣ i) is a posteriori probability of a object o accompanied with an observation i. p(i) is the probability of observing CBCT i and is a constant here. p(o) is the prior information about true objects. p(i ∣ o) is the posterior probability density of observing image i given true object o. Based on the assumption of signal-independent Gaussian noise model, p(i ∣ o) is denoted as

$$p(i\mid o)=\text{exp}(-\frac{1}{2{\sigma }_n^2}\sum _r(i(r)-o(r)\otimes h(r){)}^2)$$ (4)

where ${\sigma }_n^2$ is a Gaussian noise variance which could be estimated from background or uniform tissue regions and assumed to be spatial independent.

2.2. CT-based Patch-wise Prior Information

In a Bayesian framework, prior information regarding the true object is important for artifact correction. We modeled the true object as a MRF and described the prior information as intensity interaction between voxels in order to account for the regularization of local smoothness. The prior information is described by Gibbs formulation as

$$p(o)=\frac{1}{G}\text{exp}(-\eta \sum _{c\in C}{U}_c(o))$$ (5)

where U_c (o) is Gibbs potential defined on each possible set c of voxels, G is a normalizing factor, and the cliques C determine the range of voxel interactions. In the proposed method, only the interaction between neighboring voxels is considered and the prior information is expressed as

$$p(o)=\frac{1}{G}\text{exp}(-\eta \sum _r\sum _{s\in N(r)}w(r,s)(o(r)-o(s){)}^2)$$ (6)

where N(r) is neighborhood around voxel r, that is, 26 voxels in 3D or 8 pixels in 2D, and w(r, s) is a weighting coefficient. The prior information constrains, the local smoothness between neighboring voxels by the square of intensity difference, and w(r, s) determines the weight to enforce this regularization.

Originated from the non-local strategy which has been widely used in the computer vision area, such as image denoising and super resolution [17, 18], most patch-based methods work in a non-local manner [19]. The similarity between two pixels r and s depends on the similarity of the intensity gray level vectors o(P_r) and o(P_s), where P_k denotes a patch of fixed size and centered at a pixel k. The pixels with a similar grey level patch to o(P_r) have larger weights in the average. In order to reduce the computational time, here we performed a preselection of the patches. By using simple statistics such as mean or variance, it is possible to discard the most dissimilar patches. In the proposed approach, we used luminance and contrast criteria to achieve the patch preselection. Based on the well-known structural similarity measure (SSIM) [20, 21], the preselection procedure can be written as follows:

$${}_{ss}=\frac{2{\mu }_r{\mu }_s}{{\mu }_r^2+{\mu }_s^2}\times \frac{2{\sigma }_r{\sigma }_s}{{\sigma }_r^2+{\sigma }_s^2}$$ (7)

where μ represents the means and σ represents the standard deviations of the patches centered on voxel r and voxel s. If the value of ss is greater than a given threshold th, the intensity distance between patches P_r and P_s is computed. The threshold th was set to 0.90 in this study. This value was chosen empirically because it provides a good balance between accuracy and computational time reduction. Patch mean and variance were precomputed as maps of local means and local variances that avoid multiple computations.

Depending on the similarity between the patches surrounding r and s, these weights w(r, s) are computed as [22, 23],

$$w(r,s)=\{\begin{array}{cc}\frac{1}{Z(r)}\text{exp}(-\frac{\Vert o(P_r)-o(P_s){\Vert }_2^2}{l^2})\hfill & ifss>th\hfill \\ 0\hfill & \mathit{else}\hfill \end{array}\phantom{\}}$$ (7)

with Z(r) is the normalizing constant

$$Z(r)=\sum _s\text{exp}(-\frac{\Vert o(P_r)-o(P_s){\Vert }_2^2}{l^2})$$ (8)

and the parameter l controls the decay of the exponential function and therefore the decay of the weights as a function of the Euclidean distances. ‖·‖₂ is the normalized L2 norm (i.e., normalized by the number of elements) computed between each intensity of the elements of the patches P_r and P_s. The non-local mean not only compares the grey level in a single point but the geometrical configuration in a whole patch [24]. We used patches with 5×5 pixels here.

2.3. CT-guided Scatter Correction

The true object is restored by maximizing a posteriori probability as

$$o=\text{arg}\underset{o}{\max }p(o\mid i)=\text{arg}\underset{o}{\max }[p(i\mid o)p(o)]$$ (9)

With the definition of p(i ∣ o) and p(o), the maximization becomes a minimization of the following cost function:

$$o=\text{arg}\underset{o}{\min }E(o)=\text{arg}\underset{o}{\min }[\sum _r(i(r)-o(r)\otimes h(r){)}^2+\eta \sum _r\sum _{n\in N(r)}w(r,n)(o(r)-o(n){)}^2]$$ (10)

where η is a parameter to balance the convolution and the MRF smoothness constraint, which is chosen heuristically in this study but will be simultaneously estimated based on image noise distribution.

The correction o is sought by minimization of the cost function E using a conjugate gradient (CG) method. CG minimization requires analytical derivatives of the cost function with respect to the true object in each voxel. Because PSF h is a symmetric Gaussian function, the correlation is equivalent to a convolution operation. It is widely accepted that x-ray CBCT PSF can be approximated as an anisotropic 3D Gaussian function that is written as

$$h(r)=\frac{1}{(2\pi {)}^{3∕2}{\sigma }_x{\sigma }_y{\sigma }_z}\text{exp}[-\frac{1}{2}(\frac{x^2}{{\sigma }_x^2}+\frac{y^2}{{\sigma }_y^2}+\frac{z^2}{{\sigma }_z^2})]=\text{exp}(-\frac{x^2}{2{\sigma }_x^2})\text{exp}(-\frac{y^2}{2{\sigma }_y^2})\text{exp}(-\frac{z^2}{2{\sigma }_z^2})$$ (11)

where σ = [σ_x,σ_y,σ_z]is the standard deviation in each direction. The PSF can be measured by fitting the Gaussian function to CBCT images of a point object [25].

3. EXPERIMENTS AND RESULTS

This technique was evaluated using Catphan 404 with multiple inserts. Contrast-to-noise ratios (CNR) and signal-to-noise ratios (SNR) [26] of the different inserts, and the image spatial non-uniformity (ISN) [27] in selected volume of interests (VOIs) were calculated to assess the proposed correction method. The CNR after our correction increased by a factor of 1.96, 3.22, 3.20, 3.46, 3.44, 1.97 and 1.65 for the Air, PMP, LDPE, Polystryrene, Acrylic, Delrin and Teflon inserts. While the SNR increased by a factor 1.05, 2.09, 1.71, 3.95, 2.52, 1.54 and 1.84 for the above inserts, respectively. The ISN decreased from 21.1% to 4.7% in the corrected images. All values of CNR, SNR and ISN in the corrected CBCT image were much closer to those in the planning CT images. Figure 1 shows the corrected results of Catphan phantom, which includes the planning CT, the CBCT image before and after correction, and fused images between CT and original/corrected CBCT. Figure 2 displays a profile through the planning CT, the original CBCT and the corrected CBCT images. The results demonstrated that the proposed method significantly reduces the relevant artifacts and recovers CT numbers.

Figure 1.

Results of the Catphan phantom. (a) CT image, (b) CBCT image, (c) fused image between CT (red) and original CBCT images (green), (d) corrected CBCT image, and (e) fused image between CT (red) and corrected CBCT images (green).

Figure 2.

The profile comparison of CT, CBCT and corrected CBCT image through the red dotted line in Figure 1.

4. CONCLUSION

We have developed a novel artifact correction method to improve CBCT imaging for quantitative use. In this method we integrated the prior x-ray image information from co-registered planning CT images and the MRF smoothness constraint into a Bayesian deconvolution framework to iteratively perform scatter artifact correction for CBCT mages. We demonstrated that the proposed CT-guided correction method could significantly reduce scatter artifacts and improve the image quality. This method has great potential to correct CBCT images allowing its quantitative use in adaptive radiotherapy.