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Improving image quality is a critical objective in low dose computed tomography (CT) imaging and is the primary focus of CT image denoising. State-of-the-art CT denoising algorithms are mainly based on iterative minimization of an objective function, in which the performance is controlled by regularization parameters. To achieve the best results, these should be chosen carefully. However, the parameter selection is typically performed in an ad hoc manner, which can cause the algorithms to converge slowly or become trapped in a local minimum. To overcome these issues a noise confidence region evaluation (NCRE) method is used, which evaluates the denoising residuals iteratively and compares their statistics with those produced by additive noise. It then updates the parameters at the end of each iteration to achieve a better match to the noise statistics. By combining NCRE with the fundamentals of block matching and 3D filtering (BM3D) approach, a new iterative CT image denoising method is proposed. It is shown that this new denoising method improves the BM3D performance in terms of both the mean square error and a structural similarity index. Moreover, simulations and patient results show that this method preserves the clinically important details of low dose CT images together with a substantial noise reduction.

While X-ray computed tomography (CT) enables ultrafast acquisition of patient images obtained with excellent spatial resolution, the dose needed to achieve diagnostic image quality can result in a significant increase in the risk of developing cancer [

The main source of noise in X-ray projection data is quantum noise caused by statistical fluctuations of X-ray quanta reaching the detectors, so that the CT projection noise follows the Poisson distribution [

A simplified noise model is usually used in image based denoising algorithms, in which, following the Central Limit Theorem (CLT) [

Different image based denoising algorithms have been used to estimate the noiseless CT images, such as anisotropic diffusion [

There is a strong dependence of the quality of the result on the regularization parameter. It is a challenging task to find the regularization parameter

One straight forward approach used in many algorithms is to use a heuristic

In this paper, a noise confidence region evaluation (NCRE) method is used to address the regularization selection and the algorithm stopping problems. It adaptively updates the regularization parameters at the end of each iteration by validating the result of that iteration. The algorithm stops when the statistical properties of the denoising residual resemble those of the additive white Gaussian noise. Using NCRE, a new iterative block matching and 3D filtering (BM3D) method is proposed, which outperforms BM3D [

Recently, it has been shown that nonlocal patch based algorithms outperform others in CT image denoising [

Our proposed algorithm makes use of the block matching and 3D filtering (BM3D) technique [

To denoise the images, patch based methods generally use a model based on

Although a reasonable statistical model for the CT projection data is the independent Poisson distributions [

Based on the above discussion and our experimental results, presented in the Appendix, it can be assumed that the noise in 3D similar patches of the CT images follows a white additive Gaussian distribution, with different variances for different 3D patches

If

In [

As shown in Figure

Three possible regions for the residual at the end of each iteration. If it lies in Region II (noise confidence region), denoising is stopped.

Noise statistics of the soft tissue region surrounding the lung. (a) Top: the thoracic phantom which is used to evaluate the noise characteristics and bottom: the soft tissue region of the phantom (denoted by

Algorithm

To denoise CT images the fundamentals of BM3D were used in an iterative scheme: the output of the Wiener filter is a better estimate of the original image than the input of Wiener filter from the first step. Therefore, this output can be fed into the first step to provide better Wiener coefficients in the second iteration. The modified BM3D formulation (

Three test methods were used to evaluate the performance of the proposed algorithm. The first method consisted of a simulated Shepp-Logan phantom corrupted by adding Poisson noise to the fan beam X-ray projections. The images were reconstructed using the

Figure

Squared error (blue line) and the Structural Similarity Index (SSIM) (green dashed line) showing the changes with each iteration when using BM3D-NCRE. The shading colors show the region in which

Shepp-Logan phantom simulations: (a) original phantom, (b) noisy reconstructed phantom, (c) denoised by BM3D, and (d) denoised by BM3D-NCRE.

In the second test, the CATPHAN phantom was scanned using a low dose (50 mAs, 120 kVp) and a high dose (300 mAs, 120 kVp) protocol. Image reconstructions were performed with a Toshiba Aquilion One CT using the proprietary lung kernel FC52 and the proprietary iterative reconstruction algorithm Adaptive Iterative Dose Reduction 3D (AIDR3D) [

Top: line pair slice of the CATPHAN phantom scanned with 50 mAs and 120 kVp (window width/window level = 400/60 HU). Bottom: red rectangular ROI of the images with the red line showing the cut-off line pair resolution (window width/window level = 400/500 HU). Left to right: image reconstructed with FC52 (STD = 64 HU) and reconstructed with AIDR3D (STD = 41 HU), FC52 denoised with the proposed method (STD = 22 HU), FC52 denoised with nonlocal mean (STD = 34 HU), and FC52 denoised with BM3D method (STD = 27 HU).

Figure

Low contrast study using CATPHAN low contrast slice. Top: images scanned with 50 mAs/120 kVp and bottom: scanned with 300 mAs/120 kVp. Left to right: image reconstructed with FC52, reconstructed with AIDR3D, reconstructed with FC52 and denoised by BM3D-NCRE, reconstructed with FC52 and denoised by nonlocal mean, and reconstructed with FC52 and denoised by BM3D. In all images window width/window level = 100/70 HU.

The final comparison was made using a low dose (50 mAs, 120 kVp) lung CT of a patient reconstructed using FC52 and processed by anisotropic diffusion denoising, BM3D-NCRE, nonlocal mean, and BM3D. A single axial slice of the images is shown in Figure

Comparison of the effects of anisotropic diffusion, nonlocal mean, BM3D, and BM3D-NCRE. (a) In the original image, the circular regions show the area from which the noise variance is measured, the dashed rectangular region is the area which is shown in (d)-(e), and average noise of the three regions is around 55 HU. (b) Denoised by anisotropic diffusion, noise is around 25 HU. (c) Denoised by BM3D-NCRE, noise is around 25 HU. (d) Denoised by nonlocal mean, noise is around 21 HU. (e) Denoised by BM3D, noise is around 28 HU. ((f)–(j)) The zoomed-in region shown by dashed rectangle in image (a). The difference between original image and the image denoised by (k) anisotropic diffusion, (l) BM3D-NCRE, (m) nonlocal mean, and (n) BM3d are shown. The window width/window level in (a)–(j) is 1600/−300 HU and is 100/0 HU in (k)–(n).

An iterative denoising scheme was proposed for low dose CT images, which adjusts the denoising parameters at each iteration based on the effect of the denoising method in the previous iteration. Noise confidence region evaluation (NCRE) was used to compare the Gaussian noise with denoising residual to determine if the denoising was effectively, weakly, or strongly executed. Based on this information the denoising parameters were adjusted for the next iteration. BM3D was used in the new proposed iterative scheme. The phantom study showed that our proposed method improved low contrast detectability. The patient study demonstrated that the image was efficiently denoised and the visibility of small objects was preserved. However, it should be noted that the modified optimization model is not accurate when the electronic noise dominates the photon fluctuations as could occur for very low doses. In addition, the streak artifacts would still be present in images denoised by the proposed method.

The noise statistics in CT images were studied using a Toshiba phantom containing five circular regions of differing CT#

Phantom scanned with eight different X-ray source currents with the same peak voltage: top left to right 5, 10, 25, and 50 mAs and bottom left to right 100, 150, 200, and 250 mAs.

Comparison of the noise distribution in the six regions of the phantom shown in Figure

Showing the noise variance changes for the background and the five circular regions of the phantom as the dose was increased from 5 mAs to 250 mAs.

Two small soft tissue regions in the lung of a thoracic anthropomorphic phantom are shown. The noise distribution of these regions (blue dots), which could be used in patch based denoising, is compared to that of the fitted Gaussian distribution (dashed red lines).

The authors declare that there is no conflcit of interests regarding the publication of this paper.

This study was partially supported by Toshiba Canada, Medical Systems Group, and NSERC Canada Grant no. 3247-2012.