Denoising images of dual energy X-ray absorptiometry using non-local means filters

Abstract

BACKGROUND:

In general, the image quality of high and low energy images of dual energy X-ray absorptiometry (DXA) suffers from noise due to the use of a small amount of X-rays. Denoising of DXA images could be a key process to improve a bone mineral density map, which is derived from a pair of high and low energy images. This could further improve the accuracy of diagnosis of bone fractures and osteoporosis.

OBJECTIVE:

This study aims to develop and test a new technology to improve the quality, remove the noise, and preserve the edges and fine details of real DXA images.

METHODS:

In this study, a denoising technique for high and low energy DXA images using a non-local mean filter (NLM) was presented. The source and detector noises of a DXA system were modeled for both high and low DXA images. Then, the optimized parameters of the NLM filter were derived utilizing the experimental data from CIRS-BFP phantoms. After that, the optimized NLM was tested and verified using the DXA images of the phantoms and real human spine and femur.

RESULTS:

Quantitative evaluation of the results showed average 24.22% and 34.43% improvement of the signal-to-noise ratio for real high and low spine images, respectively, while the improvements were about 15.26% and 13.55% for the high and low images of the femur. The qualitative visual observations of both phantom and real structures also showed significantly improved quality and reduced noise while preserving the edges in both high and low energy images. Our results demonstrate that the proposed NLM outperforms the conventional method using an anisotropic diffusion filter (ADF) and median techniques for all phantom and real human DXA images.

CONCLUSIONS:

Our work suggests that denoising via NLM could be a key preprocessing method for clinical DXA imaging.

Keywords

DXA images radiography dual-energy scanned projection DXA noise modelling non-local means filter (NLM)image denoising

1 Introduction

Dual energy X-ray absorptiometry (DXA) is a low X-ray dose imaging technique that is commonly used to diagnose bone fractures or bone diseases such as osteoporosis [1]. For instance, DXA is especially useful for menopausal women who exhibit a high probability of bone fractures and for patients who are over 50 years old and more likely to experience disability and mortality due to bone problems [2 –4]. There are no precautions to prevent early osteoporotic fractures [2]. Furthermore, due to the high radiation dose and cost of quantitative computed tomography, a DXA system is considered the gold standard clinical technique to screen for bone-related diseases [4, 5].

Recently, DXA has gained attention since it can provide a measure of bone mineral density (BMD), which reflects the fragility of bone [6]. The configuration of a DXA system consists of a paired X-ray source and detector to capture the X-ray photons that penetrate the patient. A DXA imaging system utilizes two different energy levels, producing high and low energy images [7]. At the high energy level, the amount of detected photons is considered larger than that detected at the low energy level. This means that a DXA imaging system produces two different images at the same time from the same object during data acquisition [8, 9]. Based on this pair of images, a DXA imaging system is able to distinguish between bone and tissue regions [3]. Then, a DXA system utilizes high and low energy images to produce a BMD map for several body parts such as the spine and femur, from which the probability of bone fractures can be deduced [7]. However, due to the low X-ray dose of a DXA system, the quality of the image is reduced. To improve the quality of bone diagnostics, reduction of noise in both high and low energy images is an essential preprocessing procedure.

With regard to denoising DXA images, there have been very few attempts reported. In [9], Kwon et al. presented a methodology of modeling DXA image noise, but only low energy DXA images were used for both source and detector noise modeling and denoising. They sequentially applied Wiener and scale-wavelet BayesShrink filters to reduce the detector and source noises from only low energy DXA images. Their denoising technique was evaluated in terms of the mean to standard deviation ratio (MSR), showing an improvement of 5.86%. Up to now, research on the denoising of DXA images is very rare.

Recently, non-local means filters (NLMs) have been gaining popularity in the fields of medical image denoising of digital X-rays, X-ray computed tomography (CT), ultrasound, and magnetic resonance imaging [10 –17] due to their ability to eliminate noise by comparing the similarity of patches through the pixel neighborhoods. NLM relies on the similarity among the patches in the nearby image to obtain more of the prominent fine structure of the image with a low rate of noise. Previously in [13], Irrera et al. applied NLM to reduce the Poisson noise of EOS images. EOS is an X-ray imaging system that uses a low dose of X-ray to scan the whole body. Their results presented image enhancement for both pelvis and knee regions from whole body X-ray images. In 2015, Wang et al. applied NLM on both sinograms of CT images and reconstructed noise-reduced images of Shipp-Logan phantoms [14]. The smoothness parameter of NLM was adjusted by implementing a noise model for the sinogram data of the CT images. Their results demonstrated 3.67% enhancement compared to an anisotropic diffusion filter (ADF) [14]. In 2014, Zhang et al. applied NLM on magnetic resonance (MR) images to reduce Rician noise and improve the visual quality of brain images. They found that the noise was removed without affecting edge details [17]. In 2016, Ertas et al. used NLM filters with an algebraic reconstruction technique to reduce artifacts and preserve edges. They found that the noise in the images of a 2D Shepp-Logan phantom was reduced, and the edges and details were preserved very well [18]. In 2014, Ertas et al. proposed a combination of total variant (TV) with NLM during a 3D algebraic reconstruction technique of tomosynthesis phantom imaging. They first applied TV method in order to remove the background noise with edge preserving. Then, they consecutively applied NLM to suppress out the slice blurring. Utilizing this combination, a significant improvement ratio in the image quality is achieved with 27.49% and 51.25% in terms of SSIM and SNR, respectively [19]. So far, NLM, despite its successful application to medical images, has not been adopted and applied to DXA images.

In this work, we propose a denoising technique to enhance the quality of both high and low energy DXA images using NLM. We modeled the noise of DXA images and derived the optimal parameters for NLM. Then, the optimized NLM was applied to both high and low energy DXA images of spine phantoms and real objects (e.g., spine and femur). In addition, we examined the BMD maps derived from the denoised DXA images for three clinical case studies: normal, osteopenia, and osteoporosis of both spine and femur. The performances of NLMs have been evaluated quantitatively in terms of mean-to-standard deviation ratio (MSR), signal-to-noise ratio (SNR), contrast-to-noise ratio (CNR), and Beta index, an edge quality metric [20, 21]. Our quantitative evaluation results show that the proposed denoising technique significantly reduces the noise from both high and low energy DXA images while preserving the fine details of anatomical structures. For qualitative evaluations via visual inspections, we examine the line profiles of the original and denoised DXA images.

The paper is organized as follows. First, we present an overview of our proposed denoising method using NLM. Second, we present our noise modeling processes of DXA noise from the information of both the source and detector of a DXA system. Then, the main principle of NLM and its parameter optimization processes utilizing the spine phantom are demonstrated. After that, we present the results of the proposed denoising technique on DXA images of phantoms and real human spine and femur. Finally, the effect of denoising in clinical case studies of spine and femur is presented.

2 Materials and methods

The overview of the denoising process for DXA images via NLM is given in Fig. 1. It starts by acquiring the DXA images, building the noise model, optimizing the parameters of NLM, denoising the DXA images, and finally investigating the effects of NLM on the derived BMD maps.

Fig.1

Block diagram of our proposed technique for denoising of DXA images via a non-local means filter (NLM).

2.1 Non-local means filter for DXA image denoising

NLM was first proposed by Buades et al. [22]. The principle of NLM depends on a weighted averaging of the neighboring patches. This procedure relies on the degree of similarity among these involved patches [14, 22]. It is currently considered as one of the effective techniques in terms of reducing noise while preserving the edges and fine details of objects [23]. NLM is considered more promising than other neighborhood filters such as bilateral and Gaussian filters [14 , 23]. In order to reduce the noise and preserve the edges with fine details, we separately apply NLM to each noisy DXA image I. Let ω be a certain discrete grid of image pixels and P = {P_i|i ∈ ω} be a noisy image. As in [14 , 22], the denoised intensity NLM (P_i) at a pixel i is expressed as follows: $NLM (P_{i}) = \frac{\sum_{j \in ω} w (i, j) \cdot P_{j}}{\sum_{j \in ω} w (i, j)},$ (1) where w (i, j) is the average weight that depends on the similarity between the pixels i and j [14 , 23]. This weight should satisfy two conditions, which are 0 ⩽ w (i, j) ⩽1 and ∑_jw (i, j) =1 [22]. This weight is defined at both similarity windows, N_i and N_j, which are centered at pixels i and j, respectively, as follows: $w (i, j) = exp {- \frac{{∥ p (N_{i}) - p (N_{j}) ∥}_{2, σ_{g}}^{2}}{h^{2}}},$ (2) where ∥ · ∥ _{2,σ_g} indicates the Gaussian distance between two similarity patches with a standard deviation σ_g that must be greater than zero [14, 22]. The smoothness parameter h is considered as a degree of filtering that controls the decay of the exponential function in Equation (2). The normalizing factor is presented in the denominator of Equation (1). For the high and low energy DXA images, the smooth parameters are denoted as h_H and h_L, respectively. From the noise model, h_H and h_L are derived corresponding to the noise variance of the DXA system as follows: $h_{H} = k_{H} \times σ_{H},$ (3) $h_{L} = k_{L} \times σ_{L},$ (4) where k_H and k_L are constants, and σ_H and σ_L are the standard deviations of the noise for the high and low energy DXA images, respectively. In fact, NLM has three specific parameters, which are the smoothness parameter, search window, and similarity window. A large value of h causes smoothing of DXA images while leaving much noise from the original image [22]. The search and similarity patches that satisfy short distances among the neighborhood pixels increase the weight value, and then a small denoising rate will be attained, and vice versa [22, 23]. Thus, the weights of NLM should be adjusted and estimated carefully to obtain more robust denoising of DXA images. All of these parameters, σ_H, σ_L, h_H, and h_L, are found and derived from the noise modeling as described in the following sections.

2.1.1 DXA noise modeling: σ_H and σ_L

A pair of source and detector noises is represented in the DXA imaging system [8, 9]. It has been reported that these DXA noises are Poisson and Gaussian noises, respectively [9]. The source noise is captured by measuring X-ray photons at the detector without any object between the source and detector of a DXA system. To acquire multiple noise measurements of the source noise for high and low energy images, we repeated the scans at the same settings of a DXA system. To measure the detector noise, we first measured X-ray photons at the detector after covering the source aperture with a lead sheet to prevent the rays from reaching the detector. Then, we repeated the scans several times to obtain multiple measurements. In [9], Kwon et al. proposed a noise model of DXA that involves two kinds of noise: namely, source and detector noise. Detector noise has an additive property based on the similar distributions of the images obtained from the same DXA system, while the source noise has complex properties due to the different distributions of the DXA images acquired. As presented in [9, 10], the noise model for both source and detector noises is derived with respect to the variance of noise as follows: $σ (η_{s}) = \sqrt{var (η_{s})} = \sqrt{\frac{(σ_{s})^{2} - (σ_{d})^{2}}{{(I_{μ} / I_{o})}^{2}}}$ (5) $and σ (η_{d}) = \sqrt{var (η_{d})} = σ_{d},$ (6) where σ (η_s) and σ (η_d) are the standard deviations of the source and detector noises η_s and η_d, respectively. The quantities σ_s and σ_d are the standard deviations from the averaged noise images for the source and detector noises, respectively. In addition, I_μ is the average value of the X-ray photons that are captured at the detector, and I₀ represents the source incident photons. Our empirical experiments show that the DXA noises are stationary, and that the detector noise is sufficiently smaller than the source noise, as shown in Table 1. Thus, detector noise is neglected in this study. Then, the standard deviations of the source and detector noises become $\begin{matrix} σ (η_{s}) = \frac{σ_{s}}{(Iμ / I0)} \\ and σ (η_{d}) = σ_{d} = 0 . \end{matrix}$ (7)

Table 1

Means and standard deviations of averaged DXA maps of source and detector noises

Index	Source noise		Detector noise
	High energy	Low energy	High energy	Low energy
Mean (μ)	25,881	7,174.5	0.0559	0.0267
SD (σ)	1,124.75	322.175	0.2345	0.1677

Finally, from Equation (7), the standard deviations of noise for high and low DXA images are reduced to Equations (8 and 9) as follows: $σ_{H} (η_{s}) = (\frac{I_{o}^{H}}{I_{μ}^{H}}) \times σ_{s}$ (8) $and σ_{L} (η_{s}) = (\frac{I_{o}^{L}}{I_{μ}^{L}}) \times σ_{s},$ (9) where $I_{o}^{H}$ and $I_{o}^{L}$ are the incident X-ray photons for high and low energy, respectively, and $I_{μ}^{H}$ and $I_{μ}^{L}$ are the average values of the captured photons at the detector for high and low energy.

2.1.2 Smoothing parameters via CIRS-BFP phantoms: h_H and h_L

To optimize the smoothing parameters h_H and h_L of NLM, we utilized a uniform phantom for DXA. In this study, we used the Bona Fide Phantom (CIRS-BFP, Pacific Northwest X-ray Inc., USA), which is considered an evaluation phantom for most DXA systems. The CIRS-BFP spine phantom represents a homogenous soft tissue (i.e., acrylic) in the tissue region. Meanwhile, the bone region is demonstrated by an equivalent embedded bone material with different thicknesses for the vertebrae. This phantom clinically satisfies the density of the lumbar spine vertebrae in the human body, and uniformity within this phantom image is expected. Thus, this phantom was considered uniform in the areas used for the analysis. According to Equations (3 and 4), the smoothness parameters (i.e., h_H and h_L) can be obtained at the maxima of some objective measures. In this study, we utilized MSR, SNR, and CNR to determine the optimized values of k_H and k_L.

2.2 Evaluation metrics for the performance of NLM

For quantitative evaluation, we utilized the quality metrics MSR, SNR, and CNR. MSR is the ratio of the mean value of the whole DXA image μ_I to the standard deviation σ_{ROI_o} of the extracted region of interest (ROI) inside of an object with a size of 10 × 10 pixels [8 –10]. As in [9], MSR measures the image quality, where a higher value signifies better image quality, and is defined as follows: $MSR = \frac{μ_{I}}{σ_{{ROI}_{o}}}$ (10)

To evaluate image quality for our proposed denoising technique in terms of structure-based similarity, we also utilized the structural similarity (SSIM) index for all DXA images [24, 25]. A higher value of SSIM indicates better image quality.

SNR in decibels was computed for both original and denoised DXA images with respect to the mean pixel value μ_o of a whole object (i.e., a bone) and the standard deviation σ_{ROI_bg} of the extracted ROI from a background region with a size of 10 × 10 pixels. The noise reduction is successfully satisfied when the SNR is higher, where SNR is defined as follows [10 , 14]: $SNR (dB) = 10 {log}_{10} (\frac{μ_{o}}{σ_{{ROI}_{bg}}}) .$ (11)

Also, we estimated CNR in decibel as follows: $CNR (dB) = 20 {log}_{10} (\frac{μ_{o} - μ_{g}}{σ_{{ROI}_{bg}}}),$ (12) where μ_g is the mean pixel value of the whole background. CNR is a quantitative measure used to measure the quality of an image [10 , 26]. Unfortunately, none of these metrics reflect the degree of edge preservation. Therefore, we use another index, Beta [20, 21], which depends on the correlation function between the original and denoised DXA images and is defined as follows: $Beta = \frac{Γ (Δ I - \bar{Δ I}, Δ \hat{I} - \bar{Δ \hat{I}})}{\sqrt{Γ (Δ I - \bar{Δ I}, Δ I - \bar{Δ I}) \cdot Γ (Δ \hat{I} - \bar{Δ \hat{I}}, Δ \hat{I} - \bar{Δ \hat{I}})}},$ (13) $and Γ (I_{1}, I_{2}) = \sum_{(i, j) \in I} I_{1} (i, j) \cdot I_{2} (i, j),$ (14) where $Δ \hat{I}$ and $Δ \hat{I}$ are the original and denoised DXA images after applying a 3 × 3 Laplacian high-pass filter, respectively, and $\bar{Δ I}$ and $\bar{Δ \hat{I}}$ are the mean values of the $Δ \hat{I}$ and $Δ \hat{I}$ images [20, 21]. A higher ratio of edge preservation is achieved when the Beta value is higher, and vice versa.

3 Results and discussion

The proposed denoising technique via NLM for both high and low DXA images is evaluated experimentally with phantom and real data.

3.1 DXA image acquisition and experimental environment

In this study, we acquired two sets of DXA images using a spine phantom and from human data involving the spine and femur. All of the data is acquired using a DXA imaging system (OsteoPro MAX, B.M. Tech Worldwide Co., Ltd., Republic of Korea) with a maximum tube voltage of 76 keV and current of 1 mA. This system utilizes a samarium filter to distinguish the X-ray spectrum into high and low energy levels. For the phantom data, we utilized a spine phantom (i.e., CIRS-BFP) to obtain the DXA images with the spinal scanning protocol, where the resolution of the phantom DXA images was 2.6×3.1 mm² with 68×36 mm² in the field of view (FOV). For the real data, the real femur image resolution was 2.6×2.6 mm² with a 50×50 mm² FOV, while the real spine image had 2.6×3.1 mm² resolution and a 68×36 mm² FOV.

3.2 Estimation of denoising parameters

The dynamic range of the low DXA images is significantly larger than that of the high DXA images [9]. The optimized parameters of NLM are derived from the CIRS-BFP phantom study. For this, we separately estimated the smoothing parameter h by adjusting the value of k. Figure 2 shows the percentage values of MSR, SNR, and CNR for the high and low energy DXA images of the phantom with respect to the value of k. The optimization procedure was achieved through two steps. First, we increased the value of k gradually and examined the values of MSR, SNR, and CNR, as shown in Fig. 2. Note that increasing the value of k increased the degree of smoothing. Second, based on the results in Fig. 2, we attempted to estimate the optical values of k for the high and low energy images. Due to the homogeneous structure of the phantom, we only utilize one region of interest, ROI_o, inside the bone to measure MSR, and another region is designated as ROI_bg in the background to measure SNR and CNR. However, we note that MSR is not a suitable measure, since it increases as the value of k increases. Thus, we only utilized SNR and CNR to obtain the optimal smoothing parameter that supports NLM. Based on our phantom experiments, we derive the values of k to be k_H = 4 and k_L = 8 for the high and low energy DXA images, respectively. In this study, we test and verify this optimization process through different window sizes of NLM. Furthermore, based on our empirical experimentation, one can utilize other similarity window sizes of 3×3, 5×5, or 7×7 for NLM with both DXA images. The similarity window of size 5×5 is sufficiently large to achieve the desired denoising and small enough to be robust in preserving the fine structure and edges of the images.

Fig.2

Optimization of the smoothing parameter h corresponding to the k values for (a) a high energy image and (b) a low energy image with a similarity window size of 5×5.

3.3 Denoising results of phantom DXA images

Figure 3 shows the denoising results of the phantom high and low energy images with the optimized parameters of NLM. Figure 3(a) and (b) show the original high and low energy DXA images, and Fig. 3(c) and (d) show the denoised images utilizing the optimized NLM. The noise in both high and low energy images seems to be effectively reduced. Also, the object edges seem to be preserved where the Beta index is 98.01% and 97.84% for the high and low energy denoised images, respectively. For the high energy images, the MSR, SNR, and CNR are improved, as shown in Fig. 2(a), by about 3.01%, 30.36%, and 21.45%, respectively. In the low energy images, as shown in Fig. 2(b), the improvements of these metrics are about 3.80%, 27.02%, and 15.93%, respectively. As shown in Figs. 2 and 3, the proposed NLM preserved the edges and increased the image quality with SSIM indices of 98.25% and 98.02% for the high and low energy images, respectively. In Fig. 4, the horizontal line profiles of both the original and denoised DXA images are plotted, showing that the denoised line profiles for both the high and low energy DXA images had the same attitude and preserved edges and fine details.

Fig.3

High and low energy absorptiometry phantom DXA images. The original (a) high energy and (b) low energy images before denoising; (c) high energy and (d) low energy images after denoising.

Fig.4

Horizontal line profiles for the high and low energy DXA images in Fig. 3. (a) The line profiles of the original (dotted line) and denoised (solid line) high energy DXA images at the overlaid lines in Fig. 3, and (b) the line profiles of the original and denoised low energy DXA images.

3.4 Denoising results of real DXA images

This section presents the results of our proposed denoising algorithm on real human spine and femur DXA images. In this study, three ROIs in different locations, where the noise characteristics are expected to be different, are examined via the evaluation metrics. Thus, three ROIs are manually determined within the bone region (i.e., ROI_o₁, ROI_o₂, and ROI_o₃) to derive MSRs for all of the spine and femur DXA images according to Equation (10). Meanwhile, another three ROIs in the background (i.e., ROI_bg₁, ROI_bg₂, and ROI_bg₃) are determined to estimate SNR and CNR according to Equations (11 and 12), respectively. All of these different ROIs are fixed in the same positions for high, low, and BMD spine and femur DXA images for each clinical case, as shown in Figs. 5(a) and 8(a).

Fig.5

Real high and low energy absorptiometry spine DXA images: (a) and (b) represent the original pair of high and low energy images before denoising, while (c) and (d) are the same images after denoising.

3.4.1 Spine DXA images

Figure 5(a) and (b) show the original high and low energy DXA spine images, and Fig. 5(c) and (d) show the denoised images acquired via the optimized NLM corresponding to Fig. 5(a) and (b), respectively. The denoised images in Fig. 5 show more details for each vertebra in comparison to the original ones. This implies that our proposed method seems to remove the noise and increase the image quality with 97.05% and 95.92% SSIM indices for high and low energy images, respectively. The proposed NLM technique with its optimized parameters is able to remove the noise and preserve the edges without an increase in blurriness. To assess the effects of denoising the spine DXA images, the center-horizontal line profiles for both the original and denoised images are shown in Fig. 6. The proposed NLM technique seems to preserve the edges of the main objects with Beta indices of 97.33% and 96.34% for the high and low energy images, respectively, while smoothing out the noise. Average improvement ratios in MSR, SNR, and CNR of 5.49%, 24.22%, and 2.58% are obtained for the high energy images, and those of the low energy images are 9.63%, 34.43%, and 1.77%, respectively, over three different ROIs. Table 2 summarizes the values of these metrics before and after denoising over these three ROIs. This variation in improvement ratios over three different ROIs is due to the nature of NLM, which handles the noise locally.

Fig.6

Horizontal line profiles for the real spine high and low energy DXA images depicted in Fig. 5: (a) the line profiles of the original (dotted line) and denoised (solid line) high images at the overlaid lines in Fig. 5, and (b) the line profiles of the original and denoised low DXA images.

Table 2

Performance analysis for high and low energy DXA images of the spine

	Index	High Energy Image		Low Energy Image
		Original	Denoised	Original	Denoised
${ROI}_{1}^{*}$	MSR	29.55	31.01	18.76	20.52
	SNR	5.70	6.97	3.38	4.51
	CNR	28.11	28.75	28.11	28.53
ROI₂	MSR	28.85	30.42	17.34	19.02
	SNR	5.61	6.88	4.07	5.48
	CNR	27.15	27.86	28.27	28.79
ROI₃	MSR	31.25	33.15	19.06	20.93
	SNR	5.12	6.54	4.06	5.49
	CNR	28.11	28.91	27.32	27.86
	SSIM	97.05		95.92
	Beta	97.33		96.34

^*Each ROI_i involves two different ROIs: ROI_{o_i}, which is utilized for MSR, and ROI_{bg_i}, which is utilized to compute both SNR and CNR. All of these ROIs are superimposed on Fig. 5(a) for spine case. ROI, region of interest; MSR, mean-to-standard deviation ratio; SNR, signal-to-noise ratio; CNR, contrast-to-noise ratio.

We also estimate the BMD maps for real spine DXA images to show the effects of NLM. Both original high and low energy images, presented in Fig. 5(a) and (b), are utilized to compute the original map of BMD, as shown in Fig. 7(a). Then, we utilized both the denoised high and low energy images depicted in Fig. 5(c) and (d) to compute the denoised map of BMD, as shown in Fig. 7(b). To investigate the effects of the proposed NLM technique, the center-horizontal profile data are plotted for both the original and denoised BMD spine maps, as shown in Fig. 7(c). The proposed denoising technique seems to retain the edges and fine details of the data. All evaluation measures of this BMD map, which represents an osteopenia case, are reported in Table 3 for the three different ROIs.

Fig.7

BMD maps for a real spine DXA image. (a) Original BMD map with the superimposed ROIs, (b) the BMD map from the denoised high and low energy images, and (c) the line profiles of the BMD maps from the original (dotted line) DXA images and the denoised (solid line) at the overlaid lines in (a) and (b).

Table 3

Performance analysis for three diagnostic cases of spine DXA BMD maps

	Index	Normal Case		Osteopenia Case		Osteoporosis Case
		Original	Denoised	Original	Denoised	Original	Denoised
ROI₁	MSR	10.91	11.30	10.33	10.87	16.75	18.35
	SNR	18.79	19.77	14.94	16.10	17.03	18.28
	CNR	35.74	37.75	27.89	30.26	31.74	34.25
ROI₂	MSR	8.18	8.51	10.43	10.93	17.19	18.93
	SNR	17.05	18.32	9.28	10.02	18.21	19.65
	CNR	34.01	35.97	17.49	19.05	31.88	34.65
ROI₃	MSR	11.50	12.00	10.43	11.06	15.81	17.44
	SNR	17.37	18.73	12.89	13.97	16.49	17.89
	CNR	35.02	37.08	23.71	25.96	29.38	31.96
	SSIM	90.03		92.80		89.18
	Beta	87.16		89.59		85.65

For further evaluation of our proposed NLM technique on spine DXA images, three representative clinical cases including normal, osteopenia, and osteoporosis cases are investigated. Table 3 summarizes all of the performance metrics for each clinical case over the same positions of the three ROIs in the bone region to measure MSR and the other three ROIs in the background to estimate SNR and CNR. The results in Table 3 show the capability of NLM to enhance the spine DXA images locally by reducing the noise and preserving the edges. To show the effect of our proposed denoising technique on BMD, we compute BMD and T-score values for all clinical cases presented in Table 3. A T-score value is utilized to determine each diagnosis status, which is recorded in the ranges of T-score ≥ –1.0, –2.5 ≤ T-score < –1.0, and T-score < –2.5 for normal, osteopenia, and osteoporosis, respectively [27, 28]. The BMD and T-score values of the original and denoised BMD images for all clinical cases are summarized in Table 4. It should be noted that there are slight changes in BMD and T-score after denoising, but the statuses of diagnoses according to the modified T-score values remain the same.

Table 4

BMD and T-score values for three diagnostic cases of spine DXA images

ROI	Normal Case				Osteopenia Case				Osteoporosis Case
	Original		Denoised		Original		Denoised		Original		Denoised
	BMD	T-Score	BMD	T-Score	BMD	T-Score	BMD	T-Score	BMD	T- Score	BMD	T-Score
L1^*	0.983		0.954		0.936		0.902		0.587		0.553
L2	1.207	–0.4	1.192	–0.6	1.066	–1.1	1.019	–1.4	0.648	–3.0	0.602	–3.3
L3	1.330		1.311		1.123		1.127		0.671		0.624
L4	1.278		1.262		1.022		1.025		0.699		0.713

^*L1, L2, L3, and L4 are the regions of interest (ROIs) in the lumbar spine vertebrae, as shown in Fig. 7(a). BMD, bone mineral density.

3.4.2 Femur DXA images

Figure 8(a) and (b) show the original high and low energy femur DXA images, and Fig. 8(c) and (d) show the images denoised via NLM corresponding to Fig. 8(a) and (b), respectively. For the high energy images, the averaged improvement ratios of MSR, SNR, and CNR are 3.33%, 15.26%, and 2.11%, respectively. In contrast, the enhancements for the low energy images are increased by 7.80%, 13.55%, and 22.68% for MSR, SNR, and CNR, respectively. Table 5 summarizes all of the evaluation metrics for the original and denoised femur DXA images over three different ROIs. To examine the effects of the proposed NLM technique, the center-horizontal line profiles are plotted from both the original and denoised femur DXA images, as shown in Fig. 9. Similar to the spine results, NLM maintains the edges while smoothing the noise. From Tables 2 and 5, we observed that the improvements in SNR in the spine DXA images are higher compared with those of the femur images. This might due to the different attenuation effects in the femur and spine [28]. The improvements in SNR after denoising are due to the different noise models of the high and low energy images; therefore, different and independent denoising degrees are observed between the high and low energy images.

Fig.8

Real high and low energy femur DXA images: (a) and (b) represent the original pair of high and low energy images before denoising, while (c) and (d) are the same images after denoising.

Fig.9

Horizontal line profiles for the real femur high and low energy DXA images in Fig. 8. (a) The line profiles of original (dotted line) and denoised (solid line) high energy DXA images at the lines in Fig. 8, and (b) the line profiles of original and denoised low energy DXA images.

Table 5

Performance analysis for high and low energy femur DXA images

	Index	High Energy Image		Low Energy Image
		Original	Denoised	Original	Denoised
${ROI}_{1}^{*}$	MSR	74.32	77.71	43.67	47.79
	SNR	5.27	6.15	8.62	9.97
	CNR	28.55	29.05	28.55	36.14
ROI₂	MSR	60.71	62.21	40.03	42.81
	SNR	5.43	6.15	10.32	11.47
	CNR	28.92	29.79	29.35	34.98
ROI₃	MSR	60.74	62.53	55.01	58.87
	SNR	4.87	5.64	10.76	12.25
	CNR	27.87	28.31	28.02	34.26
	SSIM	95.20		91.40
	Beta	98.37		97.71

^*Each ROI_i involves two different ROIs: ROI_{o_i}, which is utilized for MSR, and ROI_{bg_i}, which is utilized to compute both SNR and CNR. All of these ROIs are superimposed on Fig. 8(a) for femur case. ROI, region of interest; MSR, mean-to-standard deviation ratio; SNR, signal-to-noise ratio; CNR, contrast-to-noise ratio.

The original BMD data compared to the denoised data are illustrated in Fig. 10(a) and (b), respectively, for a normal case. The edges of the denoised image seem to be preserved, as shown in the center-horizontal line profiles in Fig. 10(c) and as the Beta index of 88.54% indicates. Meanwhile, the image quality of the BMD map is increased by 93.44% in terms of SSIM. Table 6 includes the MSRs over three regions of bone and SNRs with CNRs over three ROIs in the background for three femur clinical cases, which represent normal, osteopenia, and osteoporosis statuses.

Fig.10

BMD maps for a real femur DXA image. (a) The original BMD map with the superimposed ROIs, (b) the BMD map from the denoised high and low energy images, and (c) the line profiles of the BMD maps from the original (dotted line) and the denoised (solid line) DXA images at the overlaid lines in (a) and (b).

Table 6

Performance analysis for each diagnostic case of femur BMD DXA images

	Index	Normal Case		Osteopenia Case		Osteoporosis Case
		Original	Denoised	Original	Denoised	Original	Denoised
ROI₁	MSR	38.48	42.47	50.20	57.77	43.71	51.96
	SNR	15.93	17.25	15.33	17.45	13.61	15.70
	CNR	29.60	32.31	28.25	32.65	27.86	33.04
ROI₂	MSR	39.25	42.89	41.03	44.98	40.85	44.65
	SNR	15.76	17.02	15.13	16.87	12.89	13.94
	CNR	28.74	31.20	28.41	31.82	28.02	30.81
ROI₃	MSR	42.63	47.73	48.76	54.55	59.12	64.89
	SNR	15.27	16.72	15.08	17.11	11.49	12.97
	CNR	28.73	31.43	27.99	32.01	27.21	31.56
	SSIM	93.44		94.56		92.83
	Beta	88.54		90.42		87.23

For all femur cases, slight changes in the BMD values are observed, as shown in Table 7. The proposed NLM improves the quality of DXA images, but the diagnosis status of each case remained the same with respect to the modified T-score values. Further investigations with more clinical cases are needed to examine the population effects of denoising.

Table 7

BMD and T-score values for each diagnostic case of femur BMD DXA images

ROI	Normal Case				Osteopenia Case				Osteoporosis Case
	Original		Denoised		Original		Denoised		Original		Denoised
	BMD	T-Score	BMD	T-Score	BMD	T-Score	BMD	T-Score	BMD	T-Score	BMD	T-Score
Neck	1.082		1.027		0.831		0.791		0.623		0.601
Ward	0.814	0.3	0.791	–0.1	0.588	–1.5	0.581	–1.8	0.417	–3.0	0.396	–3.1
GT	0.988		1.103		0.822		0.857		0.539		0.573

BMD, bone mineral density; ROI, region of interest; Neck, femoral neck; Ward, Ward’s region; GT, greater trochanter ROI in the femur, as shown in Fig. 10(a).

NLM has the capability to remove noise locally. Tables 2, 3, 5, and 6 present the effects of NLM in terms of the evaluation metrics over three different ROIs for real spine and femur DXA images. Regarding the results in Fig. 4, since the phantom should reflect homogeneous tissues or backgrounds, after NLM, the smoothed line profiles reflect noise-removed homogenous regions. The smoothed line profiles shown in Figs. 6, 7(c), 9, and 10(c) also reflect the effects of NLM. Thus, these center-line profiles for the human spine and femur seem to suppress only the noise ripples while preserving the fine details and edges. The proposed DXA image denoising technique outperforms those in the literature, as summarized in Table 8. In our proposed technique, we modeled noise and optimized NLM to denoise both high and low energy DXA images, which have different dynamic ranges of photon counts. Finally, we validate the proposed NLM against the conventional techniques such as median and anisotropic diffusion filters [14] using 14 clinical cases of spine and femur BMD DXA images. Figures 11 and 12 show the comparison results in terms of SSIM and Beta values for the spine and femur, respectively. From these figures, it is clear that NLM outperforms the conventional techniques by its capability to reduce the noise locally while preserving the edges and fine details of anatomical structures.

Fig.11

Comparison of the proposed NLM against conventional techniques in terms of (a) SSIM and (b) Beta for spine BMD DXA images.

Table 8

Comparison of our denoising technique for low energy DXA images with previously published results

Reference	Denoising Technique	Site of DXA Image	MSR (%)
J. Kwon et al. [9]	Wavelet Improved BayesShrink (IBS)	Forearm	3.77
	Logarithmic wavelet BayesShrink	Forearm	5.86
Proposed Technique	NLM	Spine	9.63
		Femur	7.80

Fig.12

Comparison of the proposed NLM against conventional techniques in terms of (a) SSIM and (b) Beta for femur BMD DXA images.

4 Conclusion

Due to the low X-ray doses used to generate dual high and low energy DXA images, DXA images tend to be noisy. Denoising could be an essential preprocessing step for image enhancement. Furthermore, improvement of the quality of both high and low energy DXA images could be useful for bone segmentation and bone detection. In our study, the effect of denoising did influence the BMD values, but the diagnostic decisions remained the same with the denoised images. In this paper, we present a technique for denoising both high and low energy DXA images via non-local mean filtering. We first presented the noise modeling of DXA images through the analysis of the noise characteristics of a DXA system. The experimental results utilizing the optimized NLM parameters demonstrated high performance to improve the quality of real DXA images, remove the noise, and preserve both the edges and fine details of the images.

Conflict of interest

All authors declare that they have no conflicts of interest regarding the publication of this paper.

Footnotes

Acknowledgments

This work was supported by the Center for Integrated Smart Sensors funded by the Ministry of Science, ICT & Future Planning as Global Frontier Project (CISS- 2011-0031863). This work was supported by International Collaborative Research and Development Programme (funded by the Ministry of Trade, Industry and Energy (MOTIE, Korea) (N0002252).

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