1 Introduction

Recently, there has been an increase in studies on the early diagnosis of lesions owing to the importance of early treatment for a favorable prognosis [1, 2]. In particular, medical imaging devices and techniques, which can clearly acquire information of tissues and lesions using non-invasive methods, have shown rapid developments. Among the medical image acquisition devices, computed tomography (CT) is mainly used for early diagnosis because it can immediately and accurately describe the three-dimensional anatomical structure [3]. However, noise is necessarily generated in CT images owing to various physical characteristics, and photon deficiency is a representative factor of white Gaussian noise that degrades the image quality [4, 5]. The CT images degraded by noise distorts the patient information, thereby reducing the accuracy of diagnosis [6, 7].

To the most obvious resolution to improve noise generation due to photon deficiency is to increase the radiation dose. However, an excessive exposure of patients to radiation increases the probability of fatal diseases. Thus, hardware and software techniques were applied to solve the noise problem without considering the increase in radiation dose [8]. In particular, smoothening using filters in the software has various advantages, such as high versatility, simple optimization, and low cost compared to hardware development [9]. Although the filter-based smoothening effectively removes the noise, the application of filter is accompanied by a blurring effect caused by to the damage to high-frequency signals [10, 11]. To solve the problem of blurring effects, various filtering methods have been proposed to minimize the distortion of images necessary for diagnosis.

Among these techniques, the analytical-based filtering methods, such as total variation (TV), non-local means (NLM), wavelet transform, and deep learning, can selectively remove the noise by analyzing the characteristics of CT images by considering various parameters [12,13,14,15,16]. In contrast, complex computations are not suitable for CT scanners that acquire large amounts of axial images because they require considerable operation time for image processing and are difficult to optimize.

However, local filters are based on the principle of estimating pixel values by referring to values within a specific area. In addition, only the kernel size is required as a parameter, thereby has the advantage of quick applicability. The median filter, which is a non-linear spatial local filter using a median value of the pixel signals inside the kernel, can effectively reduce the noise [17, 18]. In addition, the Wiener filter is an adaptive local filter that controls the blurring effect by changing the smoothening strength by considering for the standard deviation [19, 20]. The median-modified Wiener filter (MMWF) has been proposed to remove the noise and preserve the high-frequency signal by applying the median value based on Wiener filter [21]. However, the blurring effect caused by simple operations, which is an inherent limitation of local filters, has not been completely solved.

To solve this problem, a segmentation technique, that can increase the accuracy of medical image analysis, such as CT images, and obtain information regarding tissue boundaries, can be in addition considered as a pre-processing method. Segmentation techniques have been proven for CT images to accurately analyze various anatomical structures and lesions, including liver, lungs, and teeth. Segmentation techniques can be classified into automatic and passive methods. Automated techniques have the advantage rapid processing but at the expense of precision and reproducibility [22, 23]. The passive technique is more accurate than the automatic technique; however, it is time-consuming, and finding the proper seed point is difficult in CT images [24]. In addition, the passive technique has the disadvantage of low reproducibility because the result changes depending on the skill of the user [25]. Thus, a semi-automatic region-growing (RG) technique, which automatically divides the regions after manually setting the seed points, was used as a pre-processing method in this study. The RG technique can selectively segment for the same tissue signals by only retaining the neighboring pixels that satisfy specific conditions based on the pixel value of a seed point [26, 27]. This implies that the RG technique can detect the boundary signals of a specific tissue and has potential applications to solve the problem of blurring effects caused by local filters.

Therefore, in this study, we proposed the improved MMWF with RG based pre-processing technique to solve the problems of noise and blurring effect in CT images.

2 Materials and methods

2.1 Acquisition of CT image for abdominal phantom

The CT images for whole-body phantom PBU-50 (Kyoto Kagaku, Japan) were obtained under condition a tube voltage of 100 kVp, a rotation time of 0.5 s, a slice thickness of 3 mm, and tube current-exposure time of 50, 100, 200, and 300 mAs using DECT scanner (SOMATOM Definition AS + , Siemens Healthcare, Germany). The CT images of the whole-body phantom were acquired in 54 slices at each mAs condition. Among them, local filters were applied for the 20th slice CT images that the liver, tissue, and spine were clearly depicted. Figure 1 shows an abdominal CT image with regions of interest (ROIs) for the quantitative evaluation of the liver (yellow box) and tissue (blue box). In addition, magnified images of the white box area in Fig. 1 were obtained for visual qualitative evaluation. To evaluate the high-frequency signal preservation performance, the intensity profile was measured corresponding to the black line in Fig. 1.

Fig. 1
figure 1

CT image of anthropomorphic abdominal phantom with ROIs for quantitative evaluation

Full size image

2.2 Median modified Wiener filter (MMWF) modeling

Although the conventional local filters have shown a high noise reduction performance, the loss of high-frequency signals is inevitable. To solve this problem, the MMWF has been proposed as a fusion of the median and Wiener filters, which have the advantages of noise reduction and edge signal preservation, respectively. The MMWF is based on the Wiener filter as shown in Eq. (1), where the mean value is replaced with the median value.

$${g}_{wie}(n)= \mu +\frac{{\sigma }^{2}-{\nu }^{2}}{{\sigma }^{2}}(f\left(n\right)-\mu )$$
$${g}_{mmwf}(n)= \overline{\mu }+\frac{{\sigma }^{2}-{\nu }^{2}}{{\sigma }^{2}}(f\left(n\right)-\overline{\mu })$$
(1)

where \(f\) represents the degraded CT image, and \({g}_{wie}\) and \({g}_{mmwf}\) represent the filtered images with Wiener filter and MMWF, respectively. In addition, \(\mu\) and \(\overline{\mu }\) denote the mean and median values of the pixels inside the kernel, and \(\sigma\) and \(\nu\) denote standard deviation of pixels and noise, respectively. Based on Eq. (1), herein, the MMWF was modeled using the MATLAB software (ver. 2022b), and the kernel size was set to 7 \(\times\) 7.

2.3 Pre-processing methods for improved MMWF

Beginning with an initially set seed point, the RG technique calculates the difference between the values of specific and neighbor pixels. When the difference value between the two pixels satisfies a specified condition (threshold value = \(\Delta\)) set by the user, the corresponding pixel is selected. Subsequently, the same operation is repeated on the selected pixels until all the targeted tissues are selected as follows:

$${g}_{seg}= \left\{\begin{array}{c}Selection, if\left|f\left(n\right)- \mu \right|\le \Delta \\ Non-selection, Otherwise \end{array}.\right.$$
(2)

The liver was segmented by applying the RG technique for CT images affected by noise before filtering, and the threshold value was set to 80, which was empirically shown to achieve the best results. In addition, morphology operation and internal filling methods were applied as additional pre-processing methods for improved MMWF to include edge and lumen signals that were not selected due to strong noise. Eventually, the improved MMWF was deionized using the following process:

  1. 1.

    Pre-processing algorithms were used to segment all anatomical structures and regions (e.g., tissue, bone, and air in Fig. 1, including the liver).

  2. 2.

    The padding was performed with the mean signal of each tissue, considering the mask size of the local filters.

  3. 3.

    MMWF was applied for each segmented anatomical structure and region.

  4. 4.

    The signals from all filtered structures and regions were assigned in the original coordinates from a new window.

2.4 Quantitative evaluation

To quantitatively evaluate the performance of noise reduction for improved MMWF, the coefficient of variation (COV) and contrast-to-noise ratio (CNR) were calculated as follows:

$${\text{COV}}= \frac{{\sigma }_{A}}{\mu },$$
(3)
$${\text{CNR}}= \frac{\left|{S}_{A}-{S}_{B}\right|}{\sqrt{{{\sigma }^{2}}_{A} + {{\sigma }^{2}}_{B}}},$$
(4)

where, \({S}_{A}\) and \({\sigma }_{A}\) denote the average signal intensity and standard deviation of the ROI 1 (yellow box), and \({S}_{B}\) and \({\sigma }_{B}\) denote the average signal intensity and standard deviation of the ROI 2 (blue box) in Fig. 1, respectively. In addition, the intensity profiles were measured and tended to assess the signal differences, fluctuations, and edge signal preservation performance between the two tissues.

3 Results

Figure 2 shows the magnified CT images of the white box shown in Fig. 1, to which no-algorithm (noisy), MMWF, and improved MMWF are applied under conditions of various tube currents. Visually, the noise is effectively removed from the CT images with MMWF and improved MMWF compared with noisy images. The improved MMWF shows a similar noise reduction and better boundary information preservation compared with MMWF.

Fig. 2
figure 2

Enlarged image of the edge signal between the liver and normal tissue of an abdominal CT image with noisy, MMWF, and improved MMWF

Full size image

To quantitatively analyze the results of the visual evaluation, the COV and CNR were measured (Fig. 3). The COV values of MMWF and improved MMWF were measured for CT images under various tube current conditions. As shown in Fig. 3a, the measured COV values of noisy, MMWF, and improved MMWF are 0.062, 0.024, and 0.024, respectively, for the CT image at 50 mAs of tube current. In addition, the COV value of both MMWF and improved MMWF is 0.012 for the CT image at 300 mAs of tube current; this is approximately 3.42 times better than the noisy image.

Fig. 3
figure 3

Results of a the coefficient of variation (COV) and b contrast-to-noise ratio (CNR) for filtered anthropomorphic abdominal of noisy image, MMWF, and improved MMWF

Full size image

As shown in Fig. 3b, the CNR results are similar to the COV results; MMWF and improved MMWF are superior to noisy in CT images for all tube current conditions. The measured CNR values of noisy, MMWF, and improved MMWF are 7.79, 21.79, and 21.79, respectively, for the CT image at 50 mAs of tube current. In addition, the CNR value of both MMWF and improved MMWF is 37.67 for the CT image at 300 mAs of tube current; this is approximately 3.51 times better than the noisy image.

Figure 4 shows the intensity profiles of noisy, MMWF, and improved MMWF images according to 50, 100, 200, and 300 mAs tube currents. Boxes A and B in Fig. 4a show the signal of liver and normal tissue, respectively. Box C shows the boundary signal between liver and normal tissue. Considering the boxes A and B, the noisy images show large signal fluctuations in the same tissues. This implies that noise has a significant negative impact on the CT images. In contrast, MMWF and improved MMWF show almost constant signal fluctuations owing to the smoothening. In addition, box C shows that the boundary signal between liver and tissue changes most sharply in the improved MMWF. In contrast, the MMWF and noisy images show a rounded change of edge signals.

Fig. 4
figure 4

Intensity profiles of filtered CT images with noisy, MMWF, and improved MMWF under tube current conditions of a 50, b 100, c 200, and d 300 mAs

Full size image

4 Discussion

To improve the accuracy of diagnosis, noise reduction is an essential objective of most medical imaging techniques. Filters and algorithms for noise reduction have been actively proposed because they can solve the problems of excessive exposure and high cost [28]. Among them, the local filter is a simple and classic method that exhibits a strong noise reduction with an excellent computation image efficiency. However, it produces blurring effects, which can significantly degrade the image characteristics, owing to limited pixel data and excessive smoothening [29]. Thus, the overall image restoration performance considering various image characteristics may be inferior to relatively newer techniques, such as TV, NLM, wavelet transform, and deep learning.

The TV is a typical iterative reconstruction technique that uses repetitive computation to find the optimal solution [30]. Although, TV shows a high performance of image restoration through precise computation, it is extremely time-consuming and expensive [31]. The NLM, which applies the distance-weight method for regions similar to the kernel signal inside the search window, can overcome the disadvantage of referencing only the limited data of the local filter [32]. However, the image processing time for NLM is long because the distance-weight should be calculated based on the data in a wide area [33,34,35]. The wavelet transform performs image processing in the time–frequency domain and can efficiently remove the noise based on the high resolution of time and frequency [36]. To improve the performance of wavelet transform, numerous parameters and formulas need to be understood [37]. This implies that only experts with relevant knowledge can use the optimized wavelet transform. In addition, deep learning-based denoising methods require large amounts of data to produce acceptable performance [38]. However, for the common user, patient data is not easily accessible due to ethical considerations. Furthermore, the output data generated by deep learning may contain false information, thereby limiting the application in clinical fields [39].

Overall, various noise reduction techniques for medical imaging have been proposed, and most of them have been shown to replace the local filters. However, the proposed techniques have limitations in computation time, optimization, and accessibility owing to the reference of several parameters and data. These limitations are unsuitable for CT imaging, which requires processing of large amounts of data in a limited amount of time and flexibility in anatomical structures and examination conditions. Thus, in this study, we applied a local filter, which solves the blurring effect problem, to consider the characteristics of CT imaging.

Although various approaches, such as formula transformation and fusion of local filters as with MMWF, have been developed, the problem of blurring effect has not been completely solved. RG can be used to detect edge signals from each segmented tissue. The lumen signal can be accurately smoothened because the segmented images based on the detection of edge signal provide only the same tissue signal to the local filter. Thus, we proposed an improved MMWF with the RG method, which was applied as a pre-processing algorithm.

The COV and CNR were calculated to evaluate the performance of improved MMWF (Fig. 3). The COV and CNR values of MMWF and improved MMWF were the same because smoothening was performed by calculating the same formula in CT images with various tube currents. Compared with the noisy image, MMWF and improved MMWF showed COV improvements of approximately 2.57, 4.46, 3.26, and 3.42 times, and CNR improvements approximately 2.80, 3.55, 3.43, and 3.51 times, in CT images at tube currents of 50, 100, 200, and 300 mAs, respectively. These results indicate that MMWF and improved MMWF can provide effective image restoration for low-dose CT images with sparse and inaccurate data, including high-dose CT images.

Figure 4 shows the intensity profile for edge signal analysis of filtered CT images. The signal intensity results of the improved MMWF shows that two different tissues can be clearly segmented. For the improved MMWF, the shape of the graph is similar for all tube currents. The similarity of the shape of the graph between low and high doses implies that when acquiring CT images, a boundary signal similar to the case of using high dose can be obtained even for low-dose images. In box C of the intensity profile, the noisy images show more distinct boundary compared with the MMWF images. This implies that the edge signal is inevitably damaged even after the application of the local filter for maintaining the edge signal. The COV, CNR, and intensity profile results confirmed that the improved MMWF with RG method removed the noise and showed accurate edge signals compared with the noisy images.

Moreover, to analyze the usefulness of improved MMWF under low-dose conditions, a quantitative comparative evaluation was performed using various noise reduction techniques for a CT image at a tube current of 50 mAs. Figure 5 shows the filtered CT images using improved MMWF, median filter, NLM, TV, and Wiener filter including noisy image. Figure 6a and b show the COV and CNR values, respectively, of the improved MMWF and various noise reduction techniques. The performance of the improved MMWF is similar or slightly worse compared with local filters, such as median and Wiener filters. The reason is that the MMWF is modeled more for edge signal preservation than for noise reduction performance [40, 41]. In addition, NLM has a valid performance difference because complex computations based on massive amounts of data are used to simulate filtered CT images [42]. However, the performance difference in the noise reduction of improved MMWF can be overcome by the increase in kernel size. Conversely, the edge signal preservation performance is improved compared with TV and NLM techniques, which have a large difference of computation time and amount of data, including local filters. The intensity profile of the Wiener filter shows the typical limitation of local filters that leads to a significant loss of edge signals despite a higher noise reduction.

Fig. 5
figure 5

Magnified CT images with various noise reduction techniques: a Noisy, b median, c Wiener filter, d TV, e NLM, and f improved MMWF

Full size image
Fig. 6
figure 6

Results of a COV, b CNR, and c intensity profiles for filtered CT images with noisy, median filter, Wiener filter, TV, NLM, and improved MMWF

Full size image

Compared with TV, NLM, and several local filters, the improved MMWF has a lower noise reduction performance, although it can prevent the blurring effect. However, the results in Fig. 4 show that the edge signal is maintained even when computing with limited data, regardless of the tube current or radiation dose. These results prove that the improved MMWF has no adverse effect on the edge signal, although the smoothening strength is set higher compared with other local filters and noise reduction techniques to improve the noise reduction performance. Thus, this study confirms that the improved MMWF is a suitable method for application in CT imaging. However, further studies should be conducted for optimization of the kernel size according to the purpose of CT imaging, and evaluation of the difference in computation time between TV and NLM to more clearly propose the feasibility of the improved MMWF.

5 Conclusion

In this study, an improved MMWF with the RG technique as a pre-processing method was proposed to reduce the noise and blurring effects at the edge signal. The calculated COV, CNR, and intensity profile showed that the improved MMWF had a high performance compared with the noisy and MMWF images. In addition, a comparative evaluation with various noise reduction techniques confirmed the advantages and potential of the improved MMWF. In conclusion, the improved MMWF for CT images demonstrated the noise reduction performance of local filters and the feasibility to resolve the blurring effect with only a limited computation time.