## 1 Introduction
Consequently, active research is being conducted to investigate the development of a noise-reduction algorithm that can feasibly address the issue [27]. Filter-based noise reduction is a well-established and commonly used approach for restoring low-dose CT images. Gaussian and median filters work in the same manner in all directions to suppress high-frequency components or align the surrounding pixel values to select a median value. This can provide effective noise reduction but can result in a loss of detail [28; 29]. Wiener filters perform optimal filtering based on the statistical characteristics of noise, such as the signal-to-noise ratio. The Wiener form is particularly effective when the specific type of noise in a CT image is known in advance. However, this can only be effectively applied to CT images when the characteristics of the noise are accurately known; if the noise model is inaccurate or variable, the filter performance may deteriorate, resulting in overly smoothed results [30; 31]. Anisotropic diffusion filters effectively remove internal noise while protecting the image boundaries. These filters suppress noise by considering the structural characteristics of the image and distinguish boundaries and flat areas using different diffusion coefficients [32; 33; 34]. However, when the diffusion coefficient value is set incorrectly, the edges of the image may be lost or excessively smoothed. Additionally, the implementation of these filters involves a particularly high computational complexity. The total variation (TV) filter removes noise efficaciously from an image while preserving the edge information. It uses a total-variance minimization algorithm to flatten the image while preserving sharp changes [35]. However, it has a long processing time and can produce blocky artifacts in flat areas of the image. In addition, significant detail in the image can be lost when the filter strength is incorrectly adjusted [36]. In contrast to the TV filter method, which works based on local information and therefore only uses information from a small neighborhood around a pixel to remove noise, the nonlocal-TV (NL-TV) filter is an extension of the TV filter that searches for similar patterns in a larger area of the image to remove noise, allowing for finer noise reduction and the preservation of detail based on a larger group of pixels that share the same structure or pattern [37; 38]. NL-TV filtering mitigates many of the problems associated with conventional TV filtering; however, the method requires further improvement. This filtering method works by searching for similar patterns in nonlocal regions, but its performance can vary depending on the image. This means that if the criteria for measuring similarity are inaccurate (e.g., differences between pixel patches and gradient information), the noise-reduction performance can be degraded, and unwanted blurring or loss of detail can occur [39]. [PERSON] et al. introduced an advanced NL means filter using an adaptive search window based on the gray-level differences in natural images [40]. They proposed a method that effectively removes noise by changing the search window for each pixel according to the texture characteristics of the image while maximizing the preservation of the edge and texture components. We propose a noise-reduction method based on an adaptive search window-based NL-TV filter for low-dose CT images and present the results and discussion of the method. A comparative evaluation of the proposed method for accurate image restoration in low-dose CT images compared with conventional TV and NL-TV was performed based on CT images acquired from a quantitative validation phantom.