**1. Introduction**

Bone disease exploration is assured by a variety of modalities of medical imaging. Bone mineral density is determined by standard scanners and x-rays. Although this technique delineates the bone structure, it remains an invasive method with qualitative information on bone structures. Ultrasound computed tomography (USCT) is the best to give us more details and a very interesting procedure for bone imaging associated with signal and image processing methods [1, 2]. A variety of medical imaging techniques such as x-rays and standard scanners determine bone mineral density.

However, these modalities represent an ionizing method without giving quantitative results. USCT hardware has been propounded to solve this issue [1, 2]. USCT presents an important radiological technique because of its non-ionizing properties. However, it has been the subject of several studies due to the complexity of its visualization and the noisy USCT image quality [3]. In the light of this issue, noise reduction should be the first step to be interested in, to enhance the USCT image resolution and to detect bone diagnosis. Hence, many researchers have studied different techniques for ultrasound image noise reduction, and obtained results achieved the terms of quality improvement (37.14 dB of peak signal-to-noise ratio [PSNR]) [3]. But, these methods cannot be applied to USCT bone images due to its complexity. Actually, USCT bone imaging is a very difficult method that encounters many problems mainly related to high bone echogenicity. Noise reduction is one of the crucial topics in digital image processing and has been conducted in various fields such as ultrasound imaging [4]. Many obstacles still exist, but several results have been successful [5, 6]. Accordingly, we will try here to propose optimizations for image processing by implementing discrete Haar wavelet algorithm and a proposed hybrid algorithm combining k-means with the Otsu method. It is an important process for removing noise, as it produces promising results in terms of image resolution, noise removal and diagnosis detection. In this work, our objective aims to automatically remove noise levels generated during the rebound of ultrasonic waves against bony structures, from USCT images, improving the PSNR.

In this chapter, we divide the work into seven sections: Section 2 presents an overview of the medical history in this area, some physical considerations and the description of existing algorithms. Section 3 presents fundamental mathematical theorems that will be implemented in the next section. Section 4 describes the proposed hardware and software method to segment USCT. Section 5 shows the obtained results, the comparison of our work with previous work and the discussions. Section 6 concludes this chapter.

### **2. State of the art**

In 2019, a Ram-Lak filter is implemented in the Radon domain to reduce the noise levels in the USCT images and facilitate their observation giving a PSNR with a value of 13.07 [3]. In 2018, different filters such as median and a high pass filter have been used to reduce noise in Magnetic Resonance Imaging (MRI) images as a preprocessing step and the first results are promising [7]. In addition, bilateral filter and trilateral filter are used for noise removal in [8] by considering the small structure as noise to be removed and conserving the large structure. Moreover, in [9] adaptive filter of Kuan, Frost or maximum medium median (MMM) have been produced to enhance ultrasound images resolution giving promising results. However, these methods fail to give encouraging results when applied to USCT images [3, 9].

The Fourier transform with its decomposition of a trigonometric series has been widely introduced in the field of signal processing as well as in medical image processing, but it is insufficient for giving a piece of complete information in both time and frequency areas simultaneously. Indeed, using the classical Born approximation and the spatial Fourier transform, the result is a poor contrast-to-noise ratio (CNR) image. Some previous work to improve the CNR has been introduced while handling signal and image processing [2, 5]. Although image analysis is an important process for noise removal, it cannot produce the intended result in some digital image processing [4]. Actually, a flow of image processing should be applied to improve the USCT *Automatic Noise Reduction in Ultrasonic Computed Tomography Image for Adult Bone Fracture… DOI: http://dx.doi.org/10.5772/intechopen.101714*

image quality and to achieve automatic diagnosis detection. The active contour method was introduced in the process of USCT image segmentation. Its use avoided the issue of noise in USCT images [10]. In [11], authors appended this algorithm on USCT paired-bone images. However, the results were not good enough and the detection of the distances between the two bone forms (tibia and fibula) was not possible.

The method, called the "Wavelet-based Coded Excitation" (WCE) method [5] is based on the wavelet decomposition of the signal and on a suitable transmitted incident wave correlated with the experimental set-up. Indeed, the contrast with reports of noise was improved, but the detection of edges and areas of child-matched bone by ultrasound with USCT was impossible [5, 11]. However, this method has remained very interesting. During the last two decades, a lot of research has involved the use of the transformed wavelet for removing noise through its energy compaction and its multiresolution parameter proprieties [12, 13]. Thanks to these parameters, we can obtain different versions (dilated or compressed, and translated or shifted) from the same mother wavelet.

The k-means algorithm is known for its simplicity in clustering a database into clusters. Nevertheless, this number of clusters has to be identified. It has been used for resolving the issue of data clustering. k-means followed by fuzzy c-means were introduced by Alan Jose et al. in [14, 15] to detect a brain tumor, and the result of the segmented image remained for the feature extraction and the image resolution was improved. Image segmentation using the k-means algorithm is a process of separating images into different regions with high resolution. The purpose of such segmentation is the detection of regions of interest simultaneously with noise removal in an image. Moreover, image segmentation has been an increasingly expanded issue especially in the area of medical imaging and more specifically in USCT considering the inhomogeneity of pixels and complex anatomical topology [6].

Otsu method has been used for a long time to medical image analysis for image resolution enhancement [16] obtaining the right diagnostic. In [7], a proposed Otsu method has been used for MRI images for tumor brain detection.

### **3. Mathematical theoretical**

#### **3.1 Wavelet transform**

The wavelet transform is a mathematical function that allows image compression and signal processing. It resolves the problem of the Fourier analyses. It is defined by the following equation:

$$
\Psi'(a,b) = \frac{1}{\sqrt{\mathbf{a}}} \Psi \left( t - \frac{\mathbf{b}}{\mathbf{a}} \right) \tag{1}
$$

where *a* is the scale parameter or the expansion factor, and *b* is the translation or proposition parameter. The bigger *a* is, the more the wavelet is dilated.

#### *3.1.1 Principle of wavelet transform*

The wavelet transform is a multiresolution analysis tool able to transfer accurate temporal and spatial information. In the literature, various noise reduction techniques concerning wavelet approaches have been put forward [14]. From an original image, low frequencies are analyzed by the application of a low-pass filter. Then, high

frequencies are analyzed by the application of a high-pass filter. It allows dividing the information of the image in an approximation and detail as depicted in **Figure 1**. We will use the Haar wavelet to keep the edge detection of an image as follows:


$$YH[k] = \sum\_{n} \mathfrak{x}[n] \, G[2k - n] \tag{2}$$

$$Yl[k] = \sum\_{n} \mathfrak{x}[n]H[2k - n] \tag{3}$$
