Early diagnosis of skin cancer by ultrasound frequency analysis

Abstract The diagnosis of cancer by modern computer tools, at the very first stages of the incident, is a very important issue that has involved many researchers. In the meantime, skin cancer is a great deal of research because many people are involved with it. The purpose of this paper is to introduce an innovative method based on tissue frequency analyzes to obtain the accurate and real‐time evaluation of skin cancers. According to the Biological resonance theory, body cells have natural and unique frequencies based on their biological fluctuations, which, if the structure, profile and cellular status change, its frequency also varies. This concept and theory is considered as the basis for analyzing skin tissue health in the proposed method. Reflected ultrasound waves from tissue have been processed and studied based on frequency analysis as a new method for early detection and diagnosis of accurate location and type of skin diseases. The developed algorithm was approved through 400 patients from CRED; its ability to evaluate benign and malignant skin lesions was shown (AUC = 0.959), with comparable clinical precision; as for the selected threshold, sensitivity, and specificity were 93.8% and 97.3%, respectively. Therefore, this method can detect skin malignancy with an accurate, noninvasive and real‐time procedure.


| INTRODUCTION
Currently detection of the malignancy of skin lesions, is doing by dermatologists based on their professional experience using the pathologic results from the skin biopsy of the suspicious area; and in some cases, meanwhile the skin biopsy of the suspected area, they also recommend the sonography imaging in order to inspect the skin tissue better and in more details. 1 Sonography is a noninvasive method by which radiologists try to capture unusual symptoms in the skin sonograms. 2 Due to the complication of sonograms in appearance, the diagnosis of malignant skin depends on the self-experience of the dermatologist. This means that in most cases, the early symptoms of malignant lesions seems to be normal, and ignored. 2 This causes the many false detection. Since these errors are always hazardous, there is significant interest in developing intelligent methods for detecting these abnormalities as a useful tool for dermatologists to accelerate the detection and prevention of unnecessary skin biopsy. 3 The aim of this research is developing an intelligent diagnosis method for diagnosing malignant skin lesions, but the distinction between this work and previous researches is the new perspective on processing the sonograms based on frequency analyzes. that everything in universe is a compressed energy and that each emits its own unique electromagnetic frequency. This means that all substance and therefore all cells, parts of body, etc. emit electromagnetic waves. Depending on their nature, all substances have a unique wavelength or frequency with highly individual characteristics. This is known as a frequency pattern. 4 Thus any exchange of body nature oscillations that take place between the various cells in the body, can lead to detect an abnormality in that part of body. 4 The main issue raised in this research is the use of the above concept to carry out the diagnostic process. In fact, both benign and malignant cells of skin are alive and have their natural oscillations that indicate their mode of life; based on research, the effect of nature oscillation frequency attend in ultrasonic echoes received from one part of the skin tissue, so they can be extracted and identified by using frequency processing and applied to classify these cells.
Two major tools utilized in this research are discrete cosine transform (DCT) and Otsu's thresholding method. DCT transform as the frequency analyzer and Otsu's method as the thresholder for distinguishing healthy and suspicious tissues from each other in a single sonogram. Both are widely used in biomedical image processing. DCT transform is used for different applications such as water marking, 18,19 compression, 20,21 and classification. 22,23 For example, Gutta and Cheng in their work used DCT of an autocorrelation function for biometric recognition using ECG signals. 37 38 These researches support the idea that cosine transform is promising as a feature. Otsu's method is also used for different purposes including thresholding 29,30 and segmentation. 31 For instance, Lahmiri in his work 39 has tried to outperform Otsu's method by improved variants of particle swarm optimization (PSO) algorithms in segmentation of biomedical images, namely brain, breast and prostate tissues. This shows the stability of this method and its promising results, although it could be replaced by more improved methods. Moreover, George in their work 40 has used Otsu's method as a means for elimination of false-positive (FP) findings (noisy circles and blood cells) in the cytological images of breast cancer. Using Otsu's thresholding, c-means clustering technique and different topologies of neural networks, they have developed a remote computer-aided breast cancer diagnosis system with a challenging performance.
According to the above, in brief, the conceptual principles of the study, the methods, and the results are described in this paper. Following the introduction to the first part, Part 1 examines background, Section 2 describes the methods of research, and in Section 3 the two algorithms proposed in this research are presented. Finally, in Section 4, the discussion and conclusion of the proposed methods are described.

| BACKGROUND
Skin, the body's first defense system against invasive pathogens, is the largest and most prolific organism and has more than 16% of the body weight. Because of its importance, research on skin structure and its functionality has been so extensive that their achievements in the last decade are greater than those found over the last two centuries. 5

2.A | Skin cancer
Skin cancer is one of the most common cancers in the world. In fact, the number of skin cancers in the world that is diagnosed every year is more than the number of all other cancers. The number of cases of skin cancer has increased significantly over the last few decades. 6 Depending on the type of cells eroded, there are several types of skin cancer that have certain symptoms. The most common types of skin cancer in the ascending order of harmful effects include basal cell carcinoma (BCC), squamous cell carcinoma (SCC), and melanoma. 2

2.B | Current diagnosis methods
Until now, diagnosing of skin diseases has been performed by the specialist physician's self-experience and results of pathological tests; meaning that in most cases, if the specialist figures out any sign of disease, the patient is directed to pathology laboratory to do skin biopsy. To increase diagnosing accuracy, some specialists prescribe imaging as well as biopsy process. As we know anatomically, skin is classified as soft tissues, so an appropriate imaging method is needed. 2 Among all of the image acquisition methods, sonography is one of the appropriate methods. With the ability of feature extraction of skin tissues, it can not only separate the lesions from the healthy parts but also specification detection of the lesion is noticeable. 2 The common frequency range for skin sonography is 20-100 MHz. There are two parameters for determining the range of frequency in ultrasound waves in sonography imaging system. First the depth of examining part of skin and second the desired resolution. 2 Figure 1 shows the sample two-dimensional (2D) sonogram of a normal skin with 14 × 7 mm dimensions. The length of the mentioned image shows the motion of the probe along the surface of the skin, and the width of the image shows the depth of the texture. 7 In the normal skin epidermis, dermis and hypodermis sections are approximately alike and monotonous. 8 Because of the fat existence in these layers, these normal parts of skin seem brightly. On the other hand, the structure of malignant skin lesions with angiogenesis texture 9 is not homogeneous; therefore, depending on the skin layer in which the lesion is located, there is a dark gap screened in the sonogram. These lesions have little ultrasonic echoes therefore they generally appear in dark colors in the sonograms (Fig. 2). 2

2.C | The effect of tissue changes on sonograms frequency pattern
The main feature of this research is described in this section, which is the main difference with other related studies in this area. Here is focused on analyzing the frequency of the image that shows the structure of the skin tissue. Depending on the concept of biological resonance, corrupted body cells emit certain energy wavelengths that can be investigated. 10 This theory states that each cell in the body has a specific frequency based on the current biological status. In another perspective, this idea can be considered correctly as the concept behind the strings 11 in the so-called M-theory 12 or the energy of the particle photon E with its associated ν frequency in the Planck-Einstein relation (Eq. 1).
where E = energy of the photon, h = Planck's constant, and ν stands for frequency.
It can also be deduced from this concept that cells in the body produce a certain frequency in the event of a disorder. Accordingly, and based on numerous studies in this field, it should be noted that so far no research has been done to analyze the effect of resonance. In other words, in this research the mechanical response of skin tissue analyzes to find a main feature for diagnosing the skin condition.
In this paper, the cells of the body are exposed to ultrasonic pulses. Since the wave length of these mechanical pulses is much smaller than the normal wavelength of the cells, therefore it can be considered relatively as an impulse in cells. Dirac delta input is a useful method to analyze systems' dynamics is the impulse response or the response of a system in control theory and signal processing.
The dynamic system and its impulse response may be actual physical objects. 13 The cells have an impulse as the input, thus stimulated to intensify their natural frequency; and this frequency will be in the content of each sample scan, by ultrasound device in this case, at that time. [14][15][16] The sonography probe sends ultrasound waves and records the

| ME TH ODOLOGY
In the next sections, two algorithms are designed to perform the diagnosis procedure. But before discussing the algorithms we first need to enlighten some topics about our sonogram dataset, their format (RF and B-Mode) and the transform we are using to take the sonograms into the frequency space.

3.A | Preparing dataset
Since the main objective of this study is to distinguish malignant skin lesions from benign, the analysis of the tissue requires a large amount of data, so that access to more information increases the accuracy  Table 1.
This vast database includes different types of skin lesions, such as melanomas, basal cell carcinomas, squamous cell carcinomas, actinic keratosis, atypical nevi, benign melanocytic nevi, blue nevi, and seborrheic keratosis. Of the 400 ultrasound samples used in this study, 220 cases are malignant, and the remaining lesions are benign.
All of these samples were examined with pathologic results that were performed after scanning.

3.B | Preprocessing
The ultrasound scanner records data scans along with the patient's metadata in the binary file. The most important metadata in this study, other than image size, was the frequency of transducer. All samples of the ultrasound wave database are at a frequency of 50 MHz.  image. The goal is to enhance the quality of the images in order to be analyzed. Because the analysis and processing of images in the RF mode are hard and not precise. We use Eq. (2) to compute the B-Image from the RF data: where offset would be a constant integer that the device uses in order to easily have all the recorded values as unsigned integers. However, this is not visually familiar, so a custom color scheme has been applied to it, the result of which is shown in Fig. 3(c).

3.C | Frequency analysis
To frequency analysis of ultrasound imaging data from skin texture, the data must be transmitted to the frequency space. The most common frequency conversions used in image processing are fast fourier transform (FFT) and discrete cosine transforms (DCT).
A DCT shows a set of finite sequence of data points as complete cosine functions at different frequencies. These transformations are widely used in image processing. From compression, the loss of audio data, such as MP3s and images such as JPEGs, can be removed by small particles with high frequencies, to spectral methods for numerical solutions of the differential equation with partial derivatives in the range of DCTs.
Since less cosine functions are needed to approximate an ordinary signal (relative to sinusoidal functions), using the cosine function instead of sinus is necessary in compression. Also, in the case of differential functions, cosine functions have more specific boundary conditions.
Mainly, DCT is used for those processes in which low-frequency content (such as nature frequencies of the body), should be considered. Nevertheless, the discrete fourier transform (DFT) offers a better means or intentions for spectral analysis, and the maps draw those results to very simple physical frequencies. 17 The great advantage of DCT calculation is that it contains the required frequencies based on the size of the image, and the calculations will be meaningful and, accordingly, the DCT is chosen for this study. Mathematical expressions of DCT calculations of an M-by-N matrix "A" are presented in Eqs. (2), (3), and (4).
where B pq are called the DCT coefficient of "A".
DCT transform is widely used in biomedical image processing for different applications such as water marking, 18,19 compression, 20,21 and classification. 22

4.A | Sonogram classification
The first diagnosis method is used to classify the sonogram based on a frequency transform of the whole image. We also have compared this method to our previous work on the same dataset in terms of diagnosis quality and computation complexity and speed. The flowchart of the classification procedure is shown in Fig. 4. Each step is explained as following.

4.A.1 | Convert RF Image to B-Mode
As mentioned before, first and foremost we need to do some preprocessing in order to build the B-Mode image from the RF data.
This is a critical step in the procedure since it is much easier to analyze the B-Mode image than the raw RF input. This is a great way to find the lesions or infected parts of skin in the image. By measuring the amplitude and frequency, the size of the affected parts can also be calculated.

4.A.3 | Find Eigen values using SVD
When we calculate the DCT for the whole sonogram, we have a 2D matrix with the same dimensions of the original sonogram. We can use this image as the input vector for a deep network which is F I G . 4. Procedure scheme for sonogram classification.
widely used nowadays, however, the computational resources for the deep-learning approaches is much high and it would be better to avoid using them in case we can find a better solution. The dimension reduction algorithms such as principal component analysis (PCA) offer us a way to reduce the feature map size to a more affordable and concentrated values that have more eclectic covariance. A very powerful tool is singular value decomposition (SVD). SVD is a factorization of a real or complex matrix. It is the generalization of the Eigen decomposition of a positive semidefinite normal matrix to any matrix via an extension of the polar decomposition. SVD is extensively used in biomedical image processing algorithms as image compressor or feature extractor and so on. 24,25 In this research, we apply an economy-size SVD as following equation: A sample plot of the eigenvalues is shown in Fig. 6. We can see that the first eigenvalues have more energy than the other, but since in biomedical image processing, the high energy parts are mostly alike in different images and the differences lies within the low energy values, we keep all the values as the feature map for classification.    This also enforces the idea of bioresonance theory presented in this research. Figure 9 shows the ROC curve of the classifier presenting the good diagnosing result. Figure 10 shows the confusion matrix and Table 2 presents the percentages values (represents the percentage of false negatives, false positives, true positives, and true negatives) for the proposed algorithm. Figure 11 shows the ROC curve of the proposed algorithm in Ref. [ 2 ] and Table 3 and Fig. 12 show the confusion values. From these evidences we can see the improvements of the new classification based on frequency features

4.C | Sonogram semantic segmentation
The second method is used for sematic segmentation of the sonogram in order to differentiate the healthy parts from the suspected parts. The flowchart of this method is presented in Fig. 13 and the algorithm is described below.

4.C.1 | Dividing sonogram into blocks
The first step is to split the image. On one hand, the image frequency is a cumulative concept, and there is no frequency value for a single pixel; on the other hand, if the frequency transform is applied to the whole image, there will be a common frequency result in all scanned sectors. To be more specific, we can divide the image into blocks, and apply the frequency transform to each, and eventually reconstruct the image using the resulting blocks. An important consideration here is the dimensions of each block.
If the frequency conversion is applied to the entire image, the result of the diagnosis is obtained, but if the process is performed for each block, it can be determined which part of the tissue is still healthy or damaged precisely. The whole image is split into blocks that block size plays an important role in the accuracy of analyzes.
The minimum size for each block is 4 × 4 pixels, but in sonogram with a resolution of 1024 × 384 (as in this research), 32 × 32, and 16 × 16 blocks are optimal blocks that contain neighboring frequencies in comparison to the exact detection of each image. Figure 14 shows the properly segmented and cropped image.

4.C.2 | Apply DCT transform on each block
Two main notes are important here; first, for the detailed analysis, there is a need for alternations in the textual data, so the DC portion of the transformation should be eliminated, and secondly, there is only a need for the transform amplitude index. The DCT matrix of each block is as large as the original block in the primary image.

4.C.3 | Feature extraction and segmentation
After using DCT conversion and DC removal, a two-dimensional matrix is calculated for each block, which represents the average intensity of each frequency in the block. Each row and column of this resulting matrix actually represents a frequency of the same block, and each element of that is in fact derived from the correlation of the image signal with that specific and constant frequency.
Thus, by performing a frequency conversion, a matrix will be obtained, in which the elements indicate how many pixels of each block have that row frequency and that particular column frequency.
More precisely, the elements of the resulting matrix indicate the intensity of the presence of that specific frequency in that block.
According to researches and studies related to this project, in general, healthier parts of the tissue have a higher average value for the frequencies in the image. 13 However, the intensity of different frequencies in a particular sonogram is a relative property that is not absolute. Therefore, judging whether it is high or low should be taken separately in each image and based on its characteristic parameters. In the sense that it cannot be expressly stated that, for example, if the frequency value in images or in blocks was less than a constant limit, it indicates the malignancy of the lesion in the image captured in that photograph or not. Accordingly, they must be individually calculated for each block in accordance with their own parameters, and then accurate values for the threshold of the frequencies should be calculated and determined as the main golden feature used in the diagnosis process. This is due to the complexity of the information in the signals and some of the inherent differences in the skin of different people. This causes complexity and difficulty as well as the sensitivity of the diagnostic process. To achieve a high-power precision method, many calculations and surveys were carried out.
Finally, the Otsu's adaptive method is selected to perform autocluster-based image thresholds 27,28 based on investigations. This is completely as the solution here matches. This criterion gives judgment for each part of sonogram in comparison with other parts. Ultimately, the ability to separate any sonogram into suspicious and healthy blocks will be created by doing the above calculations and comparing with the thresholds.
In image processing, Otsu's method, is used to automatically perform clustering-based image thresholding 15 or, the reduction of a gray level image to a binary image. The algorithm assumes that the image contains two classes of pixels following bimodal histogram (foreground pixels and background pixels), it then calculates the optimum threshold separating the two classes so that their combined spread (intraclass variance) is minimal, or equivalently (because the sum of pairwise squared distances is constant), so that their interclass variance is maximal. 28 In this way, the matrix obtained in the previous step, which is the frequency matrix, enters the calculation program, and the output of the program will be a number, which will be the threshold for that image. Therefore, by applying this program for each image, the threshold for determining the healthy blocks from the lesion blocks of that image is determined by the intensity of the presence of different frequencies in each block of that image.
When the threshold value is found for each image, the image is reset to the original matrix and the following steps are reexamined.
From the original image of the RF, a B-mode image will be created and then the image will be blocked. In the next step, for each block,

4.D | Computation results
According to Fig. 5, if we apply DCT transformation to image blocks and combine the whole image using the resulting frequency

| 165
The designed algorithm is evaluated with the mentioned database and the results are shown in Fig. 17 In this research, a novel and innovative way to achieve the ability to diagnose skin malignancy is presented. Based on this research concepts, the biological organism has a cellular oscillations, whose frequencies depend on the type of cells in that part of tissue or organ, where there is a specific frequency for a specific tissue under normal conditions, and if the tissue conditions change and there is a complication, then its natural frequency will be changed. So that the frequency response of these two parts and, consequently, the frequency of the return echoes received by the ultrasound probe, are different from each other. This difference is the basis of the classification in this study. As is detailed in the text of the article and in the previous sections, the innovation and novelty of this study is to use skin tissues natural frequency variations as a very suitable and powerful bio marker of skin malignancy for the diagnosis of skin Using these ideas and concepts to diagnose skin condition has created a very high level of fast, noninvasive and accurate detection that is evaluated by experimental database and could help dermatologists, to improve the accuracy of skin cancers diagnosis via a noninvasive and real-time approach.

CONF LICT OF I NTEREST
None declared.