# Noise Reduction Method of Nanopore Based on Wavelet and Kalman Filter
## 1 Introduction  
Nanopore detection technology is a single molecule detection technology with rapid detection, no PCR amplification, and low cost [1; 2]. In the chamber filled with electrolytes, an insulating impermeable membrane with nanoscale pores divides the chamber into two small chambers. When voltage is applied to the electrolyte chamber, ions pass through the pores under the electric field, forming a stable detectable ion current, as shown in Figure 1. When biomolecules to be tested are added to the electrolyte, the biomolecules pass through the nanopore under the electric field, thus blocking the passage of ions and forming a pulse of ion current that can be detected. Therefore, the size and surface properties of the nanopore, the applied voltage strength, and the solution conditions can be mastered to detect different types of biomolecules. However, there is more background noise in the nanopore current signal, which greatly affects the data analysis. It has been studied that the noise in the nanopore detection system  
Figure 1: Nanopore detection principle. consists of Gaussian white noise, low-frequency noise, and high-frequency noise [3]. Gaussian white noise is one of the main noises of solid-state nanopores, it is especially necessary to explore the methods to reduce Gaussian white noise. Gaussian white noise is the noise caused by the electron Brownian motion in the nanopore channel and the interaction of ions with the nanofilm surface. The spectral density of its noise voltage is \(S_{v}(f)=4 kRT\), and the corresponding mean square value of the noise voltage \(\overline{V^{2}}=4 kRT(BW)\) (\(BW\) is the bandwidth of the noise voltage), which shows that the thermal noise is related to temperature, resistance, and bandwidth. Gaussian white noise across the entire spectrum, reducing the physical temperature of the detection system, system resistance, selecting the appropriate operating band, and using low-noise electronic components is a more direct way to reduce thermal noise. The low-frequency noise of the nanopore detection system mainly refers to 1/f noise, and the high-frequency noise is closely related to the capacitance of the nanopore system, so the nanopore signal noise fills the whole frequency domain. Most of the current researchers reduce the noise by improving the device conditions. [PERSON] et al. [4] proposed a high-frequency noise reduction structure to reduce the capacitance of silicon nitride film. [PERSON] et al. [5] used the same scheme and replaced the covering layer of silicon nitride film with a polymer material to reduce the noise. Demonstrated that limiting the contact area between the silicon nitride film and the electrolyte solution through a cover layer to reduce the nanofilm capacitance is an effective solution for reducing high-frequency noise. However, when a solid-state nanopore device is selected based on the biomolecule to be measured, the measurement temperature, nanopore resistance, detection equipment, and experimental parameters of the system have been determined, and it is difficult to perform noise reduction by the above means. Therefore, a noise reduction method based on wavelet transform and Kalman filter is proposed to perform multi-scale decomposition and optimal estimation of the nanopore current signal to achieve the purpose of noise reduction. The nanopore current signal proposed in this paper is an IgG antibody signal, as shown in Figure 2. IgG is the most abundant natural antibody component of plasma proteins (10-20%) and provides protection primarily against bacterial and viral infections. IgG not only allows intercellular signaling and cell activation, but because it is a soluble adhesion molecule, it can bind and neutralize antigens alone, making it useful for localizing the immune system and assessing related diseases [6; 7; 8; 9]. For example, the working principle of HIV 3 rd generation ELISA reagents and various rapid detection reagents is to detect IgG antibodies in infected patients.