Noise is a part of data whether the data is from measurement, experiment or ... A few techniques are suggested for noise reduction to improve the data quality in recent years some of which are based on wavelet, orthogonalization and neural networks. The computational cost of existing methods are more than expected and that's why their application in some cases is not beneficial. In this paper, we suggest a low cost techniques based on special linear algebra structures (tridiagonal systems) to improve the signal quality. In this method, we suggest a tridiagonal model for the noise around the most noisy elements. To update the predicted noise, the algorithm is equipped with a learning/feedback approach. The details are described below and based on presented numerical results this algorithm is successful in computing the noise with lower MSE (mean squared error) in computation time specially when the data size is lower than 5000. Our algorithm is used for low-range noise while for high-range noise it is sufficient to use the presented algorithm in hybrid with moving average. The algorithm is implemented in MATLAB 2019b on a computer with Windows 11 having 8GB RAM. It is then tested over many randomly generated experiments. The numerical results confirm the efficiency of presented algorithm in most cases in comparison with existing methods.

翻译：噪声是数据中不可避免的组成部分，无论数据来源于测量、实验还是其他途径。近年来，为提升数据质量，研究者提出了若干降噪技术，其中部分方法基于小波变换、正交化及神经网络。然而，现有方法的计算成本普遍高于预期，这限制了其在某些场景下的应用价值。本文提出一种基于特殊线性代数结构（三对角系统）的低成本技术，用于改善信号质量。该方法针对噪声最显著的成分构建三对角模型，并引入学习/反馈机制迭代更新预测噪声。下文详述算法细节，数值结果表明：在数据规模小于5000时，该算法能以较低均方误差（MSE）和更短的计算时间有效估算噪声。本算法适用于低幅值噪声场景，而针对高幅值噪声，可将其与移动平均方法混合使用。算法基于MATLAB 2019b实现，运行环境为配备8GB内存的Windows 11系统，并通过大量随机生成的实验进行验证。数值结果证实，与现有方法相比，本算法在多数情况下具有显著效能优势。