自适应多尺度窗口平均光谱平滑

去噪算法是极其重要的光谱预处理步骤，能够显著提高后续光谱分析算法的准确性。然而，大多数去噪算法都需要通过反复试验的方式来人为设置初始参数，不能自动完成光谱去噪。为了能够对光谱进行自动且可靠的平滑去噪，提出了一种自适应多尺度窗口平均平滑(AMWA)去噪算法。该算法针对光谱中不同位置采用不同宽度的平滑窗口，这些窗口的宽度将直接影响到平滑效果。当窗口宽度选择不合适时，可能出现去噪过度，使得峰畸变或者丢失;也有可能导致去噪不足，使得光谱的较平坦区域仍包含大量的噪声。因此判断每个窗口宽度是否合适，是光谱平滑的关键。该算法通过迭代的方法不断优化各个窗口的宽度，并以统计学中的Z检验来判断窗口宽度是否为最佳。另外，为了提高假设检验的可靠性，用不同信噪比的模拟数据对假设检验中使用的阈值进行比较，发现当阈值设为1.1时可使去噪效果最佳。用模拟光谱和实际光谱对该算法进行了测试，该算法能够自动适应不同的光谱形状和噪声强度。还将AMWA去噪算法与SG算法及移动窗口平均平滑算法进行了全面的比较，AMWA算法都明显优于其他两种算法。结果表明AMWA算法不仅去噪效果更好，而且准确性及保真性也更高，对模拟光谱和实际光谱都具有极好的平滑效果。

Spectral Smoothing with Adaptive Multiscale Window Average

In order to smooth the spectra automatically and reliably, a spectral smoothing algorithm with adaptive multiscale window average (AWMA) is demonstrated. In this method, different positions of the spectra are smoothed by windows of different width, and the width of the windows will directly affect smoothing. The window with inappropriate width may cause excessive denoising (peak distortion or loss) or inadequate denoising (the flat region of the spectra still contains a lot of noise). So, how to get the right width of the window is the key of spectral smoothing. The algorithm optimized the width of windows by an iterative method, and verified whether the width is the best according to statistical Z-test. In order to increase the reliability of the algorithm, a comprehensive comparison of the thresholds of hypothesis according to simulation data of different SNR was performed. When the threshold is set to 1.1, the denoising effect can be the best. In this work, the AMWA algorithm was tested by simulated spectra and real spectra, and it can automatically adapt to different spectral shape and different noise intensity. A comprehensive comparison of AMWA smoothing, Savitzky-Golay smoothing and moving average smoothing was performed in this paper, and the AMWA algorithm is better than the other two algorithms. Results show that the AMWA algorithm not only has better denoising effect, but also has higher accuracy and fidelity. This method has achieved great effect not only to simulated spectra but also to real spectra.