摘 要

基于光谱成像技术，提取兴趣区域的均值光谱进行化学计量学建模，在对兴趣区域中各像素位置处的品质指标进行预测的研究中，目前通常认为所得到的指标像素预测值就是指标在空间的定量分布情况。另一方面，虽然对指标的像素预测结果明显偏离理论正确值的情况有所报导，但由于难以获取像素位置处的参考值，无法直接验证像素位置处指标预测结果是否正确。

本文从计算仿真途径，利用已知各像素位置指标参考值的模拟数据区域集，开展像素指标预测过程及准确性开展计算研究。

通过两类空间分布的随机填充模式，即“空间扩散”与“整体衰减”模式，分别模拟由两种材质及单一材质构成的兴趣区域及其品质差异。利用60条已知指标参考值的光谱曲线数据为基础，随机填充生成5组、每组包含60个尺寸为16×16像素的空间区域，作为仿真研究的输入数据及预测结果的参考数据。

基于偏最小二乘回归法，以区域均值光谱及其相应的区域内指标均值作为输入，进行线性化学计量学全波段建模，对指标的区域均值及像素值进行预测。通过与参考数据进行比对，发现不论是区域均值(R² gt;0.999)还是像素值(R² gt;0.98)均可准确预测，表明通过区域均值建模进行像素预测的方案在理想情况下是可行的。

随后，通过向光谱图像数据加入不同幅度的正态随机噪声，模拟实际检测中光谱图像采集中不同等级的随机噪声。重复建模预测，结果显示，相较于区域指标检测，像素指标检测受噪声影响严重得多。当区域均值预测误差仍可接受(R² gt;0.81)时，像素指标的预测误差则可能已经严重恶化(R² lt;-0.1133)。

接下来，对基于SG方法对输入光谱进行光谱平滑、一阶微分以及二阶微分预处理。重复建模预测，结果显示，在不加噪的理想情况下，经各光谱滤波处理，均可实现指标的区域均值(R² =1)与像素值(R² gt;0.998)的准确预测。而加噪情况下，同样出现当区域均值预测精度仍可接受(R² gt;0.91)时，像素指标的预测误差同样可能已经严重恶化(R² lt;-4.1225)；在受到少量噪声污染情况下（噪声强度＝0.02），观测到平滑滤波可以提高像素预测的质量(R² 从0.87升高到0.92)。

研究中发现，在仅考虑光谱图像采集受随机噪声影响情况下，当像素预测值明显偏离正确值时，像素预测均值仍保持与平均光谱得到的区域均值预测结果一致，因此在无法得知像素指标参考值的情况下，不能作为像素预测是否失准的观测依据。同时发现，像素指标相对与建模指标范围的发散程度，随像素预测准度下降而发散。因此，利用箱形图统计工具，从而在无法获取指标像素参考值情况下，仍可作为判断像素指标是否失准的观测工具。

关键词：光谱成像；偏最小二乘回归建模；区域检测；指标像素检测；指标分布

Simulation of inspection of pixel-wise distribution of attributes based on spectral imaging

ABSTRACT

Predicted values of an attribute at pixels are often regarded as the spatial distribution of the attribute in the realm of spectral imaging where chemometric models were built, in contrast, according to the average spectra and the corresponding over all attribute values of regions of interest. Although it has been occasionally reported that the average of pixel-wise prediction deviated from theoretical possible ranges or the measurement of over all values, the lack of pixel-wise reference value as the ‘gold plate’ in practice forbids any direct validation.

Simulated spatial patterns were generated and used in this work with known values at pixels to investigate the mechanism as well as the accuracy of pixel-wise prediction.

2 different random algorithms, i.e. the spatial growth, and the ominous decay, regulated the generation of the simulated data patterns, mimicking regions that were composed of 2 different materials or 1 single material as well as their spatial changes in quality. 60 spectra with corresponding attribute values were used as the data basis, from which 5 sets of spectral images having 60 randomly generated 16×16 pixels patterns in each set served as both the data input and the reference for pixel validation.

Over all attribute value of a pattern as well as all its pixel values within were calculated from the input of the average full range spectra and attribute values of patterns with partial least squares regression modeling. Validation results showed that prediction of both the average (R² =0.999) and pixel-wise (R² gt; 0.98) values are valid, meaning the scheme of predicting pixel values with only region averages is feasible under ideal conditions.

In order to mimic the random noise present in an actual acquisition, normal random noise of different amplitudes were added to the test spectral image patterns. The same process of modeling and prediction were repeated. Validation results showed that pixel-wise prediction is more vulnerable to noise in comparison to that of regional average. While the predicted region average agrees quite well (R² gt;0.81) with reference, the pixel-wise predictive may have already strayed far away (R² lt;-0.1133).

The final step is to test pixel-wise and average prediction with Savitzky-Golay filter-based spectral preprocessing and the vulnerabilities to noise of 3 different filters, i.e. the smoothing, the 1^st order derivative, and the 2^nd order derivative. Results showed that both pixel-wise(R² =1) and region average (R² gt;0.998) could be accurately predicted with any of the 3 filters when no noise was introduced into the data. However, after noise adulteration, similar situations occurred that acceptable region average predictions (R² gt;0.91）were accompanied with seriously erroneous pixel-wise predictions (R2 lt;-4.1225). An interesting observation was that under minor noise corruption (amplitude level = 0.02) SG smoothing filter increased the goodness of pixel-wise prediction (from R² =0.87 to R² =0.92).

2 important findings were made. First, the average of pixel-wise prediction of a pattern always agrees with the prediction by the pattern’s average spectrum even when individual values at most pixels are seriously erroneous if considering only the random noise during spectral image acquisition. Thus the 0 difference between them could not be regarded as a necessary condition for accurate pixel-wise prediction. Second, the divergence of pixel-wise prediction of a set of patterns increases when pixel-wise prediction worsens. Consequently, with the help of the visual tool of box plot it is possible to be alerted when pixel-wise prediction goes wrong even when reference data at pixel resolution was not available as most cases do in real world scenarios.

Key words: spectral imaging; Partial least squares chemometric model; Regional detection; Index pixel detection; Index distribution.