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首页> 外文期刊>Chemometrics and Intelligent Laboratory Systems >Discriminant image resolution: a novel multivariate image analysis method utilizing a spatial classification constraint in addition to bilinear nonnegativity
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Discriminant image resolution: a novel multivariate image analysis method utilizing a spatial classification constraint in addition to bilinear nonnegativity

机译：判别图像分辨率：一种新颖的多元图像分析方法，除了双线性非负性之外，还利用空间分类约束

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Spectroscopic image analysis can be characterized as two different and distinct problems depending on the kind of information required from the solution. In its simplest form, the data can be decomposed into two submatrices, each of which carries different aspects of pure component information. Typically, this means information about pure spectra and pure intensities are obtained from the solution. This is the well-known and well-characterized bilinear form that by itself cannot guarantee a unique solution due to the rotational ambiguity inherent in the mathematical solution. This problem has been addressed in a number of ways by different authors using novel constraints applied to the least-squares solution. This usually takes the form of natural constraints as suggested by Tauler as the standard methodology to improve the resolution of data during alternative least squares (ALS) iterative process. A second type of multivariate image analysis problem is proposed in this paper that is quite different from the tradition methods and in some ways potentially is more useful. This involves the solution as a class problem in which the relevant information is not necessarily contained in pure component information, but rather, in unique combinations of the pure components that are allowed to be spatially collocated. This discriminant image resolution (DIR) method theoretically can be treated as a more generalized solution to the problem because the distribution of components is allowed to freely mix in simplified combinations of solutions. The result is a constrained least-squares solution where the constraints are more limited and therefore less restrictive. The constraints in this case employ the results of probabilistic class partition information by applying Bayesian discriminant clustering to the intensity submatrix. This amounts to a spatial constraint because the probability of class association is used as a way of limiting the components that are allowed to appear in a given pixel. This is a unique modification of the original modified alternating least squares (MALS) concept and to the authors' knowledge, the first time this type of constraint has been combined with an ALS algorithm for analysis of multivariate or hyperspectral data. Modified alternating least squares (MALS) is used as the computational engine to drive good convergence while imposing the constraints in this modified ALS model. This kind of analysis produces single and simple multicomponent images and spectra based on classification from spectral information. The present constraint is most useful in resolving image data when the true images are not severely overlapped but it will also perform well under conditions of more severe collinearity.
机译：根据解决方案所需的信息种类，光谱图像分析可被描述为两个不同且不同的问题。以最简单的形式，数据可以分解为两个子矩阵，每个子矩阵都承载纯组分信息的不同方面。通常，这意味着从溶液中获得有关纯光谱和纯强度的信息。这是众所周知的和特征化的双线性形式，由于数学解决方案中固有的旋转歧义，它本身不能保证唯一的解决方案。不同的作者已使用应用于最小二乘解的新颖约束以多种方式解决了此问题。这通常采用Tauler建议的自然约束形式，作为在替代最小二乘（ALS）迭代过程中提高数据分辨率的标准方法。本文提出了第二种类型的多元图像分析问题，它与传统方法完全不同，并且在某些方面可能更有用。这涉及作为类别问题的解决方案，其中相关信息不一定包含在纯组件信息中，而是包含在允许在空间上并置的纯组件的唯一组合中。从理论上讲，这种判别式图像分辨率（DIR）方法可以看作是对该问题的更一般化解决方案，因为允许组分的分布在解决方案的简化组合中自由混合。结果是约束最小二乘解，其中约束受到更多限制，因此约束性降低。在这种情况下，约束通过将贝叶斯判别聚类应用于强度子矩阵来利用概率类划分信息的结果。这相当于空间限制，因为类关联的可能性被用作限制允许出现在给定像素中的分量的方式。这是对原始修改的交替最小二乘（MALS）概念的独特修改，并且据作者所知，这是首次将这种类型的约束与ALS算法结合用于分析多变量或高光谱数据。修改后的交替最小二乘（MALS）用作计算引擎，以驱动良好的收敛性，同时在此修改后的ALS模型中施加约束。这种分析基于光谱信息的分类产生单个和简单的多组分图像和光谱。当真实图像没有严重重叠时，本约束对于解析图像数据最有用，但在更严重的共线性条件下，它也会表现良好。

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