Orthogonal Subspace Projection
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This article refers to the following documents. You can also refer to a look
1.Hyperspectral Image Classification and Dimensionality Reduction Ap An Orthogonal Subspace Projection
Link .
2.Chein the I-Chang-Hyperspectral the Data Exploitation_ Th
Author 1: Luna_Lovegood_001
1.1 algorithm target
This algorithm was first seen in Document 2, with a good introduction:
He believes that high spectrum channel (channel) too much:
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Data toooverwhelming and not necessary
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This can lead to so-called data pollution, say the original book (Document 2):
some information resulting from unknown signal sources may contaminate and distort the information that we try to extract.
1.2 algorithm steps
In Document 2, he proposed a two-step strategy, referred to herein as
the first step: eliminate interference signals (including unknown and unwanted signals)
The second step: to extract the signal of interest
to this end, the authors show three algorithm described here only explanation OSP algorithm
1.3 Principles algorithm
More than the introduction of good, but the principle of this part of the bad to say (maybe I did not understand).
1.3.1 premise
We need to know the full prior knowledge.
- p target t (classification) is fully known (such as water, soil, urban)
- m p target spectrum signal known
drawings
1.4 model
(Original translation is attached below)
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Each pixel of the image is regarded as a vector R & lt , each end element by mj of the linear combination
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Plus a noise vector of the n- :
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The M open eager signal and no desire signal (undesired signatures) (3.2), d is that the object of our desire, and U is the object of desire.
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Then r orthogonal projection in the space of U. The aim is to eliminate U . As for how to find the orthogonal space U, is the basic knowledge of higher mathematics. .
Procedure is as follows, after projection is completed, it becomes (3.4), can be found in (3.4) one less than (3.2), which is orthogonal space projection effect.
This, the first step in a two-step strategy to complete.
But from (3.4) to (3.5) we are talking about will be very true, difficult to understand. But we can see the second step is to optimize the maximum signal to noise ratio target. Specifically how we should do the references 1
2 OSP original
2.1 Second look at algorithm objectives
算法目标文献1说的很清楚：Dimensionality Reduction数据降维。但是文献2中说这个是为了完成分类（或者说像素分割）这就很迷惑，暂时称为问题1，下文有解决。
2.2二看算法步骤
首先也是得到了上一个文献中（3.2）。然后分三步：
- 正交投影，消除干扰
- 信噪比最大化
- 正交投影分类（这里就解决了问题一）
2.2.1正交投影，消除干扰
这个和上个文献说的一样，也容易理解，直接附图，过程同 1.4 节
2.2.2信噪比最大化
- 作者希望通过一个x 向量来最大或信噪比：
- 即（4）左右乘上一个x得到（5），然后构造信噪比表达式（6），接下来就是最大化（6），求x。
其实数学家已经帮我们求好了，就是（6）。
至此求出信噪比（6）
至此求出x，发现x就是d为什么这么巧呢（问题二）
2.2.3 正交投影分类（这里就解决了问题一）
然后把（8）带入（5）就可得到（9）
我们称（9）为正交子空间投影算子。
然后我们把算子（9）与每个像素相乘，就可以得到每个像素与感兴趣目标的相似的测量。因为每个像素都是一个（L*1）的向量（有L个通道），可以看为一个图像立方体。（9）与像素乘过以后就成了标量，即：从一个图像立方体变成了一个图片。
2020年1月22日10:46:16更新
如果以上你没有看懂这方法到底是要干什么，可以看看以下其他论文的评论
3其它论文对于它的简述
其实看看后人对于这篇论文（文献1）的评价和总结更能理解
这里引用了以下文章
Document [3]: using a local orthogonal subspace projection hyperspectral image abnormality detection Link .
Document [4]: in an orthogonal subspace projection hyperspectral image endmember extraction algorithms Link .
3.1 Document 3
Document 3 summed OSP algorithm:
- Linear mixed model based
- The mixed pixel is divided into interest and objectives are not interested
- Enhanced features of an object of interest, not interested in repression of target features, to solve the problem
Thus the third point of view, this is a traditional image processing algorithm (after the 1994 document)
to sum up
OSP algorithm is first pixel vector r projected onto orthogonal subspaces, and then projected onto the target of interest vector d on.
