Hilbert space image processing mathematical principle explain 23

Label Hilbert spaceimage processingMathematicsfunctional analysis
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Exchange learning can be added to image processing research groupFive hundred and twenty-nine million five hundred and forty-nine thousand three hundred and twenty)

There was a time when I didn't continue to update "Detailed mathematical principle in image processing"Column. Because the previous part of the foundation has been released almost, and now has entered the deep water area". On the one hand, the length of the article has increased, so I wrote it more trouble. On the other hand, the topic is now in the field of differential equations and functional analysis, and this part of the content is too difficult for people who are not mathematics majors. And if it is a beginner image processing, which is still pondering Gauss smoothing and median filtering of people, basically can not use these things.So if you are in this situation, I do not recommend you look at this.Also, if your goal is to write a similar House Magic program (, then you do not have to learn so deep. And the study of the following topics of people, more suitable for use MATLAB.

My opinion is that the image processing researchers who want to see Paper every day to study differential equations and functional analysis. If every day you are to see some full formula of image processing paper, but do not know L1 norm and L2 norm, do not understand the Hilbert space, do not understand the Poisson's equation or Green's function method, I really cannot imagine you have much pain. Of course, this part of the content is also based on the article I posted in front of, for example, you will see me again in the Fu Liye transformation of the Pa Sewall equation, I hope you remember what this is:

2.3.6 Hilbert space

DefinitionIn the norm defined by the inner product of the complete inner product space is calledHilbert (Hilbert) space.
Hilbert space is a kind of very good linear space, and it has a very wide application in engineering, and the best approximation problem in Hilbert space can be solved perfectly.

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