An introduction to smoothing--forcked from matthew-brett
2017-12-07 22:12
423 查看
Smoothing is a process by which data points are averaged with their neighbors in a series, such as a time series,
or image. This (usually) has the effect of blurring the sharp edges in the smoothed data. Smoothing is sometimes referred to as filtering, because smoothing has the effect of suppressing high frequency signal and enhancing low frequency signal. There are many
different methods of smoothing, but here we discuss smoothing with a Gaussian kernel.
The primary reason for smoothing is to increase signal to noise. Smoothing increases signal to noise by the matched filter theorem. This theorem states that the filter that will give optimum resolution of signal from noise is a filter that is matched to the
signal. In the case of smoothing, the filter is the Gaussian kernel. Therefore, if we are expecting signal in our images that is of Gaussian shape, and of FWHM of say 10mm, then this signal will best be detected after we have smoothed our images with a 10mm
FWHM Gaussian filter.
Sometimes
you do not know the size or the shape of the signal change that you are expecting. In these cases, it is difficult to choose a smoothing level, because the smoothing may reduce signal that is not of the same size and shape as the smoothing kernel. There are
ways of detecting signal at different smoothing level, that allow appropriate corrections for multiple corrections, and levels of smoothing. This Worsley 1996 paper describes such an approach: Worsley
KJ, Marret S, Neelin P, Evans AC (1996) Searching scale space for activation in PET images. Human Brain Mapping 4:74-90
source: https://matthew-brett.github.io/teaching/smoothing_intro.html
or image. This (usually) has the effect of blurring the sharp edges in the smoothed data. Smoothing is sometimes referred to as filtering, because smoothing has the effect of suppressing high frequency signal and enhancing low frequency signal. There are many
different methods of smoothing, but here we discuss smoothing with a Gaussian kernel.
Why smooth?
The primary reason for smoothing is to increase signal to noise. Smoothing increases signal to noise by the matched filter theorem. This theorem states that the filter that will give optimum resolution of signal from noise is a filter that is matched to thesignal. In the case of smoothing, the filter is the Gaussian kernel. Therefore, if we are expecting signal in our images that is of Gaussian shape, and of FWHM of say 10mm, then this signal will best be detected after we have smoothed our images with a 10mm
FWHM Gaussian filter.
Sometimes
you do not know the size or the shape of the signal change that you are expecting. In these cases, it is difficult to choose a smoothing level, because the smoothing may reduce signal that is not of the same size and shape as the smoothing kernel. There are
ways of detecting signal at different smoothing level, that allow appropriate corrections for multiple corrections, and levels of smoothing. This Worsley 1996 paper describes such an approach: Worsley
KJ, Marret S, Neelin P, Evans AC (1996) Searching scale space for activation in PET images. Human Brain Mapping 4:74-90
source: https://matthew-brett.github.io/teaching/smoothing_intro.html
相关文章推荐
- 《An Introduction to Signal Smoothing》译文
- 《An Introduction to Signal Smoothing》译文
- Swift from Scratch: An Introduction to Functions
- An Introduction to Thread in the upcoming book From: Introduction to the C++ Boost Libraries
- 20年架构师写给程序员的一封信《From an architect to a programmer 》
- Coursera-An Introduction to Interactive Programming in Python (Part 1)-Mini-project #4 —"Pong"
- An Introduction to Proxy Server
- From an architect to a programmer
- An introduction to bitwise operators
- An Introduction to Java Stack Traces
- fixed: error C2784 from compiling adding an entry to a std::map
- An introduction to class loading and debugging tools
- From an architect to a programmer
- An Introduction to Interactive Programming in Python (Part 1) - Week 0
- Building bug-free O-O software: An Introduction to Design by Contract™(翻译)
- An introduction to KProbes
- Designing BSD Rootkits: An Introduction to Kernel Hacking
- An association from the table PersonAddress refers to an unmapped class
- Building Automated Trading Systems: With an Introduction to Visual C++.NET 2005
- How to project an icon to the map taken from gps at com port