Some test for Top-hat filter

1. Peak standard deviation:
Set the peak std for 1, 2.5, 5, 10 and 20. After std=10, the signals are difficult to identify.

2. Noise:
Set different noise for 0%, 25%, 50%, 75% and 100%. The peaks are hard to identify from 75% noise.

3. Different THF signal window:
Set the noise to 100% and use the different signal window to identify the signal. The result shows the wider window can improve the peak identification.

Summary:
The THF can help us to identify the weak signal from the high exponential background. It is noted that the S/N ratio would affect the THF result. If we want to identify the rare element in the material, we may use the high S/N ratio spectrum for applying THF or using the large signal window for noisy data.

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MLLS in matlab

MLLS stands for multiple linear least squares fitting, which is the common strategy for the solving EELS edge overlapping and which is also built-in the GMS software. The target spectrum Y and the reference spectrum X Y = A * X Assuming Y is 1*256 matrix and we have three reference spectrums, ie, X is 3*256 matrix. So A is 1*3 matrix. The target is to solve A. If Y and X are n*n matrices, we can use the simple formula Y * inv(X) = A * X * inv(X), ie., A = Y * inv(X). However, Y and X are not n*n matrices, it is necessary to have some trick to solve it. We can multiply the transpose matrix to produce n*n matrix. Y * X' = A * X * X' (ps X' means the transpose matrix of X) so A = Y * X' * inv(X * X') Here is the Matlab code: ========= % create target spectrum x=0:256; c=[90,120,155]; sig=[5,10,8]; int=[5,10,8]; xn=zeros(size(x)); ref=zeros(length(c),length(x)); factor=rand(size(c))'; for i=1:length(c) xn=xn+int(i)*ex...

Drift correction in Matlab

In order to improve S/N ratio, microscopist uses several short acquisition time images, and then sum them up. So the drift correction is very important. Here is the demo of how to use Matlab do drift correction. In the first, load an image, and using circshift function to shift the object in the image. Then use fft cross correlation to compute the moving distance. Finally, shift the object to the origial position. Here is the testing code: == % Demo of drift correction % 2018/11/15 by Renfong im1= imread('cameraman.tif'); % reference image [sy,sx]=size(im1); % shift the object im2=circshift(im1,[20,10]); % the object moved down 20 pixels and moved right 10 pixels. figure(1); subplot(121);imshow(im1); subplot(122);imshow(im2); % Using fft cross correlations to detect the moving distance[1] fftim1=fft2(im1); fftim2=fft2(im2); cc=fftshift(ifft2(fftim1.*conj(fftim2))); [shiftY,shiftX]=find(cc==max(cc(:))...

k-means clustering

In order to clustering data to reduce the noise, we can use the simple k-means clustering algorithm. The idea of k-means is quite simple. Here is the step of the k-means algorithm. 1. Randomly pick samples (depending on how many groups we want to cluster) as the references. 2. Compute the distance between each data point and references. 3. Comparing the distance to each reference, grouping the data points from the shortest distance. 4. Compute the centroid of each group as the new reference. 5. Repeat 2-4, until the centroids are the same with the previous result. Here is the Matlab code: ======================================= % An example for k-means clustering % % Renfong 2018/12/19 % % create test data % There are 3 types of sigal % 1-20, 36-70, 91-100 are the group 1 % 21-35 are group 2 % 71-90 are group 3 xx=0:1:1024; cen=[120, 360, 780]; amp=[100, 60, 55]; sig=[50, 10, 30]; % peak 1+3 for i=1:20 sp(i,:)=amp(1)*exp((-...

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