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Tutorials on imaging, computing and mathematics¶
Mathematics¶
- Notation;
- Some algebra with summation;
- The angle sum rule;
- Formula for rotating a vector in 2D;
- Sum of sines and cosines;
- Sums of sinusoids;
- Vectors and dot products;
- Vector projection;
- Angles between vectors;
- Correlation and projection;
- Matrix rank;
- Inverse of a diagonal matrix;
- Refresher on complex numbers;
- Fourier without the ei;
- Introducing principal component analysis;
- Linear interpolation.
Statistics¶
Imaging¶
- Coordinate systems and affine transforms;
- Slice timing correction;
- Calculating transformations between images;
- Mutual information as an image matching metric;
- An introduction to smoothing;
- Convolution;
- Smoothing as convolution;
- Correlated regressors;
- Notes on the Bonferroni threshold;
- Thresholding with false discovery rate;
- Thresholding with random field theory.