One-dimensional deconvolution
One-dimensional deconvolution is one of the basic examples in the book Mueller & Siltanen: Linear and nonlinear inverse problems with practical applications (SIAM 2012). It is very educational to study how Tikhonov regularization, Total Variation regularization and wavelet sparsity sharpen blurred signals, each in their own way. The Matlab codes are available here: https://github.com/ssiltane/deconv1D
- Building convolution matrices
- Simulating tomographic data without committing inverse crime
- Calculating singular value decomposition (SVD)
- Reconstruction by truncated SVD
- Reconstruction by Tikhonov regularization
- Reconstruction by Total Variation regularization
- Reconstruction by wavelet sparsity
- Reconstruction by neural networks
X-ray tomography
Two-dimensional X-ray tomography is one of the basic examples in the book Mueller & Siltanen: Linear and nonlinear inverse problems with practical applications (SIAM 2012). This learning resource offers presentation slides and Matlab codes that Professor Samuli Siltanen used in the winter school Advanced methods for mathematical image analysis in Bologna, Italy, January 2023. Codes are available in this repository:
https://github.com/ssiltane/BolognaWinterSchool2023
- Building tomographic matrices
- Simulating tomographic data without committing inverse crime
- Calculating singular value decomposition (SVD)
- Reconstruction by truncated SVD
- Reconstruction by Tikhonov regularization
- Reconstruction by Total Variation regularization
- Reconstruction by wavelet sparsity
