Introduction to Inverse Problems in ImagingCRC Press, 30 Ağu 2020 - 364 sayfa This is a graduate textbook on the principles of linear inverse problems, methods of their approximate solution, and practical application in imaging. The level of mathematical treatment is kept as low as possible to make the book suitable for a wide range of readers from different backgrounds in science and engineering. Mathematical prerequisites are first courses in analysis, geometry, linear algebra, probability theory, and Fourier analysis. The authors concentrate on presenting easily implementable and fast solution algorithms. With examples and exercises throughout, the book will provide the reader with the appropriate background for a clear understanding of the essence of inverse problems (ill-posedness and its cure) and, consequently, for an intelligent assessment of the rapidly growing literature on these problems. |
İçindekiler
Some mathematical tools | 19 |
Examples of image blurring | 50 |
The illposedness of image deconvolution | 75 |
Regularization methods | 98 |
Iterative regularization methods | 137 |
Statistical methods | 168 |
Examples of linear inverse problems | 191 |
Singular value decomposition SVD | 220 |
Fourierbased methods for specific problems | 268 |
Comments and concluding remarks | 295 |
A Euclidean and Hilbert spaces of functions | 311 |
B Linear operators in function spaces | 317 |
Properties of the DFT and the FFT algorithm | 328 |
E Minimization of quadratic functionals | 335 |
G The EM method | 343 |
Inversion methods revisited | 247 |
Diğer baskılar - Tümünü görüntüle
Sık kullanılan terimler ve kelime öbekleri
algorithm appendix applied approximation associated assume bandlimited basic behaviour blur bounded called chapter coincides components compute condition consequence consider consists contains convergence convolution corresponding deconvolution defined definition denoted depends described direct discrete discussed distance distribution domain effect eigenvalues element energy equality equation estimate example exists figure filter Fourier transform frequency function given ill-posed imaging system implies important instance integral introduced inverse problem iterations Landweber method least-squares linear mathematical matrix means measure minimization Moreover noise noisy image norm object observe obtained operator orthogonal particular physical positive possible precisely projection properties prove regularization parameter remark representation respect restoration restoration error result sampling satisfied scalar product sequence shown solution space square square-integrable step Tikhonov true unique variables vector window zero