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 |
Iterative regularization methods | 137 |
Statistical methods | 168 |
PART 2 | 189 |
Singular value decomposition SVD | 220 |
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 |
Diğer baskılar - Tümünü görüntüle
Sık kullanılan terimler ve kelime öbekleri
appendix approximate solutions approximation error bandlimited basic behaviour blur components compute condition number consider convergence convolution operator corresponding deconvolution defined in equation denoted density function discrepancy functional discrete domain eigenvalues estimate example exists figure filter fk+1 Fourier transform frequency function f Gaussian given by equation holds true ill-posed problem image deconvolution image g image restoration imaging system implies integral operator introduced inverse problem least-squares solution mathematical minimization minimum noise noise-free image noisy image norm null space number of iterations object f(0 obtained optical orthogonal orthonormal Parseval equality projected Landweber method properties Radon transform regularization methods regularization parameter regularized solution restoration error result satisfied scalar product sequence singular value decomposition singular values solution of equation square-integrable functions subspace tends to zero Tikhonov Tikhonov regularization tomography unique unknown object variables window functions Κ ω σκ