Inverse Problems and Imaging: Lectures given at the C.I.M.E. by Luis L. Bonilla

By Luis L. Bonilla

Nowadays we face a number of and critical imaging difficulties: nondestructive trying out of fabrics, tracking of business techniques, enhancement of oil construction by means of effective reservoir characterization, rising advancements in noninvasive imaging concepts for clinical reasons - automated tomography (CT), magnetic resonance imaging (MRI), positron emission tomography (PET), X-ray and ultrasound tomography, and so on. within the CIME summer season college on Imaging (Martina Franca, Italy 2002), major specialists in mathematical ideas and purposes offered huge and necessary introductions for non-experts and practitioners alike to many elements of this fascinating box. the quantity includes a part of the above lectures accomplished and up to date by means of extra contributions on different similar topics.

Show description

Read or Download Inverse Problems and Imaging: Lectures given at the C.I.M.E. Summer School held in Martina Franca, Italy, September 15-21, 2002 (Lecture Notes in Mathematics) PDF

Best imaging systems books

Morphological Image Analysis: Principles and Applications

From reports of the 1st version: "This is a scholarly journey de strength during the international of morphological photograph research […]. i like to recommend this booklet unreservedly because the top one i've got encountered in this specific subject […]" BMVA information

Handbook of Optical and Laser Scanning, Second Edition (Optical Science and Engineering)

From its preliminary e-book titled Laser Beam Scanning in 1985 to instruction manual of Optical and Laser Scanning, now in its moment version, this reference has stored execs and scholars on the vanguard of optical scanning expertise. rigorously and meticulously up-to-date in each one new release, the publication remains to be the main entire scanning source out there.

2D and 3D Image Analysis by Moments

Offers fresh major and quick improvement within the box of 2nd and 3D photograph research second and 3D snapshot research through Moments, is a distinct compendium of moment-based picture research together with conventional tools and in addition displays the most recent improvement of the sphere. The booklet provides a survey of 2nd and 3D second invariants with appreciate to similarity and affine spatial adjustments and to picture blurring and smoothing by way of a number of filters.

Additional info for Inverse Problems and Imaging: Lectures given at the C.I.M.E. Summer School held in Martina Franca, Italy, September 15-21, 2002 (Lecture Notes in Mathematics)

Example text

Imag. 13, 186-195. 5. E. Danielsson, P. Edholm, J. Eriksson, M. Magnusson Seger, and H. Turbell (1999): The original π-method for helical cone-beam CT, Proc. Int. Meeting on Fully 3D-reconstruction, Egmond aan Zee, June 3-6. 6. A. C. W. Kress (1984): ‘Practical cone–beam algorithm’, J. Opt. Soc. Amer. A 6, 612-619. 7. K. Fourmont (1999): ‘Schnelle Fourier–Transformation bei nicht–¨ aquidistanten Gittern und tomographische Anwendungen’, Dissertation Fachbereich Mathematik und Informatik der Universit¨ at M¨ unster, M¨ unster, Germany.

This is true since f g has bandwidth 2Ω. We put vˆ(σ) = 2(2π)(n−1)/2 |σ|n−1 φ(σ/Ω) . v is called the reconstruction filter. e. ⎧ ⎨ 1 , |σ| ≤ 1 , φ(σ) = ⎩ 0 , |σ| > 1 . Then, Ω2 1 s 2 sinc u(Ωs) , u(s) = sinc(s) − . 2 4π 2 2 Now we describe the filtered backprojection algorithm for the reconstruction of the function f from g = Rf . e. (14) fˆ(ξ) is negligible in some sense for |ξ| > Ω . 1 that the same is true for g. Hence, by a loose application of the sampling theorem, v(θ, s − sk )g(θ, sk ) (v ∗ g)(θ, s ) = ∆s (15) k where s = ∆s and ∆s ≤ π/Ω.

The simplest source curve one can think of, a circle around the object, does not satisfy the Kirillov–Tuy condition. For a circular source curve an approximate inversion formula, the FDK formula, exists; see Feldkamp et al. (1984). In medical applications the source curve is a helix. 4 The Attenuated Radon Transform Let n = 2. The attenuated Radon transform of f is defined to be e−(Cµ )(x,θ⊥ ) f (x)dx (Rµ f )(θ, s) = x·θ=s 24 F. Natterer where µ is another function in R2 and θ⊥ is the unit vector perpendicular to θ such that det (θ, θ⊥ ) = 1.

Download PDF sample

Rated 4.96 of 5 – based on 26 votes