LEADER 05708nam 2200517 450 001 9910812387603321 005 20200520144314.0 010 $a3-11-049802-2 024 7 $a10.1515/9783110500592 035 $a(CKB)3710000001123492 035 $a(DE-B1597)470591 035 $a(OCoLC)984643034 035 $a(DE-B1597)9783110500592 035 $a(Au-PeEL)EBL4830571 035 $a(CaPaEBR)ebr11365999 035 $a(OCoLC)980746581 035 $a(CaSebORM)9783110498028 035 $a(MiAaPQ)EBC4830571 035 $a(EXLCZ)993710000001123492 100 $a20170410h20172017 uy 0 101 0 $aeng 135 $aurcnu|||||||| 181 $2rdacontent 182 $2rdamedia 183 $2rdacarrier 200 10$aImage reconstruction $eapplications in medical sciences /$fGengsheng Lawrence Zeng 210 1$aBerlin, [Germany] ;$aBoston, [Massachusetts] :$cDe Gruyter,$d2017. 210 4$dİ2017 215 $a1 online resource (240 pages) $cillustrations 225 0 $aDe Gruyter Textbook 311 $a3-11-050048-5 311 $a3-11-050059-0 320 $aIncludes bibliographical references. 327 $tFrontmatter -- $tPreface -- $tContents -- $t1. Basic principles of tomography -- $t2. Parallel-beam image reconstruction -- $t3. Fan-beam image reconstruction -- $t4. Transmission and emission tomography -- $t5. Three-dimensional image reconstruction -- $t6. Iterative reconstruction -- $t7. MRI reconstruction -- $t8. Using FBP to perform iterative reconstruction -- $tIndex 330 $aThis book introduces the classical and modern image reconstruction technologies. It covers topics in two-dimensional (2D) parallel-beam and fan-beam imaging, three-dimensional (3D) parallel ray, parallel plane, and cone-beam imaging. Both analytical and iterative methods are presented. The applications in X-ray CT, SPECT (single photon emission computed tomography), PET (positron emission tomography), and MRI (magnetic resonance imaging) are discussed. Contemporary research results in exact region-of-interest (ROI) reconstruction with truncated projections, Katsevich's cone-beam filtered backprojection algorithm, and reconstruction with highly under-sampled data are included. The last chapter of the book is devoted to the techniques of using a fast analytical algorithm to reconstruct an image that is equivalent to an iterative reconstruction. These techniques are the author's most recent research results. This book is intended for students, engineers, and researchers who are interested in medical image reconstruction. Written in a non-mathematical way, this book provides an easy access to modern mathematical methods in medical imaging. Table of Content:Chapter 1 Basic Principles of Tomography1.1 Tomography1.2 Projection1.3 Image Reconstruction1.4 Backprojection1.5 Mathematical ExpressionsProblemsReferencesChapter 2 Parallel-Beam Image Reconstruction2.1 Fourier Transform2.2 Central Slice Theorem2.3 Reconstruction Algorithms2.4 A Computer Simulation2.5 ROI Reconstruction with Truncated Projections2.6 Mathematical Expressions (The Fourier Transform and Convolution , The Hilbert Transform and the Finite Hilbert Transform , Proof of the Central Slice Theorem, Derivation of the Filtered Backprojection Algorithm , Expression of the Convolution Backprojection Algorithm, Expression of the Radon Inversion Formula ,Derivation of the Backprojection-then-Filtering AlgorithmProblemsReferencesChapter 3 Fan-Beam Image Reconstruction3.1 Fan-Beam Geometry and Point Spread Function3.2 Parallel-Beam to Fan-Beam Algorithm Conversion3.3 Short Scan3.4 Mathematical Expressions (Derivation of a Filtered Backprojection Fan-Beam Algorithm, A Fan-Beam Algorithm Using the Derivative and the Hilbert Transform)ProblemsReferencesChapter 4 Transmission and Emission Tomography4.1 X-Ray Computed Tomography4.2 Positron Emission Tomography and Single Photon Emission Computed Tomography4.3 Attenuation Correction for Emission Tomography4.4 Mathematical ExpressionsProblemsReferencesChapter 5 3D Image Reconstruction5.1 Parallel Line-Integral Data5.2 Parallel Plane-Integral Data5.3 Cone-Beam Data (Feldkamp's Algorithm, Grangeat's Algorithm, Katsevich's Algorithm)5.4 Mathematical Expressions (Backprojection-then-Filtering for Parallel Line-Integral Data, Filtered Backprojection Algorithm for Parallel Line-Integral Data, 3D Radon Inversion Formula, 3D Backprojection-then-Filtering Algorithm for Radon Data, Feldkamp's Algorithm, Tuy's Relationship, Grangeat's Relationship, Katsevich's Algorithm)ProblemsReferencesChapter 6 Iterative Reconstruction6.1 Solving a System of Linear Equations6.2 Algebraic Reconstruction Technique6.3 Gradient Descent Algorithms6.4 Maximum-Likelihood Expectation-Maximization Algorithms6.5 Ordered-Subset Expectation-Maximization Algorithm6.6 Noise Handling (Analytical Methods, Iterative Methods, Iterative Methods)6.7 Noise Modeling as a Likelihood Function6.8 Including Prior Knowledge6.9 Mathematical Expressions (ART, Conjugate Gradient Algorithm, ML-EM, OS-EM, Green's One-Step Late Algorithm, Matched and Unmatched Projector/Backprojector Pairs )6.10 Reconstruction Using Highly Undersampled Data with l0 MinimizationProblemsReferencesChapter 7 MRI Reconstruction7.1 The 'M'7.2 The 'R'7.3 The 'I'; (To Obtain z-Information, x-Information, y-Information)7.4 Mathematical ExpressionsProblemsReferencesIndexing 606 $aMedical sciences 615 0$aMedical sciences. 676 $a618 700 $aZeng$b Gengsheng Lawrence$01110946 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910812387603321 996 $aImage reconstruction$94038790 997 $aUNINA