By Charles L. Epstein
This publication presents an built-in presentation of arithmetic and its software to difficulties in clinical imaging. Key subject matters contain info assortment, sign processing and noise research. The ebook will be compatible for self learn by way of a stimulated individual with a high-quality mathematical heritage attracted to clinical imaging.
Read Online or Download The Mathematics of Medical Imaging PDF
Similar machine theory books
This ebook offers accomplished assurance of the fashionable equipment for geometric difficulties within the computing sciences. It additionally covers concurrent subject matters in information sciences together with geometric processing, manifold studying, Google seek, cloud info, and R-tree for instant networks and BigData. the writer investigates electronic geometry and its similar positive tools in discrete geometry, supplying distinct tools and algorithms.
This booklet constitutes the refereed complaints of the twelfth foreign convention on man made Intelligence and Symbolic Computation, AISC 2014, held in Seville, Spain, in December 2014. The 15 complete papers offered including 2 invited papers have been conscientiously reviewed and chosen from 22 submissions.
This ebook constitutes the refereed court cases of the 3rd overseas convention on Statistical Language and Speech Processing, SLSP 2015, held in Budapest, Hungary, in November 2015. The 26 complete papers awarded including invited talks have been rigorously reviewed and chosen from seventy one submissions.
- Automated Theorem Proving, 1st Edition
- Probabilistic Analysis of Algorithms: On Computing Methodologies for Computer Algorithms Performance Evaluation (Monographs in Computer Science)
- Horizons of the Mind. A Tribute to Prakash Panangaden: Essays Dedicated to Prakash Panangaden on the Occasion of His 60th Birthday (Lecture Notes in Computer Science)
- Algorithmic Learning Theory: 24th International Conference, ALT 2013, Singapore, October 6-9, 2013, Proceedings (Lecture Notes in Computer Science)
- Data Integration: The Relational Logic Approach (Synthesis Lectures on Artificial Intelligence and Machine Learning)
Additional info for The Mathematics of Medical Imaging
Roughly speaking the support of a function is the set of points where the function does not vanish. To get a useful concept we need to add points that are very near to points where the function is non-zero. As the definition is the same in all dimensions we give it for functions defined on Ê n . 1. Let f (x) be a function defined on Ê n . A point x belong to the support of f if there is a sequence of points < xn > such that (1). f (xn ) = 0, (2). limn→∞ xn = x. This set is denoted by supp(f ). CHAPTER 2.
Beer’s law state that di d(log i) = −m(s)i(s) or = −m(s). ds ds Integrating this equation from s = a to s = b gives b i(b) log =− i(a) m(s)ds. 4. We consider a two dimensional example. 2(a). The X-ray source is isotropic which means the outgoing flux is the same in all directions. CHAPTER 2. A BASIC MODEL FOR TOMOGRAPHY 38 r o S source (x,y) (a) A point source of X-rays (b) The flux through a curve not enclosing the source is zero. 2: Analysis of an isotropic point source. Because the source is isotropic, the intensity of the beam is only a function of the distance to the source.
Let e(θ) ≡ 0 be a function that satisfies e(θ) + e(θ + π) = 0. 2 we know that if hD has two derivatives such that hD + hD > 0 then hD (θ) is the shadow function of a strictly convex region. 3. LINEARITY 21 as well, then hD + e is also the shadow function for a different strictly convex region. Observe that hD (θ) + e(θ) is the shadow function for a different region, D which has the same width of shadow for each direction as D. That is wD (θ) = (hD (θ) + e(θ)) + (hD (θ + π) + e(θ + π)) = wD (θ).