Frank Natterer (20 July 1941) is a German mathematician. He was born in

Wangen im Allgäu Wangen im Allgäu ( Low Alemannic: ''Wãnge'') is a historic city in southeast Baden-Württemberg, Germany. It lies north-east of Lake Constance in the Westallgäu. It is the second-largest city (Population: 26,927 in 2020) in the Ravensburg dist ...

Germany Germany,, officially the Federal Republic of Germany, is a country in Central Europe. It is the second most populous country in Europe after Russia, and the most populous member state of the European Union. Germany is situated betwe ...

. Natterer pioneered and shaped the field of mathematical methods in

imaging Imaging is the representation or reproduction of an object's form; especially a visual representation (i.e., the formation of an image). Imaging technology is the application of materials and methods to create, preserve, or duplicate images. ...

including

computed tomography A computed tomography scan (CT scan; formerly called computed axial tomography scan or CAT scan) is a medical imaging technique used to obtain detailed internal images of the body. The personnel that perform CT scans are called radiographers ...

(CT),

magnetic resonance imaging Magnetic resonance imaging (MRI) is a medical imaging technique used in radiology to form pictures of the anatomy and the physiological processes of the body. MRI scanners use strong magnetic fields, magnetic field gradients, and radio wave ...

(MRI) and ultrasonic imaging.

Career

After studies at the Universities of

Freiburg Freiburg im Breisgau (; abbreviated as Freiburg i. Br. or Freiburg i. B.; Low Alemannic: ''Friburg im Brisgau''), commonly referred to as Freiburg, is an independent city in Baden-Württemberg, Germany. With a population of about 230,000 (as o ...

and

Hamburg (male), (female) en, Hamburger(s), Hamburgian(s) , timezone1 = Central (CET) , utc_offset1 = +1 , timezone1_DST = Central (CEST) , utc_offset1_DST = +2 , postal ...

Frank Natterer in 1968 earned his PhD with a thesis "Einschließungen für die großen Eigenwerte gewöhnlicher Differentialgleichungen zweiter und vierter Ordnung" under the supervision of Prof. Lothar Collatz. In 1971, he made the habilitation "Verallgemeinerte Splines und singuläre Rand-Eigenwertaufgaben gewöhnlicher Differentialgleichungen". Following a visiting assistant professorship at

Indiana University Bloomington Indiana University Bloomington (IU Bloomington, Indiana University, IU, or simply Indiana) is a public university, public research university in Bloomington, Indiana. It is the flagship university, flagship campus of Indiana University and, with ...

Indiana Indiana () is a U.S. state in the Midwestern United States. It is the 38th-largest by area and the 17th-most populous of the 50 States. Its capital and largest city is Indianapolis. Indiana was admitted to the United States as the 19th s ...

(USA) he was full professor at the

Universität des Saarlandes Saarland University (german: Universität des Saarlandes, ) is a public research university located in Saarbrücken, the capital of the German state of Saarland. It was founded in 1948 in Homburg in co-operation with France and is organized in si ...

, Saarbrücken (Germany), from 1973-1981. He was Director of the "Institut für Numerische und instrumentelle Mathematik" of the Westfälische Wilhelms Universität,

Münster Münster (; nds, Mönster) is an independent city (''Kreisfreie Stadt'') in North Rhine-Westphalia, Germany. It is in the northern part of the state and is considered to be the cultural centre of the Westphalia region. It is also a state distr ...

, Germany, from 1981 until he retired from active teaching in 2006. In 2002, he received an honorary doctorate at

in recognition of his leading role and achievements in the field of mathematical methods in imaging. He has published close to 100 scientific papers and two books and is in possession of numerous patents.

Scientific work

In 1975, Natterer proved pointwise convergence of

finite element method The finite element method (FEM) is a popular method for numerically solving differential equations arising in engineering and mathematical modeling. Typical problem areas of interest include the traditional fields of structural analysis, heat ...

s. Starting in 1977, he focused on mathematical methods in

. In this field, he not only developed algorithms but also worked on tomographic scanners. His two books on this topic, "The Mathematics of Computerized Tomography" (1986, translated to Russian in 1990, new edition in 2001 in the series „Classics in Applied Mathematics"), and "Mathematical Methods in Image Reconstruction" (2001)) are considered standard works in this field of science. His main scientific contributions to the area of

are: *Stability analysis of the

Radon transformation In mathematics, the Radon transform is the integral transform which takes a function ''f'' defined on the plane to a function ''Rf'' defined on the (two-dimensional) space of lines in the plane, whose value at a particular line is equal to the l ...

Sobolev space In mathematics, a Sobolev space is a vector space of functions equipped with a norm that is a combination of ''Lp''-norms of the function together with its derivatives up to a given order. The derivatives are understood in a suitable weak sense t ...

s *Consistency conditions for the exponential

with applications in

positron emission tomography Positron emission tomography (PET) is a functional imaging technique that uses radioactive substances known as radiotracers to visualize and measure changes in Metabolism, metabolic processes, and in other physiological activities including bl ...

*Regularization of

inverse problem An inverse problem in science is the process of calculating from a set of observations the causal factors that produced them: for example, calculating an image in X-ray computed tomography, source reconstruction in acoustics, or calculating the ...

s with discretization and projection methods. * sampling theorems (optimal resolution with minimal number of measurements) in tomography *Fourier reconstruction *Fast algorithms in ultrasonic tomography. In this field, he successfully regularized the classic example of

Hadamard Jacques Salomon Hadamard (; 8 December 1865 – 17 October 1963) was a French mathematician who made major contributions in number theory, complex analysis, differential geometry and partial differential equations. Biography The son of a teac ...

, the

Cauchy problem A Cauchy problem in mathematics asks for the solution of a partial differential equation that satisfies certain conditions that are given on a hypersurface in the domain. A Cauchy problem can be an initial value problem or a boundary value proble ...

for

elliptic partial differential equation Second-order linear partial differential equations (PDEs) are classified as either elliptic, hyperbolic, or parabolic. Any second-order linear PDE in two variables can be written in the form :Au_ + 2Bu_ + Cu_ + Du_x + Eu_y + Fu +G= 0,\, wher ...

s Natterer’s scientific work has been very relevant in the development of modern methods of imaging in

(CT),

(MRI), Ultrasonic Imaging and

(PET).

Service to the scientific community

From 1995 to 1999, Natterer was the honorary editor of the journal ''Inverse Problems'' and since 2000 he has been a member of the "International Advisory Panel of Inverse Problems". Since 1997, he has been on the editorial board of ''The Journal of Fourier Analysis and Applications''. He has also been involved with "IEEE Transactions on Medical Imaging", "Journal of Inverse and Ill-Posed Problems", "International Journal of Imaging Systems and Technology", and the ''SIAM Journal on Applied Mathematics''. He was member of the Committee on the Mathematics and Physics of Emerging Dynamic Biomedical Imaging of the National Research Council of the USA. Natterer has organized numerous conferences on the topics of

inverse problems An inverse problem in science is the process of calculating from a set of observations the causal factors that produced them: for example, calculating an image in X-ray computed tomography, source reconstruction in acoustics, or calculating the ...

and on the mathematical methods of

. In 1980, he founded the series of conferences "Mathematical Methods in Tomography“ at the

Mathematical Research Institute of Oberwolfach The Oberwolfach Research Institute for Mathematics (german: Mathematisches Forschungsinstitut Oberwolfach) is a center for mathematical research in Oberwolfach, Germany. It was founded by mathematician Wilhelm Süss in 1944. It organizes weekl ...

. He was a faculty member in numerous scientific summer schools.

Other work

Frank Natterer is a member of the German

Proust Valentin Louis Georges Eugène Marcel Proust (; ; 10 July 1871 – 18 November 1922) was a French novelist, critic, and essayist who wrote the monumental novel ''In Search of Lost Time'' (''À la recherche du temps perdu''; with the previous Eng ...

Society and has published an article on Proust and mathematics.

Personal life

He has been married to Renate Natterer since 1967. They have two adult sons. He is the father in law of Chinese singer

Karen Mok Karen Mok (born Karen Joy Morris (), 2 June 1970) is a Hong Kong pop diva who is one of the leading Asian pop singers and actresses with a career spanning three decades. She is the first female Hong Kong singer to win the Golden Melody Award and ...

References

External links

Homepage of Frank Natterer

Institut für Numerische und Angewandte Mathematik der Universität Münster

Mathematical Research Institute of Oberwolfach

German Proust Society
* {{DEFAULTSORT:Natterer, Frank 1941 births Living people People from Wangen im Allgäu 20th-century German mathematicians University of Münster Saarland University 21st-century German mathematicians