AIR tools swMATH ID: 9203 Software Authors: Hansen, Per Christian; Saxild-Hansen, Maria Description: AIR tools – a MATLAB package of algebraic iterative reconstruction methods. We present a MATLAB package with implementations of several algebraic iterative reconstruction (AIR) methods for discretizations of inverse problems. These so-called row action methods rely on semi-convergence for achieving the necessary regularization of the problem. Two classes of methods are implemented: Algebraic reconstruction techniques and simultaneous iterative reconstruction techniques. In addition we provide a few simplified test problems from medical and seismic tomography. For each iterative method, a number of strategies are available for choosing the relaxation parameter and the stopping rule. The relaxation parameter can be fixed, or chosen adaptively in each iteration; in the former case we provide a new “training” algorithm that finds the optimal parameter for a given test problem. The stopping rules provided are the discrepancy principle, the monotone error rule, and the normalixed cumulative periodogram criterion; for the first two methods “training” can be used to find the optimal discrepancy parameter. Homepage: http://www.imm.dtu.dk/~pcha/AIRtools/ Dependencies: Matlab Keywords: semi-convergence; relaxation parameters; stopping rules; tomographic imaging; numerical examples; MATLAB package; algebraic iterative reconstruction (AIR) methods; inverse problems; row action methods; algebraic reconstruction techniques; simultaneous iterative reconstruction techniques; discrepancy principle; monotone error rule Related Software: Regularization tools; IR Tools; UTV; LSQR; ASTRA; Matlab; RestoreTools; SparseMatrix; SNARK09; LSMR; TFOCS; TIGRE; GitHub; HyBR; SNARK93; PDCO; CVX; UNLocBoX; RecPF; FOM Cited in: 99 Publications all top 5 Cited by 172 Authors 17 Hansen, Per Christian 8 Nikazad, Touraj 7 Nagy, James Gerard 6 Andersen, Martin S. 6 Dong, Yiqiu 6 Elfving, Tommy 6 Gazzola, Silvia 4 Chung, Julianne M. 4 Jin, Qinian 4 Jørgensen, Jakob Sauer 3 Abbasi, Mokhtar 3 Gibali, Aviv 3 Hochstenbach, Michiel E. 3 Hu, Yunyi 3 Jia, Zhongxiao 3 Jiang, Jiahua 3 Karimpour, Mehdi 3 Lorenz, Dirk Alfred 2 Brogaard Riis, Nicolai André 2 Censor, Yair 2 de Sturler, Eric 2 Gu, Chuanqing 2 Heaton, Howard 2 Hubmer, Simon 2 Kilmer, Misha Elena 2 Lei, Yunwen 2 Liu, Yong 2 Luiken, Nick 2 Miller, Eric L. 2 Quinto, Eric Todd 2 Ramlau, Ronny 2 Schöpfer, Frank 2 Soltani, Sara 2 van Leeuwen, Tristan 2 van Lith, Bart S. 2 Vuong, Phan Tu 2 Webber, James W. 2 Wu, Chunlin 2 Zhou, Dingxuan 1 Abe, Kuniyoshi 1 Afzalipour, Laya 1 Babyn, Paul 1 Bangsgaard, Katrine O. 1 Bao, Wendi 1 Behling, Roger 1 Bello Cruz, Jose Yunier 1 Benvenuto, Federico 1 Bonettini, Silvia 1 Boos, Everton 1 Bubba, Tatiana A. 1 Buccini, Alessandro 1 Carter, Yasmin 1 Castañeda, Victor 1 Cegielski, Andrzej 1 Cengiz, Kubra 1 Chen, Xueqi 1 Cho, Taewon 1 Cipolla, Stefano 1 Cornelis, Jeffrey 1 Courdurier, Matias 1 Cueva, Evelyn 1 De Asmundis, Roberta 1 Debarre, Thomas 1 di Serafino, Daniela 1 Donatelli, Marco 1 Donati, Laurène 1 Dương Việt Thông 1 Durastante, Fabio 1 Fang, Xiaofeng 1 Fosodeder, Peter 1 Frøsig, J. 1 Guo, Hongbin 1 Guo, Xueping 1 Härtel, Steffen 1 Hayami, Ken 1 Heidarzade, Shsghayegh 1 Higham, Nicholas J. 1 Hinterer, Fabian 1 Hnětynková, Iveta 1 Huang, Guang-Xin 1 Jiang, Xianglong 1 Jiao, Yuling 1 Jin, Bangti 1 Kamasak, Mustafa 1 Kang, Chuangang 1 Karapiperi, Anna 1 Kazantsev, Daniil 1 Kiefer, Lukas 1 Kruschel, Christian 1 Kubínová, Marie 1 Landi, Germana 1 Lee, Peter D. 1 Lei, Jing 1 Li, Weiguo 1 Li, Yingqi 1 Lin, Youzuo 1 Lionheart, William Robert Breckon 1 Liu, Shi 1 Liu, Yanli 1 Lou, Yifei ...and 72 more Authors all top 5 Cited in 37 Serials 20 Inverse Problems 13 SIAM Journal on Scientific Computing 12 Numerical Algorithms 7 Journal of Computational and Applied Mathematics 4 Inverse Problems and Imaging 3 Linear Algebra and its Applications 3 Inverse Problems in Science and Engineering 3 SIAM Journal on Imaging Sciences 2 Applied Mathematics and Computation 2 BIT 2 Journal of Scientific Computing 2 Numerical Linear Algebra with Applications 2 Computational & Mathematical Methods in Medicine 1 Computers & Mathematics with Applications 1 Calcolo 1 Numerical Functional Analysis and Optimization 1 Numerische Mathematik 1 Quarterly of Applied Mathematics 1 SIAM Journal on Control and Optimization 1 Applied Numerical Mathematics 1 Applied Mathematics Letters 1 SIAM Journal on Matrix Analysis and Applications 1 Journal of Global Optimization 1 Applied Mathematical Modelling 1 Mathematical Programming. Series A. Series B 1 Computational Optimization and Applications 1 Applied and Computational Harmonic Analysis 1 Journal of Mathematical Sciences (New York) 1 Turkish Journal of Mathematics 1 Journal of Inverse and Ill-Posed Problems 1 Mathematical Problems in Engineering 1 Acta Mathematica Sinica. English Series 1 Foundations of Computational Mathematics 1 Journal of Industrial and Management Optimization 1 Mathematical Modelling of Natural Phenomena 1 East Asian Journal on Applied Mathematics 1 Results in Applied Mathematics all top 5 Cited in 16 Fields 84 Numerical analysis (65-XX) 24 Information and communication theory, circuits (94-XX) 19 Operations research, mathematical programming (90-XX) 18 Biology and other natural sciences (92-XX) 15 Linear and multilinear algebra; matrix theory (15-XX) 13 Computer science (68-XX) 11 Integral transforms, operational calculus (44-XX) 9 Operator theory (47-XX) 8 Calculus of variations and optimal control; optimization (49-XX) 4 Statistics (62-XX) 2 Partial differential equations (35-XX) 2 Convex and discrete geometry (52-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Probability theory and stochastic processes (60-XX) 1 Optics, electromagnetic theory (78-XX) 1 Quantum theory (81-XX) Citations by Year