Constrained Kaczmarz extended algorithm for image reconstruction
نویسندگان
چکیده
منابع مشابه
Kaczmarz extended algorithm for tomographic image reconstruction from limited-data
The Algebraic Reconstruction Technique (ART), based on the well known algorithm proposed by S. Kaczmarz in 1937, is one of the most important class of solution methods for image reconstruction problems. But unfortunately, almost all the methods from the ART class give satisfactory results only in the case of consistent problems. In the inconsistent case (and unfortunately this is what happens i...
متن کاملA Hybrid Kaczmarz – Cg Algorithm for Inconsistent Systems Arising in Image Reconstruction
Tomographic image reconstruction is the process of reconstructing an object or its cross section from several images of its projections. In the 2D case the object is illuminated by a fan-beam of X-rays, where the signal is attenuated by the object. This leads to a linear system of equations with a sparse matrix, because each observation is influenced only by the pixels on the corresponding beam...
متن کاملRandomized Extended Kaczmarz for Solving Least-Squares
We present a randomized iterative algorithm that exponentially converges in expectation to the minimum Euclidean norm least squares solution of a given linear system of equations. The expected number of arithmetic operations required to obtain an estimate of given accuracy is proportional to the square condition number of the system multiplied by the number of non-zeros entries of the input mat...
متن کاملFaster Alternatives to the Randomized Extended Kaczmarz Algorithm
In this note we compare the randomized extended Kaczmarz (EK) algorithm and randomized coordinate descent (CD) for solving the full-rank overdetermined linear least-squares problem and prove that CD is always faster than EK. For the general least-squares problems, we show that running first CD to compute the residual and then standard Kaczmarz on the resulting consistent system is more efficien...
متن کاملA Sparsity-Constrained Preconditioned Kaczmarz Reconstruction Method for Fluorescence Molecular Tomography
Fluorescence molecular tomography (FMT) is an imaging technique that can localize and quantify fluorescent markers to resolve biological processes at molecular and cellular levels. Owing to a limited number of measurements and a large number of unknowns as well as the diffusive transport of photons in biological tissues, the inverse problem in FMT is usually highly ill-posed. In this work, a sp...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 2008
ISSN: 0024-3795
DOI: 10.1016/j.laa.2008.06.024