The development of fast and accurate image reconstruction algorithms is a central aspect of computed tomography. In this paper we address this issue for photoacoustic computed tomography in circular geometry. We investigate the Galerkin least squares method for that purpose. For approximating the function to be recovered we use subspaces of translation invariant spaces generated by a single function. This includes many systems that have previously been employed in photoacoustic tomography, such as generalized Kaiser--Bessel basis functions or the natural pixel basis. By exploiting an isometry property of the forward problem we are able to efficiently set up the Galerkin equation for a wide class of generating functions and devise efficient algorithms for its solution. We establish a convergence analysis and present numerical simulations that demonstrate the efficiency and accuracy of the derived algorithm.


  1. photoacoustic imaging
  2. computed tomography
  3. Galerkin least squares method
  4. Kaiser--Bessel functions
  5. Radon transform
  6. least squares approach

MSC codes

  1. 65R32
  2. 45Q05
  3. 92C55

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Information & Authors


Published In

cover image SIAM Journal on Numerical Analysis
SIAM Journal on Numerical Analysis
Pages: 160 - 184
ISSN (online): 1095-7170


Submitted: 22 December 2016
Accepted: 19 October 2017
Published online: 9 January 2018


  1. photoacoustic imaging
  2. computed tomography
  3. Galerkin least squares method
  4. Kaiser--Bessel functions
  5. Radon transform
  6. least squares approach

MSC codes

  1. 65R32
  2. 45Q05
  3. 92C55



Sergiy Pereverzyev, Jr.

Funding Information

Tyrolean Science Fund

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