A Galerkin least squares approach for photoacoustic tomography. (English) Zbl 1422.65464
Summary: 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.
MSC:
| 65R32 | Numerical methods for inverse problems for integral equations |
| 45Q05 | Inverse problems for integral equations |
| 92C55 | Biomedical imaging and signal processing |
Keywords:
photoacoustic imaging; computed tomography; Galerkin least squares method; Kaiser-Bessel functions; Radon transform; least squares approachSoftware:
k-WaveReferences:
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