Accelerated image reconstruction using extrapolated Tikhonov filtering for photoacoustic tomography

Abstract

Purpose: Development of simple and computationally efficient extrapolated Tikhonov filtering reconstruction methods for photoacoustic tomography. Methods: The model-based reconstruction algorithms in photoacoustic tomography typically utilize Tikhonov regularization scheme for the reconstruction of initial pressure distribution from the measured boundary acoustic data. The automated choice of regularization parameter in these cases is computationally expensive. Moreover, the Tikhonov scheme promotes the smooth features in the reconstructed image due to the smooth regularizer, thus leading to loss of sharp features. The proposed extrapolation method estimates the solution at zero regularization assuming the solution being a function of regularization parameter and thus posing it as a zero value problem. Thus the numerically computed zero regularization solution is expected to have better features compared to standard Tikhonov solution, with an added advantage of removing the necessity of automated choice of regularization. The reconstructed results using this method, were shown in three variants (Lanczos, Traditional, and Exponential) of Tikhonov filtering and were compared with the stan- dard error estimate technique. Results: Four numerical (including realistic breast phantom) and two experimental phantom data was utilized to show the e ectiveness of the proposed method. It was shown that the proposed method performance was superior than the standard error estimate technique, being at least four times faster in terms of computation, and provides an improvement as high as 2.6 times in terms of standard gures of merit. Conclusion: The developed extrapolated Tikhonov ltering methods overcome the di culty of obtaining a suitable regularization parameter and shown to be reconstructing high quality photoacoustic images with additional advantage of being computationally efficient, making it more appealing in real-time applications.