Computationally efficient error estimate for evaluation of regularization in photoacoustic tomography

Exploring polynomial based interpolation schemes for photoacoustic tomographic image reconstruction

Photoacoustic tomography (PAT) imaging employing polynomial-based interpolation methods is discussed. Nearest-neighbor, bilinear, bicubic and biquintic algorithms were implemented for the construction of the model matrix, and images were formed using the Tikhonov regularization and total variation (TV) minimization procedures. The performance of the interpolation methods was assessed by comparing the reconstructed images of three numerical and two experimental phantoms. The numerical and experimental studies demonstrate that the performance of the interpolation schemes is nearly equal for large PA sources. The simplest nearest-neighbor technique provides better image reconstruction for a sparse source compared to the others. The nearest-neighbor protocol may be adopted in practice for vascular imaging using PAT.

Dimensionality reduced plug and play priors for improving photoacoustic tomographic imaging with limited noisy data

The reconstruction methods for solving the ill-posed inverse problem of photoacoustic tomography with limited noisy data are iterative in nature to provide accurate solutions. These methods performance is highly affected by the noise level in the photoacoustic data. A singular value decomposition (SVD) based plug and play priors method for solving photoacoustic inverse problem was proposed in this work to provide robustness to noise in the data. The method was shown to be superior as compared to total variation regularization, basis pursuit deconvolution and Lanczos Tikhonov based regularization and provided improved performance in case of noisy data. The numerical and experimental cases show that the improvement can be as high as 8.1 dB in signal to noise ratio of the reconstructed image and 67.98% in root mean square error in comparison to the state of the art methods.

End-to-end Res-Unet based reconstruction algorithm for photoacoustic imaging

Recently, deep neural networks have attracted great attention in photoacoustic imaging (PAI). In PAI, reconstructing the initial pressure distribution from acquired photoacoustic (PA) signals is a typically inverse problem. In this paper, an end-to-end Unet with residual blocks (Res-Unet) is designed and trained to solve the inverse problem in PAI. The performance of the proposed algorithm is explored and analyzed by comparing a recent model-resolution-based regularization algorithm (MRR) with numerical and physical phantom experiments. The improvement obtained in the reconstructed images was more than 95% in pearson correlation and 39% in peak signal-to-noise ratio in comparison to the MRR. The Res-Unet also achieved superior performance over the state-of-the-art Unet++ architecture by more than 18% in PSNR in simulation experiments.

PA-Fuse: deep supervised approach for the fusion of photoacoustic images with distinct reconstruction characteristics

The methods available for solving the inverse problem of photoacoustic tomography promote only one feature-either being smooth or sharp-in the resultant image. The fusion of photoacoustic images reconstructed from distinct methods improves the individually reconstructed images, with the guided filter based approach being state-of-the-art, which requires that implicit regularization parameters are chosen. In this work, a deep fusion method based on convolutional neural networks has been proposed as an alternative to the guided filter based approach. It has the combined benefit of using less data for training without the need for the careful choice of any parameters and is a fully data-driven approach. The proposed deep fusion approach outperformed the contemporary fusion method, which was proved using experimental, numerical phantoms and in-vivo studies. The improvement obtained in the reconstructed images was as high as 95.49% in root mean square error and 7.77 dB in signal to noise ratio (SNR) in comparison to the guided filter approach. Also, it was demonstrated that the proposed deep fuse approach, trained on only blood vessel type images at measurement data SNR being 40 dB, was able to provide a generalization that can work across various noise levels in the measurement data, experimental set-ups as well as imaging objects.

Image-guided filtering for improving photoacoustic tomographic image reconstruction

Several algorithms exist to solve the photoacoustic image reconstruction problem depending on the expected reconstructed image features. These reconstruction algorithms promote typically one feature, such as being smooth or sharp, in the output image. Combining these features using a guided filtering approach was attempted in this work, which requires an input and guiding image. This approach act as a postprocessing step to improve commonly used Tikhonov or total variational regularization method. The result obtained from linear backprojection was used as a guiding image to improve these results. Using both numerical and experimental phantom cases, it was shown that the proposed guided filtering approach was able to improve (as high as 11.23 dB) the signal-to-noise ratio of the reconstructed images with the added advantage being computationally efficient. This approach was compared with state-of-the-art basis pursuit deconvolution as well as standard denoising methods and shown to outperform them.

Accelerated image reconstruction using extrapolated Tikhonov filtering for photoacoustic tomography

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 standard error estimate technique.

RESULTS

Four numerical (including realistic breast phantom) and two experimental phantom data were utilized to show the effectiveness 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 figures of merit.

CONCLUSION

The developed extrapolated Tikhonov filtering methods overcome the difficulty 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.