Photoacoustic (PA) signals collected at the boundary of tissue are always band-limited. A deep neural network was proposed to enhance the bandwidth (BW) of the detected PA signal, thereby improving the quantitative accuracy of the reconstructed PA images. A least square-based deconvolution method that utilizes the Tikhonov regularization framework was used for comparison with the proposed network. The proposed method was evaluated using both numerical and experimental data. The results indicate that the proposed method was capable of enhancing the BW of the detected PA signal, which inturn improves the contrast recovery and quality of reconstructed PA images without adding any significant computational burden.

Model-based image reconstruction techniques yield better quantitative accuracy in photoacoustic image reconstruction. In this work, an exponential filtering of singular values was proposed for carrying out the image reconstruction in photoacoustic tomography. The results were compared with widely popular Tikhonov regularization, time reversal, and the state of the art least-squares QR-based reconstruction algorithms for three digital phantom cases with varying signal-to-noise ratios of data. It was shown that exponential filtering provides superior photoacoustic images of better quantitative accuracy. Moreover, the proposed filtering approach was observed to be less biased toward the regularization parameter and did not come with any additional computational burden as it was implemented within the Tikhonov filtering framework. It was also shown that the standard Tikhonov filtering becomes an approximation to the proposed exponential filtering.

The limited data photoacoustic image reconstruction problem is typically solved using either weighted or ordinary least squares (LS), with regularization term being added for stability, which account only for data imperfections (noise). Numerical modeling of acoustic wave propagation requires discretization of imaging region and is typically developed based on many assumptions, such as speed of sound being constant in the tissue, making it imperfect. In this work, two variants of total least squares (TLS), namely ordinary TLS and Sparse TLS were developed, which account for model imperfections. The ordinary TLS is implemented in the Lanczos bidiagonalization framework to make it computationally efficient. The Sparse TLS utilizes the total variation penalty to promote recovery of high frequency components in the reconstructed image. The Lanczos truncated TLS (Lanczos T-TLS) and Sparse TLS methods were compared with the recently established state-of-the-art methods, such as Lanczos Tikhonov and Exponential Filtering. The TLS methods exhibited better performance for experimental data as well as in cases where modeling errors were present, such as few acoustic detectors malfunctioning and speed of sound variations. Also, the TLS methods does not require any prior information about the errors present in the model or data, making it attractive for real-time scenarios.

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.

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