Improving photoacoustic imaging with model compensating and deep learning methods

Abstract

Photoacoustic imaging is a hybrid biomedical imaging technique combining optical ab- sorption contrast with ultrasonic resolution. It is a non-invasive technique that is scalable to reveal structural, functional, and molecular information of the tissue under investiga- tion. The important step in photoacoustic tomography is image reconstruction, which enables quanti cation of tissue functional properties. The photoacoustic image recon- struction problem is typically ill-posed and requires an utilization of regularization to provide meaningful results. The aim of this thesis work is to develop methods that can improve photoacoustic image reconstruction, especially in realistic imaging scenar- ios, where the utility of standard image reconstruction methods is limited in terms of providing good quality photoacoustic images. The photoacoustic image reconstruction problem is typically solved using either weighted or ordinary least squares (LS), with regularization term being added for stabil- ity, 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. Two variants of total least squares (TLS) were proposed, namely ordinary TLS and Sparse TLS, 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 re- constructed 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 do not require any prior information about the errors present in the model or data, making it attractive for real-time scenarios. The model-based reconstruction methods, such as Tikhonov regularization scheme, require an appropriate selection of explicit regularization parameter, which is a com- putationally expensive procedure. The Tikhonov scheme promotes the smooth features in the reconstructed image due to the smooth regularizer, thus leading to loss of sharp features. A simple and computationally efficient extrapolation method was developed, which provides the solution at zero regularization, by assuming that the solution is a function of regularization. The reconstructed results using this method were shown in three variants (Lanczos, Traditional, and Exponential) of Tikhonov ltering on numer- ical and experimental phantom data. The proposed extrapolation method performance was shown to be superior than the standard error estimate technique with an added advantage of being atleast four times faster in terms of computation, and providing an improvement as high as 2.6 times in terms of standard gures of merit. Photoacoustic signals collected at the boundary of tissue are always band-limited. A deep neural network (DNN) with ve fully connected layers (similar to the decoder network) was proposed to enhance the bandwidth of the detected photoacoustic signal, thereby improving the quantitative accuracy of the reconstructed photoacoustic images. A least square based deconvolution method that utilizes the Tikhonov regularization framework was used for comparison with the proposed network. The DNN-based method was evaluated using both numerical and experimental data. The results show that the DNN-based method was capable of enhancing the bandwidth of the detected photoa- coustic signal, which in turn improves the contrast recovery and quality of reconstructed photoacoustic images without adding any signi cant computational burden. Analytical photoacoustic image reconstruction methods such as back-projection re- quire large amount of data for accurate reconstruction of initial pressure distribution. Model-based iterative algorithms are proven to provide quantitatively accurate recon- structions compared to analytical methods in limited data cases. These methods start from an initial guess of the solution (obtained through analytical methods) and itera- tively improve the solution via applying regularization. These are challenging to deploy in real-time due to their high computational complexity and also difficulty in choosing optimal reconstruction parameters. A deep convolutional neural network, with archi- tecture similar to SRGAN, a generative adversarial network (GAN) to obtain images of super resolution (SR), was utilized in the photoacoustic image reconstruction pro- cess to provide desired image characteristics obtainable by model-based algorithms with computation effciency equal to analytical methods. The network was trained with back- projected reconstruction as input and output being ground truth image. The proposed method was evaluated using both numerical and experimental phantoms and was shown to be superior compared to the state-of-the-art model-based methods. Moreover, the proposed method takes approximately one second on the GPU, making the approach attractive in real-time.