Image reconstruction in Photoacoustic tomography (PAT)
Multi-angle PAT to compensate finite transducer size effects:
Tangential resolution in circular scan photoacoustic tomography is dependent on the transducer size and the distance from the scanning center. To address this problem, a multi-angle detection approach was proposed in which the transducer used for data acquisition rotates around its center (with specific angles) as well as around the scanning center. The angles are calculated based on the central frequency and the diameter of the transducer and the radius of the region-of-interest. Simulation and experimental results show a location independent tangential resolution can be achieved with this approach (similar to point-like transducer with large angular view). More details can be found in Hakakzadeh et al., Photoacoustics 27 (2022).
Tangential resolution improvement in PAT/TAT:
Spatial resolution in photoacoustic and thermoacoustic tomography is ultrasound transducer (detector) bandwidth limited. For a circular scanning geometry the axial (radial) resolution is not affected by the detector aperture, but the tangential (lateral) resolution is highly dependent on the aperture size, and it is also spatially varying (depending on the location relative to the scanning center). Several approaches have been reported to counter this problem by physically attaching negative acoustic lens in front of the non-focused transducer, or using virtual point detectors. Here, we have implemented a modified delay-and-sum reconstruction method, which takes into account the large aperture of the detector, leading to more than fivefold improvement in the tangential resolution in photoacoustic (and thermoacoustic) tomography. It is also shown that, we were able to preserve the shape of the reconstructed objects with modified algorithm. More details can be found in Pramanik, JOSA A 31 (2014).
The modified delay-and-sum reconstruction algorithm was further demonstrated for cylindrical focused transducer, which is also commonly used in photoacoustic tomography. More than threefold improvement was observed on experimental data using tissue phantoms. More details can be found in Kalva et al., Journal of Biomedical Optics 21 (2016).
Deblurring of Reconstructed Image in PAT/TAT:
Due to broad excitation of laser/microwave the reconstructed image gets blurring effect. Moreover, the limited bandwidth of the ultrasound detector used in PAT/TAT also introduces blurring. Deconvolution techniques can be used to reduce these blurring effects. Deconvolution in practical situations is considered as an ill posed problem, whose solution can’t be uniquely defined, especially if the data is corrupted with noise. Based on the practical observations, a conditioned solution set is obtained to get least error solutions. For example, a tikhonov regularization based least squares approximation to find the best possible solution. Figure below shows the blurring of reconstructed images longer excitation pulse, followed by images which have been corrected by deconvolution operation. The same procedure can be adopted to remove the blurring effect due to the band limiting effect of the transducer. Transducer response is mapped as a digital filter, whose effect is removed by performing a two level deconvolution operation. More details can be found in Rejesh et al., JOSA A 30 (2013).
Model based reconstruction for PAT/TAT:
In PAT/TAT the ultimate goal is to get the absorption map of the object from the detected pressure waves around the object boundary. This is done through reconstruction method, where, the estimation of initial pressure distribution is obtained. The initial pressure distribution is related to the absorption map. MATLAB based k-wave toolbox can be used to do the reconstruction using time reversal method, or simple delay-and-sum approach can also be used. However, use of these analytical reconstruction method and their limitations include requirement of large amount of data and are limited in terms of quantitative estimation. In order to improve the quantitative accuracy various iterative schemes were proposed but the major drawback in these schemes are solving large system of equations. To overcome this limitation, a computationally efficient approach that computes the optimal regularization parameter for the Tikhonov-minimization scheme is developed for photoacoustic imaging. This approach is based on the least squares-QR (LSQR) decomposition which is a well-known dimensionality reduction technique for a large system of equations. It is shown that the proposed framework is effective in terms of quantitative and qualitative reconstructions of initial pressure distribution enabled via finding an optimal regularization parameter. More details can be found in Shaw et al., Journal of Biomedical Optics 18 (2013).
These model based reconstruction schemes are found to induce blur due to the usage of regularization parameter. A model resolution characteristics is explored and shown that the blur induced by the usage of regularization can be modeled, and further a basis pursuit deconvolution (BPD) framework is adopted and shown that deconvolution using this framework provides accurate reconstruction with less number of data points (transducer positions). This model resolution matrix and BPD estimation is performed using a least-square QR (LSQR) approach for providing computational efficiency to the proposed method. It is also shown that the proposed method does not require estimation of optimal regularization parameter, and it is enough to have the regularization parameter within a specified bound to obtain reasonably accurate initial pressure distribution. More details can be found in Prakash et al., Biomedical Optics Express 5 (2014).