Photoacoustic computed tomography (PACT) is an emerging biomedical imaging technology that has attracted substantial attention and interest. Recently, Prof. Chao Tian from the University of Science and Technology of China, in collaboration with Prof. Meng Yang from Peking Union Medical College Hospital, Prof. Jie Tian from the Institute of Automation, Chinese Academy of Sciences, and other leading experts in the field of photoacoustic imaging, jointly authored a full review article titled "Image reconstruction from photoacoustic projections", which was published in the Issue 3 of Photonics Insights, 2024. ( Chao Tian, Kang Shen, Wende Dong, et al. Image reconstruction from photoacoustic projections[J]. Photonics Insights, 2024, 3(3): R06)

The review provides a systematic overview of the key achievements in PACT image reconstruction algorithms in the past three decades. It addresses essential topics such as the forward problem in PACT, conventional reconstruction algorithms, deep learning-based reconstruction algorithms, performance comparisons of different algorithms, critical challenges and future directions, as summarized in Figure 1.

Figure 1. Main contents covered in this review.

Prof. Alexander A. Oraevsky, a leading scientist and the "father of biomedical photoacoustic imaging", wrote a commentary article for this review (Image reconstruction from photoacoustic projections), he commented that "the article contains an in-depth and fascinating comparative analysis of PACT image reconstruction algorithms, ranging from conventional to machine learning algorithms, which is well-structured, supplemented with detailed illustrations, and presented in a manner that is accessible to both novices and experts in the field, and thus contribute to the development of novel algorithms for PACT. We believe that this review will offer new insights and perspectives that could inspire further advancements in the field of photoacoustic image reconstruction.

1. The Forward Problem

In 1880, Alexander Graham Bell discovered the photoacoustic effect—modulated light can excite sound waves in materials. Based on this phenomenon, photoacoustic tomography (PAT) uses short-pulsed lasers to illuminate biological tissues, generating acoustic signals that can reflect the structure, function, molecular, and metabolic information of deep biological tissues.

PACT, a major embodiment of PAT, employs diffused light to illuminate biological tissues and can achieve spatial resolution at the hundred-micron scale at tissue depths of several centimeters. The imaging process of PACT involves two problems: the forward problem and the inverse problem. The forward problem entails the generation, propagation, and detection of photoacoustic signals, which can be described by the spherical or circular Radon transforms (Figure 2). The inverse problem refers to reconstructing initial photoacoustic images from detected photoacoustic signals (sinograms), which can be described by the inverse Radon transform (Figure 2).

In the forward problem, signal generation refers to the process of laser excitation of photoacoustic signals. Efficient excitation of photoacoustic signals requires satisfying both the thermal and stress confinement conditions. Signal propagation refers to the travel of sound waves in complex media, which can be described by a second-order photoacoustic wave equation or three first-order equations, namely, the linearized equation of motion, the linearized equation of continuity, and the thermal elastic equation. In lossless homogeneous media, the photoacoustic wave equation can be solved analytically using the Green's function. Signal detection refers to the process of photoacoustic signals sensing by ultrasound detectors. In practice, it is necessary to capture photoacoustic signals from multiple directions via detector arrays to enable accurate image reconstruction.

Figure 2. Circular Radon transforms and its inverse in PACT.

2. Conventional Approaches

In PACT, photoacoustic signals collected by detectors are computed to form initial images using image reconstruction algorithms (inverse Radon transform). Therefore, image reconstruction algorithms play a crucial role in PACT imaging. As shown in Figure 3, current photoacoustic image reconstruction algorithms fall into two main categories: conventional methods and deep learning (DL)-based methods. Conventional reconstruction techniques mainly include delay and sum (DAS)-type algorithms, filtered back projection (FBP), series expansion (SE), time reversal (TR), and iterative reconstruction (IR) algorithms.

Figure 3 Key events in the development of PACT image reconstruction algorithms.

Delay and sum (DAS)-type algorithms, originating from ultrasound imaging, reconstruct photoacoustic images by summing delayed raw signals of each detector. Although simple, fast, and robust, the basic DAS algorithm may produce significant sidelobes. Subsequent variants such as delay multiply and sum (DMAS), short-lag spatial coherence (SLSC), minimum variance (MV), and coherence factor (CF) methods can effectively enhance the quality of image reconstruction.

Filtered back projection (FBP) algorithms first filter measured photoacoustic signals and then back-project them into the image domain for image reconstruction. They can achieve more accurate reconstructions than DAS. Under the condition of far-field approximation, FBP algorithms can approximately achieve image reconstruction by inverting the linear Radon transform. With correction to the back-projection term, FBP can achieve accurate image reconstruction under specific detection geometries without relying on the far-field approximation condition.

Series expansion (SE) algorithms utilize mathematical series to approximate the image to be reconstructed. These algorithms can achieve efficient image reconstruction for specific detection geometries such as planar surfaces by leveraging the fast Fourier transform (FFT).

Time reversal (TR) algorithms reconstruct images via numerically reversing a forward acoustic propagation model and re-transmitting the photoacoustic signals measured by each detector into the image domain in a temporally reversed order. TR algorithms can couple the acoustic properties of biological tissues, such as sound of speed (SOS), density, dispersion, and absorption, and are applicable for image reconstruction in arbitrary closed detection geometry. They are thus regarded as the "least restrictive" image reconstruction methods in PACT.

Iterative reconstruction (IR) algorithms iteratively reconstruct images by constructing a set of linear equations and a system matrix based on a discrete photoacoustic imaging model. In contrast to other algorithms, IR algorithms can integrate the physical models of an imaging system, accounting for factors such as transducer responses and acoustic heterogeneity. This ability allows for high-quality image reconstruction even under non-ideal conditions such as sparse- and limited-view imaging.

3. Deep Learning Approaches

In addition to the five conventional image reconstruction methods, deep learning (DL)-based algorithms have also been widely used in photoacoustic image reconstruction in recent years. DL-based approaches utilize neural networks to automatically map input data to output images, as shown in Figure 4. In general, the application of DL-based algorithms in PACT are mainly reflected in five aspects: preprocessing in the data domain, postprocessing in the image domain, hybrid-domain processing, learned iterative reconstruction, and direct reconstruction.

Figure 4 DL-based image reconstruction algorithms.

Preprocessing in the data domain involves enhancing raw projection data via neural networks before applying conventional methods for reconstruction. This approach helps mitigate issues such as incomplete data under non-ideal imaging conditions. Postprocessing in the image domain refines conventionally reconstructed images by removing artifacts using deep neural networks. Hybrid-domain processing combines preprocessing and postprocessing to improve image quality. Learned iterative reconstruction incorporates neural networks into conventional IR reconstruction models, improving both quality and efficiency. Direct reconstruction trains neural networks to map raw photoacoustic projection data directly to reconstructed images, bypassing conventional techniques.

4. Performance Comparisons

In terms of image reconstruction performance, photoacoustic image reconstruction algorithms can generally achieve high-quality image reconstruction under ideal imaging conditions. However, under actual non-ideal conditions, the performance of different algorithms varies. For instance, when the detector has limited bandwidth, limited aperture, sparse sampling, or restricted view angles, photoacoustic signals received by a detector are often distorted and incomplete, imposing great challenges to most algorithms. However, IR and DL algorithms can achieve high-quality image reconstruction by incorporating physical models into system matrices or training data (Table 1). When strong acoustic heterogeneities, such as bones and air cavities, are present in biological tissues, DAS and FBP algorithms are easily affected. In contrast, TR and IR algorithms can incorporate acoustic heterogeneity information into acoustic field propagation models or system matrices to achieve high-quality image reconstruction, whereas DL algorithms can handle this by constructing heterogeneity-corrected signal-image datasets.

In terms of image reconstruction speed, SE algorithms have higher computational efficiency and are faster than DAS and FBP due to the use of fast Fourier transforms. TR algorithms do not have high computational complexity but need to compute the entire acoustic field step by step, decreasing the image reconstruction speed. IR algorithms have the slowest speed due to their iterative nature. DL algorithms may have varying reconstruction speeds, depending on whether iterations are involved (Table 1).

In terms of memory consumption, DAS and FBP algorithms typically require the least amount of memory, as they only need to compute the region of interest instead of a whole imaging region. SE and TR algorithms follow, while IR algorithms usually demand the most memory due to its large system matrices. The memory footprint of DL algorithms depends on whether they involve iterative processes. Non-iterative DL algorithms generally use less memory than IR algorithms, whereas iterative DL algorithms have a memory footprint comparable to that of conventional IR algorithms (Table 1).

Table 1 Comparison of Different Image Reconstruction Algorithms in PACT

5. Discussion and Conclusions

Despite significant advancements, challenges in PACT image reconstruction remain. For example, 1) how to achieve high-quality image reconstruction when a detector has a limited bandwidth and a finite aperture? 2) How to achieve high-quality image reconstruction under sparse sampling and limited view angles? 3) How to improve the reconstruction speed of IR algorithms to achieve real-time two- and three-dimensional imaging? 4) How to build large-scale publicly available datasets for the construction of networks with good generalization properties and performance comparisons of different networks? 5) How to develop unsupervised DL-based reconstruction methods, which do not need paired data for training? 6) How to develop more powerful simulation platforms to generate reference data closely resembling experimental data? 7) How to develop physics-informed networks to improve the interpretability of DL methods? Addressing these challenges are critical for further development and practical applications of PACT imaging technologies.

Overall, this review systematically summarizes the image reconstruction problem in PACT imaging in the past three decades, encompassing the forward problem, conventional image reconstruction algorithms, DL-based image reconstruction algorithms, algorithmic performance comparisons, and major challenges. This review may help general readers better understand the image reconstruction problems in PACT imaging, provide a comprehensive reference for novices and experts, and also foster the further advancements and applications of innovative photoacoustic image reconstruction algorithms.