Learning a Filtered Backprojection Reconstruction Method for Photoacoustic Computed Tomography with Hemispherical Measurement Geometries

TL;DR

This work addresses 3D photoacoustic computed tomography with hemispherical half-scan data, where standard analytic FBP methods exhibit artifacts. It proposes a semi-analytic, learned half-scan FBP that treats the unknown filtering operation as a linear neural network and couples it with the adjoint backprojection to form a fast reconstruction pipeline. The method is trained on synthetic data from physics-based virtual phantoms and validated on in vivo breast data, showing reconstruction accuracy comparable to full-scan FBP and to a reference TV-based method, with orders-of-magnitude faster runtimes. The results demonstrate robust generalization across varied objects and measurement configurations, underscoring the approach’s practicality for clinical breast PACT and other hemispherical geometries.

Abstract

In certain three-dimensional (3D) applications of photoacoustic computed tomography (PACT), including \textit{in vivo} breast imaging, hemispherical measurement apertures that enclose the object within their convex hull are employed for data acquisition. Data acquired with such measurement geometries are referred to as \textit{half-scan} data, as only half of a complete spherical measurement aperture is employed. Although previous studies have demonstrated that half-scan data can uniquely and stably reconstruct the sought-after object, no closed-form reconstruction formula for use with half-scan data has been reported. To address this, a semi-analytic reconstruction method in the form of filtered backprojection (FBP), referred to as the half-scan FBP method, is developed in this work. Because the explicit form of the filtering operation in the half-scan FBP method is not currently known, a learning-based method is proposed to approximate it. The proposed method is systematically investigated by use of virtual imaging studies of 3D breast PACT that employ ensembles of numerical breast phantoms and a physics-based model of the data acquisition process. The method is subsequently applied to experimental data acquired in an \textit{in vivo} breast PACT study. The results confirm that the half-scan FBP method can accurately reconstruct 3D images from half-scan data. Importantly, because the sought-after inverse mapping is well-posed, the reconstruction method remains accurate even when applied to data that differ considerably from those employed to learn the filtering operation.

Figures (6)

• Figure 1: Standard FBP xu2013photoacoustic results from (a) half-scan data and (b) full-scan data. Insets in (a) and (b) show the measurement geometries used for each data acquisition. In (a), direct application of the standard FBP method to half-scan data results in concentric arc-shaped artifacts originating from the endpoints of the open measurement surface boundary.
• Figure 2: Learned half-scan FBP framework (a), where a linear 3D U-Net, consisting of convolution blocks (ConvBlocks) as shown in (b) as well as downsampling and upsampling layers, filters the half-scan data. The filtered data are subsequently backprojected to the image space for reconstruction. As illustrated in (b), each ConvBlock incorporates not only a convolution operation (Conv2) for feature extraction but also a padding approach based on prior knowledge of half-scan data, utilizing another convolution operation (Conv1) for learned padding.
• Figure 3: Examples of 3D initial pressure distributions from (a) NBP-A (b) NBP-B, and (c) MOBY datasets. Volume rendering was performed using Paraview ahrens200536, which accumulates intensities based on the chosen color and opacity maps.
• Figure 4: Visual inspections (first to third columns) and line profile comparisons (fourth column) for the ID test from (a) the noiseless NBP-A dataset and for the OOD tests from (b) the noisy NBP-A, (c) noisy NBP-B, and (d) noisy MOBY datasets. The first to third columns display the volumes reconstructed using the standard FBP method applied to full-scan data, the learned half-scan FBP method, and the standard FBP method applied to half-scan data, respectively. Volume rendering was performed using Paraview. The line along which the profiles compared in the rightmost column were extracted is annotated in the volumes contained in the first column, indicated by green lines. In the profile comparisons (fourth column), the gray solid line, blue dashed line, and red dashed lines correspond to the standard FBP method applied to full-scan data, the learned half-scan FBP method, and the standard FBP method applied to half-scan data, respectively. The comparisons reveal that the learned half-scan FBP method significantly outperformed the standard FBP method applied to half-scan data and performed comparably to the standard FBP method applied to full-scan data, for both ID and OOD test samples, even in the presence of noise.
• Figure 5: Violin plots of the MSE (top row) and SSIM (bottom row) values for the standard FBP method applied to half-scan data (white), the learned half-scan FBP method (blue), and the standard FBP method applied to full-scan data (red) under noiseless (solid fill) and noisy conditions (diagonally striped fill). Results are shown for 250 NBP-A (first column), 80 NBP-B (second column), and 10 MOBY samples (third column) for each method. The dashed box in the first column indicates the results from the ID test, while the remaining plots represent the OOD test results. The quantitative results indicate that the learned half-scan FBP method (blue) is robust in noisy conditions (diagonally striped fill) and exhibits strong generalizability across different types of objects (second and third columns), achieving a reconstruction accuracy comparable to the standard FBP method applied to full-scan data (red).