Photoacoustic image reconstruction via deep learning

TL;DR

This work addresses image reconstruction in photoacoustic tomography under sparse data and limited-view conditions, where conventional methods produce strong artifacts. It proposes a direct deep learning pipeline that first applies filtered back-projection (FBP) to generate an initial estimate and then refines it with a convolutional neural network (CNN). Two architectures are evaluated: a U-Net and a simple S-Net, both yielding reconstruction quality competitive with state-of-the-art iterative TV-based methods while enabling real-time performance. The results demonstrate robustness to sparse data and noise, with potential for faster PAT imaging in practical settings, and motivate further development using more complex phantoms and real data.

Abstract

Applying standard algorithms to sparse data problems in photoacoustic tomography (PAT) yields low-quality images containing severe under-sampling artifacts. To some extent, these artifacts can be reduced by iterative image reconstruction algorithms which allow to include prior knowledge such as smoothness, total variation (TV) or sparsity constraints. These algorithms tend to be time consuming as the forward and adjoint problems have to be solved repeatedly. Further, iterative algorithms have additional drawbacks. For example, the reconstruction quality strongly depends on a-priori model assumptions about the objects to be recovered, which are often not strictly satisfied in practical applications. To overcome these issues, in this paper, we develop direct and efficient reconstruction algorithms based on deep learning. As opposed to iterative algorithms, we apply a convolutional neural network, whose parameters are trained before the reconstruction process based on a set of training data. For actual image reconstruction, a single evaluation of the trained network yields the desired result. Our presented numerical results (using two different network architectures) demonstrate that the proposed deep learning approach reconstructs images with a quality comparable to state of the art iterative reconstruction methods.

Figures (6)

• Figure 1: Basic principles of PAT. Left: A sample object is illuminated by short optical pulses. Middle: Optical energy is absorbed within the sample, causes nonuniform heating and induces a subsequent acoustic pressure wave. Right: Acoustic sensors located outside of the sample capture the pressure signals, which are used to recover an image of the interior. In this paper we use deep learning and in particular deep CNNs for image reconstruction. Our approach allows a small number of sensor positions arranged on a possibly non-closed measurement curve ${\boldsymbol S}$.
• Figure 2: Measurement geometry used for the numerical experiments. The acoustic pressure is observed at 24 sensor positions $\mathbf{s}_1, \dots, \mathbf{s}_{24}$ (indicated by the green dots) that are located on the non-closed measurement curve ${\boldsymbol S} = \left\{\mathbf{s} \colon \lVert\mathbf{s}\rVert_2 = 50mm \wedge \mathbf{s}_2 < 11.1mm\right\}$ forming a circular arc. The phantoms to be reconstructed are contained in the rectangular domain $[-10mm ,10mm ] \times [-20mm ,5mm ]$ that has parts outside the stability region $R$ (defined as the convex hull of the measurement curve). The corresponding PAT image reconstruction problem is the combination of a sparse data (small number of sensors) and a limited view (non-closed measurement curve) problem.
• Figure 3: Training and evaluation data. Examples of randomly generated combinations of ring-shaped phantoms (top) and corresponding FBP reconstructions (bottom) containing under-sampling artifacts. The left three images contain examples from the training set; the right image is used for evaluation and is not part of the training data. In the FBP reconstructions one clearly sees the typical under-sampling artifacts.
• Figure 4: Results with the reconstruction networks. Top: Reconstructed image using the U-Net (left) and difference to the true phantom (right); the relative mean squared error is 0.026. Bottom: Reconstructed phantom using the S-net (left) and difference to the true phantom (right); the relative mean squared error is 0.33.
• Figure 5: Horizontal cross sections. The images show horizontal cross section through the upper two rings comparing the original phantom with U-Net reconstruction (top left), the S-Net reconstruction (top right), the FBP reconstruction (bottom left) and the TV-minimization (bottom right).