NETT Regularization for Compressed Sensing Photoacoustic Tomography

TL;DR

The deep learning method of [H. Li, J. Schwab, S. Antholzer, and M. Haltmeier] is applied for the first time to the CS-PAT problem, and a network architecture and training strategy for the NETT is proposed that is expected to be useful for other inverse problems as well.

Abstract

We discuss several methods for image reconstruction in compressed sensing photoacoustic tomography (CS-PAT). In particular, we apply the deep learning method of [H. Li, J. Schwab, S. Antholzer, and M. Haltmeier. NETT: Solving Inverse Problems with Deep Neural Networks (2018), arXiv:1803.00092], which is based on a learned regularizer, for the first time to the CS-PAT problem. We propose a network architecture and training strategy for the NETT that we expect to be useful for other inverse problems as well. All algorithms are compared and evaluated on simulated data, and validated using experimental data for two different types of phantoms. The results on the one the hand indicate great potential of deep learning methods, and on the other hand show that significant future work is required to improve their performance on real-word data.

Figures (7)

• Figure 1: Architecture of the residual U-net. The number of convolution kernels (channels) is written over each layer. Long arrows indicate direct connections with subsequent concatenation or addition.
• Figure 2: Network structure for the trained regularizer. The first two convolutional layers use $3\times 3$ convolutions followed by ReLU activations. The last convolutional layer (green arrow) uses $3\times 3$ convolutions not followed by an activation function.
• Figure 3: Sample from the blood-vessel data set. Left: Ground truth phantom. Middle: Initial reconstruction using $\mathcal{A}^\sharp$ from sparse data. Right: Initial reconstruction using $\mathcal{A}^\sharp$ from Bernoulli data.
• Figure 4: Reconstruction results for using simulated data. Top Row: Reconstructions from sparse data. Bottom Row: Reconstructions from Bernoulli data. First Column: Joint $\ell_1$-algorithm. Second Column: $H^1$-regularization (deterministic NETT). Third Column: Residual U-Net. Fourth Column: NETT.
• Figure 5: Reconstruction results using noisy data. Top Row: Reconstructions from sparse data. Bottom Row: Reconstructions from Bernoulli data. First Column: Joint $\ell_1$-algorithm. Second Column: $H^1$-regularization (deterministic NETT). Third Column: Residual U-Net. Fourth Column: NETT.