Efficient and accurate inversion of multiple scattering with deep learning

1 Introduction

• Linear Born and Rytov approximations become inaccurate for strong scattering, producing artifacts for large objects or high permittivity contrasts.Nonlinear measurement models can account for multiple light scattering inside the object.Source: §1 · p. 1
• Strong scattering makes nonlinear reconstruction highly nonconvex, impairing optimization speed and final image quality.Optimization formulations typically combine data fidelity with regularization to address ill-posedness.Source: §1 · p. 1
• The proposed data-driven CNN inverts multiple scattering despite a nonlinear, object-dependent, and unknown measurement operator.The approach is distinct from methods that use deep learning for reconstruction with known measurement operators.Source: §1 · p. 1
• The study reports high-quality reconstructions from multiple-scattered measurements, including strongly scattering objects for which optimization-based approaches underperform.It presents results on simulated and real datasets and identifies its findings as the first demonstration of deep learning's potential for high-quality reconstruction from these measurements.Source: §1 · p. 2

2 Nonlinear diffractive imaging

• The section reviews optimization-based reconstruction and the physical model used to describe multiple scattering.The optimization approach is presented as the traditional approach for nonlinear diffractive imaging.Source: §2 · p. 2

2.1 Nonlinear inverse problem

• The inverse problem recovers an unknown image from noisy measurements, and ill-posed instances are commonly handled by minimizing data mismatch plus a regularizer.The regularizer promotes desirable solutions; examples include spatial sparsity and total variation, with FISTA and ADMM among the discussed solvers.Source: §2.1 · p. 2

2.2 Multiple-scattering model

• The Lippmann–Schwinger model describes multiple scattering using the total field, incident field, and scattering potential.The scattering potential is defined from the permittivity contrast, and the schematic traces the incident wave's interaction with the object to the scattered field at sensors.Source: §2.2 · p. 2, Figure 1 · p. 3
• The discretized model represents the scattering potential as x and the measured scattered field as y, with Green-function operators describing propagation.The formulation also includes the input field and additive measurement noise.Source: §2.2 · p. 3
• Prior work interprets computation of the nonlinear forward operator as a CNN, enabling efficient evaluation of the data-fidelity gradient.Source: §2.2 · p. 4

3.1 Backpropagation

• Backpropagation maps measurements into image-domain features without using the nonlinear, object-dependent forward model; multiple-transmitter outputs are combined and split into real and imaginary feature maps.Source: §3.1 · p. 4

3.2 U-Net decoder

• Figure 4 plots training and validation losses for piecewise-smooth objects; horizontal lines on the validation plot mark other algorithms’ losses.Source: Figure 4 · p. 5
• U-Net’s contraction-expansion structure increases receptive field with depth, while skip connections combine local details with global texture in the reconstructed feature maps.Source: §3.2 · p. 5
• Section 4 results corroborate U-Net’s suitability for forming high-quality images from multiple scattered measurements.Source: §3.2 · p. 5

4 Experimental validation

• The validation includes simulated piecewise-smooth and face-image datasets and experimental microwave measurements from foam and plastic cylinders.The simulated datasets each contain 1,548 images, split into 1,500 training, 24 validation, and 24 test images.Source: §4 · p. 5, §4.1 · p. 5

4.1 Results on simulated datasets

• ScaDec substantially outperforms the baseline methods in simulated weak and strong scattering, producing higher SNR and more natural images without TV’s blocky artifacts.Its reconstruction SNR is nearly identical across the two scattering regimes.Source: Figure 5 · p. 6, §4.1 · p. 7
• A ScaDec reconstruction takes less than 2 seconds, while LS-TV takes over 8 minutes in weak scattering and 35 minutes in strong scattering.ScaDec uses a single GPU; the optimization-based methods were tested on two CPUs.Source: §4.1 · p. 7

4.2 Results on experimental datasets

• For the experimental settings, ScaDec was trained separately on 6,500 synthetic image-measurement pairs per setting, using simulated Lippmann–Schwinger measurements with 20 dB input SNR.The settings use 128 × 128 images; measurements are considered at 5 GHz.Source: §4.2 · pp. 7–8
• On experimental measurements, ScaDec gives the highest-quality reconstructions among the compared methods in both contrast and object shape, with clear edges and no obvious contrast degradation.The results also demonstrate deployment on experimental data after training with simulated data.Source: Figure 6 · p. 7, §4.2 · p. 8

• ScaDec successfully reconstructs high-quality images and outperforms state-of-the-art optimization-based methods across all scenarios.Source: §5 · p. 8
• A network trained on simulated data also reconstructs images from real experimental measurements of highly scattering objects.Source: §5 · p. 8
• Image formation with ScaDec is substantially faster than optimization-based reconstruction, making it a promising alternative for correcting scattering in biological samples.Source: §5 · p. 8