Solving Inverse Problems With Deep Neural Networks - Robustness Included?

Area of Science:

• Medical Imaging
• Computer Vision
• Machine Learning

Background:

• Deep learning excels at inverse problems, but reliability for safety-critical applications requires verification.
• Prior research indicated deep neural networks (DNNs) are unstable for image reconstruction, susceptible to adversarial attacks causing artifacts.
• Adversarial perturbations, small input distortions, can lead to significant reconstruction errors in DNNs.

Purpose of the Study:

• To extensively study the robustness of deep learning algorithms for underdetermined inverse problems.
• To investigate the susceptibility of DNNs to adversarial perturbations in measurement data.
• To compare the performance of DNNs against Total Variation (TV) minimization, a robust reference method.

Main Methods:

• Investigated deep learning for compressed sensing (Gaussian measurements), Fourier, and Radon measurements.
• Included a real-world magnetic resonance imaging (MRI) scenario using the NYU-fastMRI dataset.
• Focused on computing adversarial perturbations in measurements to maximize reconstruction error and compared with TV minimization.

Main Results:

• Standard end-to-end deep learning network architectures demonstrated resilience against statistical noise.
• Contrary to previous findings, networks were also found to be robust against adversarial perturbations.
• All tested networks were trained using standard deep learning techniques without specialized defense mechanisms.

Conclusions:

• Standard deep learning architectures are robust for image reconstruction tasks, even with adversarial perturbations.
• The findings challenge prior assumptions about DNN instability in inverse problems.
• Deep learning methods show potential for reliable application in safety-critical imaging fields.