# Improving Robustness of Deep-Learning-Based Image Reconstruction

ICML 2020, 2020.

Keywords:

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Abstract:

Deep-learning-based methods for different applications have been shown vulnerable to adversarial examples. These examples make deployment of such models in safety-critical tasks questionable. Use of deep neural networks as inverse problem solvers has generated much excitement for medical imaging including CT and MRI, but recently a simi...More

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Introduction

- Adversarial examples for deep learning based methods have been demonstrated for different problems (Szegedy et al, 2013; Kurakin et al, 2016; Cisse et al, 2017a; Eykholt et al, 2017; Xiao et al, 2018).
- Image reconstruction involving the recovery of an image from indirect measurements is used in many applications, including critical applications such as medical imaging, e.g., Magnetic Resonance Imaging (MRI), Computerised Tomography (CT) etc.
- Such applications demand the reconstruction to be stable and reliable.

Highlights

- Adversarial examples for deep learning based methods have been demonstrated for different problems (Szegedy et al, 2013; Kurakin et al, 2016; Cisse et al, 2017a; Eykholt et al, 2017; Xiao et al, 2018)
- Image reconstruction involving the recovery of an image from indirect measurements is used in many applications, including critical applications such as medical imaging, e.g., Magnetic Resonance Imaging (MRI), Computerised Tomography (CT) etc
- One of the most powerful methods for training an adversarially robust network is adversarial training (Madry et al, 2017; Tramer et al, 2017; Sinha et al, 2017; Arnab et al, 2018). It involves training the network using adversarial examples, enhancing the robustness of the network to attacks during inference. This strategy has been quite effective in classification settings, where the goal is to make the network output the correct label corresponding to the adversarial example
- We propose a min-max formulation to build a robust deep-learning-based image reconstruction models
- We found the linear network to converge to the same solution
- Extensive experiments with non-linear deep networks for Compressive Sensing (CS) using random Gaussian and Discrete Cosine Transform measurement matrices on MNIST and CelebA datasets show that the proposed scheme outperforms other methods for different perturbations ≥ 0, the behavior depends on the conditioning of matrices, as indicated by theory for the linear reconstruction scheme

Methods

- Where L(·) represents the applicable loss function, e.g., cross-entropy for classification, and δ is the perturbation added to each sample, within an p-norm ball of radius.
- This min-max formulation encompasses possible variants of adversarial training.
- It consists of solving two optimization problems: an inner maximization and an outer minimization problem.
- For an optimal θ∗ solving the equation 2, f (; θ∗) will be robust to all the xadv lying in the -radius of p-norm ball around the true x

Conclusion

- The authors propose a min-max formulation to build a robust deep-learning-based image reconstruction models.
- To make this more tractable, the authors reformulate this using an auxiliary network to generate adversarial examples for which the image reconstruction network tries to minimize the reconstruction loss.
- The authors theoretically analyzed a simple linear network and found that using min-max formulation, it outputs singular-value(s) filter regularized solution which reduces the effect of adversarial examples for ill-conditioned matrices.

Summary

## Introduction:

Adversarial examples for deep learning based methods have been demonstrated for different problems (Szegedy et al, 2013; Kurakin et al, 2016; Cisse et al, 2017a; Eykholt et al, 2017; Xiao et al, 2018).- Image reconstruction involving the recovery of an image from indirect measurements is used in many applications, including critical applications such as medical imaging, e.g., Magnetic Resonance Imaging (MRI), Computerised Tomography (CT) etc.
- Such applications demand the reconstruction to be stable and reliable.
## Methods:

Where L(·) represents the applicable loss function, e.g., cross-entropy for classification, and δ is the perturbation added to each sample, within an p-norm ball of radius.- This min-max formulation encompasses possible variants of adversarial training.
- It consists of solving two optimization problems: an inner maximization and an outer minimization problem.
- For an optimal θ∗ solving the equation 2, f (; θ∗) will be robust to all the xadv lying in the -radius of p-norm ball around the true x
## Conclusion:

The authors propose a min-max formulation to build a robust deep-learning-based image reconstruction models.- To make this more tractable, the authors reformulate this using an auxiliary network to generate adversarial examples for which the image reconstruction network tries to minimize the reconstruction loss.
- The authors theoretically analyzed a simple linear network and found that using min-max formulation, it outputs singular-value(s) filter regularized solution which reduces the effect of adversarial examples for ill-conditioned matrices.

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