Emerging deep learning approaches have facilitated image reconstruction at the expense of excessive model complexities and lack of theoretical guarantees of stability. In this paper, we propose a theoretically sound deep architecture, named reversible autoencoder (Rev-AE), from the perspective of well-developed frame theory for image reconstruction. Reversible blocks (Rev-Blocks) are developed as fundamental building blocks to realize nonlinear dimension invariant transform, up-sampling (with dimension growth) and down-sampling (with dimension reduction) in Rev-AE. The Rev-Block integrates CNN-based operators with the two-stream structure of lifting scheme to introduce nonlinearity and achieve reversibility. Therefore, Rev-AE only requires training and storage of encoder parameters. Furthermore, Rev-AE bridges existing nonlinear CNNs and well-established traditional signal processing tools to realize end-to-end optimized reversible networks with a guarantee of stability for image reconstruction for the first time. Theoretical analysis demonstrates that reversible blocks guarantee perfect reconstruction with derived frame bounds and are robust to noise perturbation under restricted energy propagation of noise. Moreover, we prove that Rev-AE achieves stable reconstruction with bounded projection angle under the presence of down-sampling and up-sampling. The stability and robustness of Rev-Blocks are also validated with numerical evaluations. Experimental results demonstrate that Rev-AE achieves comparable performance with halved parameters in comparison to recent leading methods ( e.g. , 3-D CNN based autoencoder and ISTA-Net $^+$ ) in the applications of image compression and compressive sensing.

中文翻译：

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可逆自动编码器：一种基于 CNN 的图像重建非线性提升方案


新兴的深度学习方法促进了图像重建，但代价是模型过于复杂且缺乏稳定性的理论保证。在本文中，我们从成熟的图像重建框架理论的角度提出了一种理论上合理的深层架构，称为可逆自动编码器（Rev-AE）。可逆模块 (Rev-Blocks) 被开发为基本构建模块，用于在 Rev-AE 中实现非线性维度不变变换、上采样（具有维度增长）和下采样（具有维度缩减）。 Rev-Block 将基于 CNN 的算子与提升方案的两流结构相结合，引入非线性并实现可逆性。因此，Rev-AE只需要编码器参数的训练和存储。此外，Rev-AE桥接了现有的非线性CNN和成熟的传统信号处理工具，首次实现了端到端优化的可逆网络，并保证了图像重建的稳定性。理论分析表明，可逆块保证了导出帧边界的完美重建，并且在噪声能量传播受限的情况下对噪声扰动具有鲁棒性。此外，我们证明了 Rev-AE 在存在下采样和上采样的情况下实现了有界投影角的稳定重建。 Rev-Blocks 的稳定性和鲁棒性也通过数值评估得到验证。实验结果表明，与图像压缩和压缩感知应用中的最新领先方法（例如，基于 3-D CNN 的自动编码器和 ISTA-Net $^+$ ）相比，Rev-AE 以减半的参数实现了可比的性能。