Dynamic Path-Controllable Deep Unfolding Network for Compressive Sensing

TL;DR

This paper focuses on CS reconstruction and proposes a novel Dynamic Path-Controllable Deep Unfolding Network (DPC-DUN), which can dynamically select a rapid and appropriate route for each image and is slimmable by regulating different performance-complexity tradeoffs.

Abstract

Deep unfolding network (DUN) that unfolds the optimization algorithm into a deep neural network has achieved great success in compressive sensing (CS) due to its good interpretability and high performance. Each stage in DUN corresponds to one iteration in optimization. At the test time, all the sampling images generally need to be processed by all stages, which comes at a price of computation burden and is also unnecessary for the images whose contents are easier to restore. In this paper, we focus on CS reconstruction and propose a novel Dynamic Path-Controllable Deep Unfolding Network (DPC-DUN). DPC-DUN with our designed path-controllable selector can dynamically select a rapid and appropriate route for each image and is slimmable by regulating different performance-complexity tradeoffs. Extensive experiments show that our DPC-DUN is highly flexible and can provide excellent performance and dynamic adjustment to get a suitable tradeoff, thus addressing the main requirements to become appealing in practice. Codes are available at https://github.com/songjiechong/DPC-DUN.

Figures (11)

• Figure 1: Two subjective examples of the impact of the active module number on the reconstruction performance (PSNR). We compare the "Baseline" model without the selectors and our models (DP-DUN and DPC-DUN) with the selectors when ratio $=30\%$. While maintaining similar high performance, our methods can adaptively select an appropriate path and an optimal number of active modules for different images.
• Figure 2: The architecture of our proposed DPC-DUN which consists of $K$ stages. $\mathbf{y}$ is the under-sampled data as the input of the model, $\mathbf{x}^{(0)}=\mathbf{\Phi^{\top}}\mathbf{y}$ denotes the initialization, $\mathbf{x}^{(K)}$ denotes the recovered result and $\mathbf{X}^{(k)}$ stands for the output features of the $k$-th unrolled stage. In addition to the main processing path marked in black, the green line controls whether the Dynamic Gradient Descent Module (DGDM) and the Dynamic Proximal Mapping Module (DPMM) are selected by the Path-Controllable Selector (PCS) which consists of the Controllable Unit (CU) and the Path Selector (PS), and the yellow line denotes the modulation process with the Lagrange multiplier $\mu$.
• Figure 3: The architecture of our proposed Path-Controllable Selector (PCS) which consists of the controllable unit (CU) and the path selector (PS). The Gumbel noise in the path selector is only added to achieve end-to-end training.
• Figure 4: Comparisons on recovering an image ("Barbara") from Set11 dataset Kulkarni2016ReconNetNR in the case of CS ratio = 25$\%$.
• Figure 5: Comparisons on an image from Urban100 dataset dong2018denoising in the case of CS ratio = 30% (upper) and an image from DIV2K dataset Agustsson_2017_CVPR_Workshops in the case of CS ratio = 40% (lower).