Practical Compact Deep Compressed Sensing

Abstract: Recent years have witnessed the success of deep networks in compressed sensing (CS), which allows for a significant reduction in sampling cost and has gained growing attention since its inception. In this paper, we propose a new practical and compact network dubbed PCNet for general image CS. Specifically, in PCNet, a novel collaborative sampling operator is designed, which consists of a deep conditional filtering step and a dual-branch fast sampling step. The former learns an implicit representation of a linear transformation matrix into a few convolutions and first performs adaptive local filtering on the input image, while the latter then uses a discrete cosine transform and a scrambled block-diagonal Gaussian matrix to generate under-sampled measurements. Our PCNet is equipped with an enhanced proximal gradient descent algorithm-unrolled network for reconstruction. It offers flexibility, interpretability, and strong recovery performance for arbitrary sampling rates once trained. Additionally, we provide a deployment-oriented extraction scheme for single-pixel CS imaging systems, which allows for the convenient conversion of any linear sampling operator to its matrix form to be loaded onto hardware like digital micro-mirror devices. Extensive experiments on natural image CS, quantized CS, and self-supervised CS demonstrate the superior reconstruction accuracy and generalization ability of PCNet compared to existing state-of-the-art methods, particularly for high-resolution images. Code is available at https://github.com/Guaishou74851/PCNet.

• The paper presents PCNet, a deep network incorporating a novel collaborative sampling operator and enhanced reconstruction that yields superior image compressed sensing performance.
• The collaborative sampling operator (COSO) in PCNet combines deep conditional filtering with dual-branch sampling (DCT/Gaussian) to improve information capture during the sampling process.
• Experiments demonstrate PCNet's superior performance over existing methods across diverse CS tasks, highlighting its flexibility and practical utility for real-world imaging applications.

An Overview of "Practical Compact Deep Compressed Sensing"

The paper "Practical Compact Deep Compressed Sensing" by Bin Chen and Jian Zhang presents a novel approach to image compressed sensing (CS) by proposing a new network, PCNet, that incorporates an innovative collaborative sampling operator (COSO) and an enhanced reconstruction backbone. The authors have made significant contributions to both the design of the sampling process and the architecture of the recovery network, aiming to overcome several limitations of existing deep CS methods.

The proposed PCNet addresses two core challenges in the CS framework: the effective design of sampling operators and the development of efficient reconstruction networks. The COSO employed in PCNet introduces a two-step sampling process that includes a deep conditional filtering step followed by a dual-branch fast sampling step. This method aims to improve information preservation during sampling by combining the strengths of DCT, Gaussian matrices, and learned network parameters.

Key Contributions and Methodologies

The paper outlines multiple contributions and methodologies:

1. Collaborative Sampling Operator (COSO): The novel COSO is designed to efficiently capture image information, providing both local and global feature perception. It includes a deep conditional filtering network to smooth input images and a dual-branch sampling that employs DCT and scrambled block-diagonal Gaussian matrices.
2. Efficient Deployment Strategy: The authors introduce a matrix extraction scheme inspired by structural reparameterization techniques to facilitate the deployment of their sampling operator on hardware such as digital micro-mirror devices (DMDs). This approach enables the conversion of the sampling operator to a matrix form suitable for practical applications.
3. Enhanced Proximal Gradient Descent Network: The reconstruction process in PCNet uses a proximal gradient descent (PGD) algorithm-unrolled network. The introduction of high-throughput feature-level refinement, combined with scalability and modern network components such as Swin-Conv blocks, allows the network to process large images efficiently.
4. Comprehensive Experimental Analysis: Extensive experiments demonstrate PCNet's superior performance across various image CS tasks, including standard CS, quantized CS, and self-supervised CS. The network shows flexibility in handling different sampling ratios and image sizes, outperforming existing state-of-the-art methods in both quantitative metrics and visual quality.

Implications and Future Directions

The introduction of the COSO and the enhanced PGD-unrolled reconstruction network represents a significant advancement in the field of image compressed sensing. The separation of smoothing and under-sampling steps helps in better preservation of essential image features, resulting in superior recovery performance.

The implications of this research are substantial. In practice, such advancements can significantly improve the efficiency and effectiveness of real-world CS systems, including applications in single-pixel imaging, MRI, and computational tomography. The theoretical framework and practical deployment aspects discussed could be influential in driving further research in CS and its application across different domains.

Future research could explore the integration of PCNet with other inverse problems, such as sparse-view CT or snapshot compressive imaging, and further optimization of the architecture to reduce complexity without sacrificing performance. Additionally, exploring the integration of emerging machine learning paradigms, such as unsupervised learning or reinforcement learning, could potentially enhance the adaptability and robustness of CS frameworks.

In conclusion, the “Practical Compact Deep Compressed Sensing” paper offers a thoughtfully designed solution to longstanding challenges in compressed sensing, laying down a path for more efficient, versatile, and robust CS techniques.