Fast Compressed Sensing SAR Imaging based on Approximated Observation (1302.3120v1)

Abstract: In recent years, compressed sensing (CS) has been applied in the field of synthetic aperture radar (SAR) imaging and shows great potential. The existing models are, however, based on application of the sensing matrix acquired by the exact observation functions. As a result, the corresponding reconstruction algorithms are much more time consuming than traditional matched filter (MF) based focusing methods, especially in high resolution and wide swath systems. In this paper, we formulate a new CS-SAR imaging model based on the use of the approximated SAR observation deducted from the inverse of focusing procedures. We incorporate CS and MF within an sparse regularization framework that is then solved by a fast iterative thresholding algorithm. The proposed model forms a new CS-SAR imaging method that can be applied to high-quality and high-resolution imaging under sub-Nyquist rate sampling, while saving the computational cost substantially both in time and memory. Simulations and real SAR data applications support that the proposed method can perform SAR imaging effectively and efficiently under Nyquist rate, especially for large scale applications.

• The paper proposes a novel compressed sensing SAR imaging approach that integrates an approximated observation model to dramatically reduce computational complexity.
• It demonstrates high-quality imaging under sub-Nyquist sampling with low sidelobe artifacts and improved noise suppression.
• The method offers significant speedup, validated by RADARSAT-1 simulations, making SAR imaging efficient and scalable for large-scale applications.

Fast Compressed Sensing SAR Imaging based on Approximated Observation

The paper "Fast Compressed Sensing SAR Imaging based on Approximated Observation" proposes a novel approach to Synthetic Aperture Radar (SAR) imaging that leverages the principles of compressed sensing (CS) to operate efficiently under sub-Nyquist sampling conditions. The core innovation lies in the use of an approximated observation model to significantly reduce computational complexity and memory requirements while maintaining robust image reconstruction capabilities.

Technical Overview

The traditional SAR imaging process is heavily reliant on matched filter (MF) based methods, which necessitate operations at the Nyquist sampling rate. Although these methods are computationally efficient, they demand extensive measurements, imposing a challenge in high-resolution and wide-swath applications. CS techniques, on the other hand, offer the potential to reconstruct images from fewer samples but are often computationally intensive due to the necessity of exact observation models. This paper introduces an alternative by integrating MF methods into a CS framework using an approximated observation model. This model is derived from the inverse of MF imaging procedures and incorporated through a sparse regularization framework solved by an iterative thresholding algorithm (ITA).

Results and Contributions

The method presents several notable findings and contributions:

• Reduction in Computational Complexity: The proposed approach achieves computational complexity and memory usage comparable to traditional MF methods, demonstrating an $\mathcal{O}(n\log n)$ complexity per iteration. This is achieved by replacing the exact observation model with the approximated observation, allowing for an MF-based iterative update process.
• High-Quality Imaging: The technique demonstrates the ability to produce high-resolution images under sub-Nyquist sampling rates while maintaining the benefits of low sidelobe artifacts and improved noise suppression, typical of CS techniques.
• Efficiency and Scalability: Simulations and applications using RADARSAT-1 data validate the method's effectiveness in both small-scale, sparse scene reconstruction and large-scale imaging applications. The generated results reveal a significant acceleration of image reconstruction processes, achieving up to hundreds of folds in speedup compared to prior CS-SAR models.

Implications and Future Directions

The introduction of an approximated observation model represents a perceptible shift in SAR imaging, highlighting a productive intersection between traditional signal processing and modern CS paradigms. Practically, this enables the deployment of SAR systems in more resource-constrained scenarios, expanding their usability in remote sensing and surveillance operations where data acquisition and processing resources are limited.

Theoretically, the approach prompts new inquiries into the extent and impact of approximation in SAR imaging. Specifically, further analysis is warranted regarding the trade-off between the degree of approximation and the reconstruction performance. Moreover, the adaptability of this method to various radar signal forms and different approximation strategies offers a fertile ground for future research.

In conclusion, this work presents a compelling advancement in SAR imaging technology, balancing practical efficiency with high-quality image reconstruction. Its implications extend across both operational deployment and theoretical research, laying a foundation for further exploration into compressed sensing applications in radar systems.