The paper "Structured Compressed Sensing: From Theory to Applications" by Marco F. Duarte and Yonina C. Eldar provides an overview of the emerging field of compressed sensing (CS), focusing on the transition from theoretical foundations to practical applications. The authors highlight the need for structured sensing architectures that align with the characteristics of feasible acquisition hardware and the extension of standard sparsity priors to include a broader class of signals, including continuous-time signals. The review emphasizes the importance of exploiting signal and measurement structure in CS, aiming to bridge the gap between theory and practice. Key topics include: 1. **Background and Motivation**: The paper discusses the challenges posed by high-bandwidth signals and the Shannon-Nyquist theorem, leading to the motivation for CS. It explains how CS aims to reduce sampling rates while maintaining essential signal information. 2. **Compressed Sensing Basics**: The fundamentals of CS are covered, including the concept of sparsity, the design of CS matrices, and recovery algorithms. The paper discusses the role of coherence and the restricted isometry property (RIP) in ensuring unique signal recovery. 3. **Structured CS Matrices**: The authors review structured CS matrices that are more feasible for real-world applications, such as subsampled incoherent bases. They provide theoretical guarantees and examples of their applications. 4. **Signal Models Beyond Sparsity**: The paper introduces more general signal models, such as the union-of-subspaces framework, which allows for a higher degree of signal compression and broader signal classes. 5. **Infinite-Dimensional Signal Models**: The authors extend CS to infinite-dimensional signal models, including Xampling and finite-rate of innovation (FRI) signals, and discuss the development of compressive analog-to-digital converters (ADCs). 6. **Recovery Guarantees**: The paper presents various recovery guarantees for different algorithms, including basis pursuit, orthogonal matching pursuit, and greedy algorithms, under both noiseless and noisy measurement settings. 7. **Conclusion**: The review concludes by emphasizing the importance of structured CS in practical applications and the need for further research to integrate these techniques into real-world systems. Overall, the paper serves as a comprehensive guide for both practitioners and researchers, highlighting the potential of structured CS in addressing the challenges of high-bandwidth signals and the need for efficient signal acquisition and processing.The paper "Structured Compressed Sensing: From Theory to Applications" by Marco F. Duarte and Yonina C. Eldar provides an overview of the emerging field of compressed sensing (CS), focusing on the transition from theoretical foundations to practical applications. The authors highlight the need for structured sensing architectures that align with the characteristics of feasible acquisition hardware and the extension of standard sparsity priors to include a broader class of signals, including continuous-time signals. The review emphasizes the importance of exploiting signal and measurement structure in CS, aiming to bridge the gap between theory and practice. Key topics include: 1. **Background and Motivation**: The paper discusses the challenges posed by high-bandwidth signals and the Shannon-Nyquist theorem, leading to the motivation for CS. It explains how CS aims to reduce sampling rates while maintaining essential signal information. 2. **Compressed Sensing Basics**: The fundamentals of CS are covered, including the concept of sparsity, the design of CS matrices, and recovery algorithms. The paper discusses the role of coherence and the restricted isometry property (RIP) in ensuring unique signal recovery. 3. **Structured CS Matrices**: The authors review structured CS matrices that are more feasible for real-world applications, such as subsampled incoherent bases. They provide theoretical guarantees and examples of their applications. 4. **Signal Models Beyond Sparsity**: The paper introduces more general signal models, such as the union-of-subspaces framework, which allows for a higher degree of signal compression and broader signal classes. 5. **Infinite-Dimensional Signal Models**: The authors extend CS to infinite-dimensional signal models, including Xampling and finite-rate of innovation (FRI) signals, and discuss the development of compressive analog-to-digital converters (ADCs). 6. **Recovery Guarantees**: The paper presents various recovery guarantees for different algorithms, including basis pursuit, orthogonal matching pursuit, and greedy algorithms, under both noiseless and noisy measurement settings. 7. **Conclusion**: The review concludes by emphasizing the importance of structured CS in practical applications and the need for further research to integrate these techniques into real-world systems. Overall, the paper serves as a comprehensive guide for both practitioners and researchers, highlighting the potential of structured CS in addressing the challenges of high-bandwidth signals and the need for efficient signal acquisition and processing.