Generalized Tensor Summation Compressive Sensing Network (GTSNET): An Easy to Learn Compressive Sensing Operation.

Area of Science:

• Signal Processing
• Machine Learning
• Applied Mathematics

Background:

• Traditional compressive sensing (CS) relies on random measurement matrices and iterative reconstruction, which are cumbersome for large signals.
• Deep learning models enhance CS reconstruction but struggle with jointly learning entire measurement matrices.
• Existing deep learning CS methods often use block-wise schemes, which can lead to artifacts.

Purpose of the Study:

• To develop a novel deep learning framework for compressive sensing matrix learning.
• To improve signal reconstruction accuracy and efficiency, particularly at low measurement rates.
• To address the limitations of block-wise CS schemes in deep learning.

Main Methods:

• Introduced a separable multi-linear learning approach for the CS measurement matrix.
• Represented the measurement signal as a summation of arbitrary tensors.
• Developed a deep learning network (GTSNET) based on this tensorial learning framework.

Main Results:

• Tensorial learning effectively reduces blocking artifacts compared to block-wise CS.
• The proposed method demonstrates improved performance, especially at low measurement rates (MRs).
• Achieved higher reconstruction accuracy and potentially faster recovery times.

Conclusions:

• Separable multi-linear tensorial learning offers a promising alternative for CS matrix design in deep learning.
• The GTSNET framework provides a robust solution for efficient and accurate signal recovery.
• The approach is particularly beneficial for scenarios with limited measurement data.