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Gradient Projection with Approximate L₀ Norm Minimization for Sparse Reconstruction in Compressed Sensing
Ziran Wei1,2,3, Jianlin Zhang4, Zhiyong Xu5
1Institute of Optics and Electronics, Chinese Academy of Science, Chengdu 610209, China. jearen_wei@163.com.
Sensors (Basel, Switzerland)
|October 12, 2018
Summary
This study introduces a novel algorithm for sparse signal reconstruction in compressed sensing. It achieves higher accuracy and faster reconstruction times for both 1D and 2D signals compared to existing L1 norm and greedy methods.
Area of Science:
- Signal Processing
- Compressed Sensing
- Optimization
Background:
- Compressed sensing requires reconstructing the sparsest signal.
- Existing methods like L1 norm and L0 norm have limitations in accuracy and computational complexity.
Purpose of the Study:
- To develop a new algorithm for sparse signal reconstruction.
- To improve reconstruction accuracy and efficiency over existing methods.
Main Methods:
- Approximating the L0 norm using a smooth function derived from the L2 norm.
- Employing gradient projection to minimize the objective function.
- Adaptive adjustment of sparse term weights based on reconstruction error.
Main Results:
- The proposed algorithm demonstrates lower reconstruction error for 1D sparse signals compared to L2 pseudo-inverse and L1 norm algorithms.
- In 2D image reconstruction, the new algorithm shows reduced reconstruction time and enhanced accuracy over greedy and minimum norm algorithms.
Conclusions:
- The novel algorithm effectively reconstructs sparse signals with improved accuracy and efficiency.
- This approach offers a viable alternative for compressed sensing applications.
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