Total variation reconstruction for compressive sensing using nonlocal Lagrangian multiplier
This work addresses image recovery in compressive sensing, offering an incremental improvement in texture preservation and noise reduction for applications like medical imaging or photography.
The authors tackled the problem of image reconstruction in compressive sensing by proposing a nonlocal Lagrangian multiplier method to reduce noise and enhance image information, achieving superior subjective and objective quality in recovered images compared to other algorithms.
Total variation has proved its effectiveness in solving inverse problems for compressive sensing. Besides, the nonlocal means filter used as regularization preserves texture better for recovered images, but it is quite complex to implement. In this paper, based on existence of both noise and image information in the Lagrangian multiplier, we propose a simple method in term of implementation called nonlocal Lagrangian multiplier (NLLM) in order to reduce noise and boost useful image information. Experimental results show that the proposed NLLM is superior both in subjective and objective qualities of recovered image over other recovery algorithms.