Denoiser-Regulated Deep Unfolding Compressed Sensing with Learnable Fixed-Point Projections

The family of regularization by denoising (RED) methods introduce denoising operator as the regularization term to perform compressed sensing (CS) reconstruction, which shows higher flexibility and scalability. However, traditional RED framework has strict requirements on several properties of denoiser, making it hard to design the specific denoiser and limits the quality of reconstructed images. Although some relaxation for denoisers can be made by incorporating the fixed point projection during the iteration process, the involved parameters have great impact on the effectiveness and efficiency of the algorithm, which is non-trivial to set them properly. In this paper, we propose an innovative Deep Unfolding Network framework termed FP-DUN based on the iterative process of Regularization by Denoising via Fixed-Point Projection (RED-PRO). In FP-DUN, fix-point projection module is implemented with learnable weights of neural networks, where an effective denoiser based on dual attention mechanism (DAM) is developed to capture the details of the reconstructed image. Additionally, we propose a new loss function based on fixed point constraints, which is able to overcome the over-smoothness caused by multi-stage denoising and maintain the structural details to progressively improve the reconstruction quality. By training the DUN model, the parameters for the process of fix point projection and denoiser are learned automatically. Extensive experimental results comparing with state-of-the-art CS algorithms and traditional RED-PRO approach validate the effectiveness of FP-DUN, especially on some images with complex details.