Due to its great learning ability and fast processing speed

deep learning-based image compressive sensing (ICS) methods attract a lot of attention in recent years. However

the design of most existing ICS neural networks architecture ignore the mathematical theory in iterative optimization-based methods and cannot effectively use the prior structure knowledge in the signal

leading to lack of the interpretability. In order to retain the core ideas of the optimization algorithm and utilize the high performance of deep learning

this paper uses learnable convolutional layers to replace the predefined filters and artificial design parameters in the traditional smooth projected Landweber algorithm (SPL)

and proposes a ICS neural network named SPLNet. In SPLNet

we design a unique network structure SPLBlock to implement three key steps in SPL iteration: (1) Wiener filter for removal of blocking artifacts; (2) approximation with projection onto the convex set; (3) bivariate shrinkage on transform domain for sparse representation and denoising. Experimental results indicate that

compared with current state-of-the-art ICS optimization iterative algorithm GSR

the average reconstructed image PSNR of SPLNet are improved by 0.78dB

and compared with state-of-the-art neural network framework SCSNet

the average reconstructed image PSNR of SPLNet are improved by 0.92dB.