Systems and methods for a computer implemented image reconstruction system that includes an input interface to receive measurements of a scene. A memory to store a sparsity enforcing neural network (SENN) formed by layers of nodes propagating messages through the layers. Wherein at least one node of the SENN modifies an incoming message with a non-linear function to produce an outgoing message and propagates the outgoing message to another node of the SENN. Wherein the non-linear function is a dual-projection function that limits the incoming message if the incoming message exceeds a threshold. Such that, the SENN is trained to reconstruct an image of the scene from the measurements of the scene. A processor to process the measurements with the SENN to reconstruct the image of the scene. Finally, an output interface to render the reconstructed image of the scene.