Mask-based lensless cameras break the constraints of traditional lens-based cameras, introducing highly flexible imaging systems. However, the inherent restrictions of imaging devices lead to low reconstruction quality. To overcome this challenge, we propose an explicit-restriction convolutional framework for lensless imaging, whose forward model effectively incorporates multiple restrictions by introducing the linear and noise-like nonlinear terms. As examples, numerical and experimental reconstructions based on the limitation of sensor size, pixel pitch, and bit depth are analyzed. By tailoring our framework for specific factors, better perceptual image quality or reconstructions with 4× pixel density can be achieved. This proposed framework can be extended to lensless imaging systems with different masks or structures.