  We analyze the signal to noise ratio (SNR) in a recently proposed lensless
compressive imaging architecture. The architecture consists of a sensor of a
single detector element and an aperture assembly of an array of aperture
elements, each of which has a programmable transmittance. This lensless
compressive imaging architecture can be used in conjunction with compressive
sensing to capture images in a compressed form of compressive measurements. In
this paper, we perform noise analysis of this lensless compressive imaging
architecture and compare it with pinhole aperture imaging and lens aperture
imaging. We will show that the SNR in the lensless compressive imaging is
independent of the image resolution, while that in either pinhole aperture
imaging or lens aperture imaging decreases as the image resolution increases.
Consequently, the SNR in the lensless compressive imaging can be much higher if
the image resolution is large enough.
