Noise analysis for lensless compressive imaging

•We perform signal to noise ratio (SNR) analysis for lensless compressive imaging (LCI).•The analysis shows that the SNR of LCI is independent of the number of pixels of an image.•Comparison is made to pinhole aperture imaging (PAI) and lens aperture imaging (LAI).•The SNR of PAI or LAI decreases as the number of pixels increases.•SNR of LCI is better if the number of pixels in the image is large enough.

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.