Signal to Noise Ratio in Lensless Compressive Imaging

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