Estimating the angular separation between two incoherently radiating monochromatic point sources is a canonical toy problem to quantify spatial resolution in imaging. In recent work, Tsang et al. showed, using a Fisher Information analysis, that Rayleigh's resolution limit is just an artifact of the conventional wisdom of intensity measurement in the image plane. They showed that the optimal sensitivity of estimating the angle is only a function of the total photons collected during the camera's integration time but entirely independent of the angular separation itself no matter how small it is, and found the information-optimal mode basis, intensity detection in which achieves the aforesaid performance. We extend the above analysis, which was done for a Gaussian point spread function (PSF) to a hard-aperture pupil proving the information optimality of image-plane sinc-Bessel modes, and generalize the result further to an arbitrary PSF. We obtain new counterintuitive insights on energy vs. information content in spatial modes, and extend the Fisher Information analysis to exact calculations of minimum mean squared error, both for Gaussian and hard aperture pupils.

The goal of this paper is to present a non-iterative and more importantly an extremely fast algorithm to reconstruct images from compressively sensed (CS) random measurements. To this end, we propose a novel convolutional neural network (CNN) architecture which takes in CS measurements of an image as input and outputs an intermediate reconstruction. We call this network, ReconNet. The intermediate reconstruction is fed into an off-the-shelf denoiser to obtain the final reconstructed image. On a standard dataset of images we show significant improvements in reconstruction results (both in terms of PSNR and time complexity) over state-of-the-art iterative CS reconstruction algorithms at various measurement rates. Further, through qualitative experiments on real data collected using our block single pixel camera (SPC), we show that our network is highly robust to sensor noise and can recover visually better quality images than competitive algorithms at extremely low sensing rates of 0.1 and 0.04. To demonstrate that our algorithm can recover semantically informative images even at a low measurement rate of 0.01, we present a very robust proof of concept real-time visual tracking application.

We present a compressive imager demonstrator based on a scalable, parallel architecture. It primarily utilizes information-optimal projections and a Piece-wise Linear Minimum Mean Square Error Estimator (PLE-MMSE) combined with a block-based statistical model of natural images. Such system delivers high-resolution images from low resolution sensor with near real-time snapshots. This testbed provides a highly programmable compressive imager that allows testing of a variety of projection designs for different tasks (e.g. random binary, PCA) and also enables adaptive or dynamic designs.