Learning to read residual images for single-pixel photography

Abstract

Continuous video scales in cost with camera count, resolution and recording duration, yet many monitoring tasks seek events rather than complete images and can operate on a compact single-pixel measurement stream. Recovering a chosen interval as video is then desirable, but at 0.24\% of the pixel count the scene correlation image looks like noise and per-clip optimization takes minutes. Correlating the residual of an estimate with the coding patterns nevertheless gives a residual image, the gradient of a centered measurement loss. Lifted through a pretrained video decoder, its agreement with the true error exceeds that of control decoders. Video-latent inversion (VLI) then outperforms frame-wise image-latent reconstruction at 1{,}000 bucket values. Measurement-Gradient-Conditioned Video Flow (MGV-Flow), trained once to read the lifted residual image with preceding frames, reconstructs five frames in 1.55\,s at 22.9\,dB median PSNR, against 398\,s and 18.1\,dB for VLI, with the largest gains in high-motion scenes. Directional fidelity ranks 30 coding configurations and selects one needing a third fewer bucket values. On a physical system, MGV-Flow outperforms per-frame reconstruction without retraining. A sliding window over the bucket-value stream yields 3.2 frames per second on one RTX~4090 and, in theory, 20 frames per second on a data-centre accelerator. Demonstrations are available at https://cavedweller509.github.io/MGV-Flow.