Fig. 3: Computing performance enhanced by nonlinear optical data compression.

a, Concept of image reconstruction using linear optical complex media for linear encoding and camera detection with quadratic response. b, Reconstruction using the speckle features from a. The orange boxes represent the wrongly reconstructed pairs. c, Multiple-scattering cavity as a nonlinear optical encoder along with camera detection and employing compressed speckle features for digital reconstruction of the original image data. d, Reconstruction from speckle features generated by the multiple-scattering cavity. In b and d, approximately 25 speckle grains are used with a compression ratio of 31:1 and are used to train two digital decoders (Methods). It is demonstrated that given the same number of compressed output modes (speckle grains), nonlinear features generated from the cavity can provide a reduced mean squared error by 0.6, resulting in a better reconstruction of the images in d compared with b. More results are provided in Supplementary Figs. 4–6. e, Concept of keypoint detection in human faces (images with 96 × 96 pixels) with compressed speckle features. f, Keypoint detection with a mode compression ratio of 576:1, using 16 output modes with relatively weaker nonlinearity (25% modulated areas in the DMD) and a five-layer MLP decoder. g, Improved keypoint detection with a reduced mean error in pixels across 15 keypoints (1.06 pixels compared with 1.86 pixels errors in f), using 16 output modes (speckle grains) with relatively stronger nonlinearity (full modulated areas in the DMD) and a nine-layer MLP decoder.