Fig. 1

Experimental layout. a An SLM combined with a polarising beam splitter (PBS) and a half-wave plate (λ/2) is used to imprint intensity images onto a laser beam that is then coupled into a multimode fibre. The fibre output is collected with a lens and recorded on a CMOS camera. b A schematic overview of the computational processing steps of the inversion process: output speckle data, x from a series of images (in our experiments, 50,000 images from the ImageNet database²²) are fully connected to a complex matrix, W which provides an output image I = |Wx|². This image is compared with the actual original image (ground truth) through a cost function: the total cost ζ is then back-propagated to W and the process is repeated for a fixed number of loops (epochs), ensuring minimisation of ζ