Fig. 1: Network architecture and imaging characterization.

a Regularized convolutional autoencoder architecture, consisting of an encoder and a decoder. The input data passed to the encoder is a lattice section containing 16 × 16 lattice sites (256 × 256 pixels, white dots mark the lattice sites). This data is transformed by a sequence of five convolution layers, where in each layer, a discrete convolution with a set of learned kernels, is applied to the respective input. The third dimension in the output shape denotes the number of distinct kernels utilized per layer. Using a step size (stride) of two when advancing the kernels through the input during the convolution allows to reduce the image size by a factor of two in each step. At the end of the encoder, the node values of the bottleneck layer, after applying a tanh activation function, represent the binarized lattice occupancy. The node values before binarization contain the deconvolved counts in each lattice site, which exhibit a bimodal distribution owing to the saturating effect of the tanh function. Subsequently, the occupation matrix is processed by the decoder with the goal of replicating the input image. The decoder network transforms and upsamples the bottleneck layer using four transposed convolution layers. b Rectified Linear Unit (ReLU) activation functions are used in all layers except in the bottleneck and the last decoder layer, which use a tanh activation function. c Measured experimental point spread function (PSF, averaged over around 2000 individual PSFs) overlaid with the lattice grid. The central peak spans several sites and we observe long-range asymmetric features extending over the whole region of 16 × 16 lattice sites. d Signal-to-noise ratio determined from the count distributions of crops (1.6 μm crop width) containing exactly zero atoms or one atom. A background image without atoms was subtracted to shift the center of the background peak closer to zero.