Fig. 6

Learning-based approach accelerates the reconstruction without sacrificing performance. a The network training pipeline. We captured ~ 120 sets of confocal image stacks to generate the paired SAsLFM images using the calibrated phase-space SAsLFM PSFs. To simulate the camera acquisition process, additional Poisson noise was added to the synthetic images. The network was trained by iteratively minimizing the loss function, which consists of the L1 loss term, the L2 loss term and the SSIM loss term. b The dataset was divided into two parts, one for network training and the other used as the validation set. After ~ 1600 epochs, the loss of the validation procedure started to increase, while the loss of the training was still decreasing. c Stitched volume covering ~ 1960 × 1960 × 600 μm³, consists of 25 reconstructed image stacks with 50% overlap. The segmentation provided by the ImageJ’s 3D objects counter function shows a sloping distribution of neurons in a depth range of ~ 600 μm. d The reconstruction performance of the ADMM-based algorithm and the network is equivalent, while the inference time of the learning-based approach is ~ 0.006 s, which is three orders of magnitude less than that of the former. Scale bars: 1000 μm (c) and 400 μm (d)