A microscopy method includes a trained deep neural network that is executed by software using one or more processors of a computing device, the trained deep neural network trained with a training set of images comprising co-registered pairs of high-resolution microscopy images or image patches of a sample and their corresponding low-resolution microscopy images or image patches of the same sample. A microscopy input image of a sample to be imaged is input to the trained deep neural network which rapidly outputs an output image of the sample, the output image having improved one or more of spatial resolution, depth-of-field, signal-to-noise ratio, and/or image contrast.