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The generation of speckle patterns via random matrices, statistical definitions, or apertures may not always result in optimal outcomes. Issues such as correlation fluctuations in low ensemble numbers and diffraction in long-distance propagation can arise. Instead of improving results of specific applications, our solution is catching deep correlations of patterns with the framework, Speckle-Net, which is fundamental and universally applicable to various systems. We demonstrate this in computational ghost imaging (CGI) and structured illumination microscopy (SIM). In CGI with extremely low ensemble number, it customizes correlation width and minimizes correlation fluctuations in illuminating patterns to achieve higher-quality images. It also creates non-Rayleigh nondiffracting speckle patterns only through a phase mask modulation, which overcomes the power loss in the traditional ring-aperture method. Our approach provides new insights into the nontrivial speckle patterns and has great potential for a variety of applications including dynamic SIM, X-ray and photo-acoustic imaging, and disorder physics.

Artificial intelligence has recently been widely used in computational imaging. The deep neural network (DNN) improves the signal-to-noise ratio of the retrieved images, whose quality is otherwise corrupted due to the low sampling ratio or noisy environments. This work proposes a new computational imaging scheme based on the sequence transduction mechanism with the transformer network. The simulation database assists the network in achieving signal translation ability. The experimental single-pixel detector’s signal will be ‘translated’ into a 2D image in an end-to-end manner. High-quality images with no background noise can be retrieved at a sampling ratio as low as 2%. The illumination patterns can be either well-designed speckle patterns for sub-Nyquist imaging or random speckle patterns. Moreover, our method is robust to noise interference. This translation mechanism opens a new direction for DNN-assisted ghost imaging and can be used in various computational imaging scenarios.