Single-shot scattering imaging beyond the optical memory effect via speckle-sparsity decoupling

Overcoming the optical memory effect range to achieve large field-of-view imaging through scattering media without prior information has remained a significant challenge. We present a single-shot large field-of-view imaging technique based on the spatial sparsity characteristics theory of speckle pattern, enabling blind reconstruction of multiple targets beyond the optical memory effect range without prior information or wavefront modulation. The theoretical innovation lies in revealing the spatially sparse distribution of speckles when multiple isolated targets exceed the optical memory effect separation distance. By establishing a sparse mapping relationship between scattering transmission and object space, the method achieves unsupervised decoupling of low-cross-talk speckle regions while simultaneously reconstructing target intensity and positional information. Combined with the modified phase retrieval algorithm, the complete scene of multiple targets beyond the optical memory effect range is reconstructed. Experiments show that under varying scattering media and spectral bandwidths, this approach achieves a field-of-view expansion exceeding 6.82 times that of conventional methods, with a relative localization accuracy of 97.5%. We present the first introduction of spatial sparsity concepts into speckle field analysis; it establishes a new theoretical framework for deep-tissue biological observation and optical sensing in complex environments.