This paper describes a generalized theoretical framework for a multiplexed spatially encoded imaging system to acquire multi-channel data. The framework is confirmed with simulations and experimental demonstrations. In the system, each channel associated with the object is spatially encoded, and the resultant signals are multiplexed onto a detector array. In the demultiplexing process, a numerical estimation algorithm with a sparsity constraint is used to solve the underdetermined reconstruction problem. The system can acquire object data in which the number of elements is larger than that of the captured data. This case includes multi-channel data acquisition by a single-shot with a detector array. In the experiments, wide field-of-view imaging and spectral imaging were demonstrated with sparse objects. A compressive sensing algorithm, called the two-step iterative shrinkage/thresholding algorithm with total variation, was adapted for object reconstruction.
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