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The coded aperture lensless imaging is a flexible system that replaces bulky lenses with a coded mask. The convolutional model expresses its forward imaging process compactly but fails when the measurements are distorted due to hardware restrictions. To overcome this problem, we generalize the convolutional model by introducing restricted factors to the imaging forward model explicitly. In detail, hardware restrictions are categorized into the linear part and the noise-like part. A compressed sensing algorithm based on the gradient sparsity of natural images is employed to solve the ill-posed inverse problem. Both numerical and experimental tests verify that the proposed model alleviates the artifact effect caused by down-sampling while performing reconstruction with higher resolution. This method is also valid for multi-wavelength and 3D imaging, lowering the using threshold of lensless cameras.
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