Compressive sensing (CS) has been used in in-line digital holography (DH) to eliminate the noise, especially the interference caused by twin image. In this work, we combine the two-step iterative shrinkage-thresholding (TwIST) algorithm in CS and autofocusing methods to accomplish high-resolution imaging from a single-exposure hologram. We preprocess all the images within a reconstruction distance through TwIST algorithm, and then evaluate the focal plane of the images according to the focusing functions including the Laplace operator and the absolute gradient operator, etc. The proposed method can not only effectively eliminate twin image to improve the imaging quality, but also perform unique advantages to estimate the in-focus distance in DH.
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