Compressed sensing (CS) is an exciting, rapidly growing field that has attracted considerable attention in recent years. CS offers a framework for simultaneous sensing and compression that relies on linear dimensionality reduction. Quite surprisingly, it predicts that sparse high-dimensional signals can be recovered from highly incomplete measurements using efficient algorithms. This sparse signal structure can also be leveraged to improve other performance measures such as denoising and resolution. In this tutorial we review some of the basics of CS and consider several applications to optical imaging including subwavelength and coherent-diffraction imaging.

© 2012 Optical Society of America

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