Noise reduction for compressive digital one-shot in-line holographic tomography

Digital holography can reconstruct 3-D data cube from a 2-D hologram for the tomographic imaging. Digital one-shot inline holography (DOIH) maintains the maximal space-bandwidth product compared with off-axis holography and keeps both amplitude and phase in the interference pattern. DOIH often suffers from intrinsic defects such as twin-image interruption and squared noise. In this work, compressive sensing is applied in the tomographic reconstruction to overcome the defects. The designed algorithm based on compressive DOIH demonstrates the feasibility in removing the squared noise from a single 2-D in-line hologram.

[1]  Loïc Denis,et al.  Inline hologram reconstruction with sparsity constraints. , 2009, Optics letters.

[2]  D. Gabor.  A New Microscopic Principle , 1948, Nature.

[3]  Zeev Zalevsky,et al.  Compressive Fresnel holography approach for high-resolution viewpoint inference. , 2015, Optics letters.

[4]  Massimo Fornasier,et al.  Compressive Sensing , 2015, Handbook of Mathematical Methods in Imaging.

[5]  L. Tian,et al.  Scanning-free compressive holography for object localization with subpixel accuracy. , 2012, Optics letters.

[6]  Mark A Foster,et al.  Single-pixel imaging using compressed sensing and wavelength-dependent scattering. , 2016, Optics letters.

[7]  Elsa D. Angelini,et al.  Compressed Sensing with off-axis frequency-shifting holography , 2010, Optics letters.

[8]  R.G. Baraniuk,et al.  Compressive Sensing [Lecture Notes] , 2007, IEEE Signal Processing Magazine.

[9]  Mehadi Hassan,et al.  Snapshot fan beam coded aperture coherent scatter tomography. , 2016, Optics express.

[10]  Emmanuel J. Candès,et al.  Tight Oracle Inequalities for Low-Rank Matrix Recovery From a Minimal Number of Noisy Random Measurements , 2011, IEEE Transactions on Information Theory.

[11]  M E Gehm,et al.  Single-shot compressive spectral imaging with a dual-disperser architecture. , 2007, Optics express.

[12]  Daniel L Marks,et al.  Compressive holography. , 2009, Optics express.

[13]  I. Yamaguchi,et al.  Phase-shifting digital holography. , 1997, Optics letters.

[14]  Lei Tian,et al.  Compressive holographic two-dimensional localization with 1/30(2) subpixel accuracy. , 2014, Optics express.

[15]  Qiang Guo,et al.  Compressive sensing based high-speed time-stretch optical microscopy for two-dimensional image acquisition. , 2015, Optics express.

[16]  Emmanuel J. Candès,et al.  A Probabilistic and RIPless Theory of Compressed Sensing , 2010, IEEE Transactions on Information Theory.

[17]  ANTONIN CHAMBOLLE,et al.  An Algorithm for Total Variation Minimization and Applications , 2004, Journal of Mathematical Imaging and Vision.

[18]  Thomas S. Huang,et al.  Digital Holography , 2003 .

[19]  T. Poon,et al.  Three-dimensional microscopy by optical scanning holography , 1995 .

[20]  José M. Bioucas-Dias,et al.  A New TwIST: Two-Step Iterative Shrinkage/Thresholding Algorithms for Image Restoration , 2007, IEEE Transactions on Image Processing.