Penalized-likelihood image reconstruction for digital holography.

Conventional numerical reconstruction for digital holography using a filter applied in the spatial-frequency domain to extract the primary image may yield suboptimal image quality because of the loss in high-frequency components and interference from other undesirable terms of a hologram. We propose a new numerical reconstruction approach using a statistical technique. This approach reconstructs the complex field of the object from the real-valued hologram intensity data. Because holographic image reconstruction is an ill-posed problem, our statistical technique is based on penalized-likelihood estimation. We develop a Poisson statistical model for this problem and derive an optimization transfer algorithm that monotonically decreases the cost function at each iteration. Simulation results show that our statistical technique has the potential to improve image quality in digital holography relative to conventional reconstruction techniques.

[1]  Thierry Blu,et al.  A novel non-diffractive reconstruction method for digital holographic microscopy , 2002, Proceedings IEEE International Symposium on Biomedical Imaging.

[2]  Saowapak Sotthivirat,et al.  Statistical image recovery techniques for optical imaging systems. , 2003 .

[3]  E Leith,et al.  Coherence confocal-imaging system for enhanced depth discrimination in transmitted light. , 1996, Applied optics.

[4]  W. Clem Karl,et al.  Edge-preserving image reconstruction for coherent imaging applications , 2002, Proceedings. International Conference on Image Processing.

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

[6]  W. Clem Karl,et al.  Feature-enhanced synthetic aperture radar image formation based on nonquadratic regularization , 2001, IEEE Trans. Image Process..

[7]  Thomas S. Huang,et al.  Image processing , 1971 .

[8]  Jeffrey A. Fessler,et al.  Grouped coordinate descent algorithms for robust edge-preserving image restoration , 1997, Optics & Photonics.

[9]  Alvaro R. De Pierro,et al.  A modified expectation maximization algorithm for penalized likelihood estimation in emission tomography , 1995, IEEE Trans. Medical Imaging.

[10]  Monson H. Hayes,et al.  Phase retrieval using two Fourier-transform intensities , 1990 .

[11]  H Chen,et al.  Electronic holographic imaging through living human tissue. , 1994, Applied optics.

[12]  Jeffrey A. Fessler,et al.  Grouped-coordinate ascent algorithms for penalized-likelihood transmission image reconstruction , 1997, IEEE Transactions on Medical Imaging.

[13]  H Ohzu,et al.  Hybrid holographic microscopy free of conjugate and zero-order images. , 1999, Applied optics.

[14]  E. Cuche,et al.  Digital holography for quantitative phase-contrast imaging. , 1999, Optics letters.

[15]  Pietro Ferraro,et al.  Wave front reconstruction of Fresnel off-axis holograms with compensation of aberrations by means of phase-shifting digital holography , 2002 .

[16]  Timothy J. Holmes.  Maximum-likelihood image restoration adapted for noncoherent optical imaging , 1988 .

[17]  E. Cuche,et al.  Spatial filtering for zero-order and twin-image elimination in digital off-axis holography. , 2000, Applied optics.

[18]  K. Lange.  Convergence of EM image reconstruction algorithms with Gibbs smoothing. , 1990, IEEE transactions on medical imaging.

[19]  Jeffrey A. Fessler,et al.  Image recovery using partitioned-separable paraboloidal surrogate coordinate ascent algorithms , 2002, IEEE Trans. Image Process..

[20]  Manuel Servin,et al.  Parallel algorithms for phase unwrapping based on Markov random field models , 1995 .

[21]  E. Leith,et al.  Reconstructed Wavefronts and Communication Theory , 1962 .

[22]  J A Conchello,et al.  Superresolution and convergence properties of the expectation-maximization algorithm for maximum-likelihood deconvolution of incoherent images. , 1998, Journal of the Optical Society of America. A, Optics, image science, and vision.

[23]  Alfred O. Hero,et al.  Ieee Transactions on Image Processing: to Appear Penalized Maximum-likelihood Image Reconstruction Using Space-alternating Generalized Em Algorithms , 2022 .

[24]  Hakan Erdogan,et al.  Monotonic algorithms for transmission tomography , 2002, 5th IEEE EMBS International Summer School on Biomedical Imaging, 2002..

[25]  C. D. Kemp,et al.  Density Estimation for Statistics and Data Analysis , 1987 .

[26]  H. V. Trees.  Detection, Estimation, And Modulation Theory , 2001 .

[27]  H Chen,et al.  Electronic holography and speckle methods for imaging through tissue using femtosecond gated pulses. , 1991, Applied optics.

[28]  H Ohzu,et al.  Fast numerical reconstruction technique for high-resolution hybrid holographic microscopy. , 1999, Applied optics.

[29]  Y. Censor.  Finite series-expansion reconstruction methods , 1983, Proceedings of the IEEE.

[30]  E N Leith,et al.  Broad-source image plane holography as a confocal imaging process. , 1994, Applied optics.

[31]  J. Goodman.  Introduction to Fourier optics , 1969 .

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

[33]  Ken D. Sauer,et al.  A unified approach to statistical tomography using coordinate descent optimization , 1996, IEEE Trans. Image Process..

[34]  R. White,et al.  Image recovery from data acquired with a charge-coupled-device camera. , 1993, Journal of the Optical Society of America. A, Optics and image science.