A Plug-and-Play Priors Approach for Solving Nonlinear Imaging Inverse Problems

In the past two decades, nonlinear image reconstruction methods have led to substantial improvements in the capabilities of numerous imaging systems. Such methods are traditionally formulated as optimization problems that are solved iteratively by simultaneously enforcing data consistency and incorporating prior models. Recently, the Plug-and-Play Priors (PPP) framework suggested that by using more sophisticated denoisers, not necessarily corresponding to an optimization objective, it is possible to improve the quality of reconstructed images. In this letter, we show that the PPP approach is applicable beyond linear inverse problems. In particular, we develop the fast iterative shrinkage/thresholding algorithm variant of PPP for model-based nonlinear inverse scattering. The key advantage of the proposed formulation over the original ADMM-based one is that it does not need to perform an inversion on the forward model. We show that the proposed method produces high quality images using both simulated and experimentally measured data.

[1]  J. Moreau.  Proximité et dualité dans un espace hilbertien , 1965 .

[2]  E. Wolf.  Three-dimensional structure determination of semi-transparent objects from holographic data , 1969 .

[3]  Y. Nesterov.  A method for solving the convex programming problem with convergence rate O(1/k^2) , 1983 .

[4]  L. Rudin,et al.  Nonlinear total variation based noise removal algorithms , 1992 .

[5]  G. Pelosi,et al.  Scattering from inhomogeneous media with rough interface illuminated by a pencil-beam: a hybrid perturbative-finite elements approach , 1995, 1995 International Geoscience and Remote Sensing Symposium, IGARSS '95. Quantitative Remote Sensing for Science and Applications.

[6]  E. Wolf,et al.  Principles of Optics (7th Ed) , 1999 .

[7]  A. R. Stokes,et al.  Principles of Optics: Scattering from inhomogeneous media , 1999 .

[8]  C. Eyraud,et al.  Free space experimental scattering database continuation: experimental set-up and measurement precision , 2005 .

[9]  Emmanuel J. Candès,et al.  Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information , 2004, IEEE Transactions on Information Theory.

[10]  David L Donoho,et al.  Compressed sensing , 2006, IEEE Transactions on Information Theory.

[11]  Alessandro Foi,et al.  Image Denoising by Sparse 3-D Transform-Domain Collaborative Filtering , 2007, IEEE Transactions on Image Processing.

[12]  C. Fang-Yen,et al.  Tomographic phase microscopy , 2008, Nature Methods.

[13]  F. Schmitt,et al.  Linear inverse problems in imaging , 2008, IEEE Signal Processing Magazine.

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

[15]  Marc Teboulle,et al.  Fast Gradient-Based Algorithms for Constrained Total Variation Image Denoising and Deblurring Problems , 2009, IEEE Transactions on Image Processing.

[16]  L. Tian,et al.  Quantitative measurement of size and three-dimensional position of fast-moving bubbles in air-water mixture flows using digital holography. , 2010, Applied optics.

[17]  José M. Bioucas-Dias,et al.  Fast Image Recovery Using Variable Splitting and Constrained Optimization , 2009, IEEE Transactions on Image Processing.

[18]  Heinz H. Bauschke,et al.  Convex Analysis and Monotone Operator Theory in Hilbert Spaces , 2011, CMS Books in Mathematics.

[19]  Brendt Wohlberg,et al.  Plug-and-Play priors for model based reconstruction , 2013, 2013 IEEE Global Conference on Signal and Information Processing.

[20]  Lei Zhang,et al.  Weighted Nuclear Norm Minimization with Application to Image Denoising , 2014, 2014 IEEE Conference on Computer Vision and Pattern Recognition.

[21]  Thomas Brox,et al.  iPiano: Inertial Proximal Algorithm for Nonconvex Optimization , 2014, SIAM J. Imaging Sci..

[22]  Michael Unser,et al.  Learning approach to optical tomography , 2015, 1502.01914.

[23]  Dehong Liu,et al.  Compressive tomographic radar imaging with total variation regularization , 2016, 2016 4th International Workshop on Compressed Sensing Theory and its Applications to Radar, Sonar and Remote Sensing (CoSeRa).

[24]  Demetri Psaltis,et al.  Optical Tomographic Image Reconstruction Based on Beam Propagation and Sparse Regularization , 2016, IEEE Transactions on Computational Imaging.

[25]  José M. Bioucas-Dias,et al.  Image restoration and reconstruction using variable splitting and class-adapted image priors , 2016, 2016 IEEE International Conference on Image Processing (ICIP).

[26]  Michael Elad,et al.  Turning a denoiser into a super-resolver using plug and play priors , 2016, 2016 IEEE International Conference on Image Processing (ICIP).

[27]  Charles A. Bouman,et al.  Plug-and-Play Priors for Bright Field Electron Tomography and Sparse Interpolation , 2015, IEEE Transactions on Computational Imaging.

[28]  Hassan Mansour,et al.  A Recursive Born Approach to Nonlinear Inverse Scattering , 2016, IEEE Signal Processing Letters.

[29]  Stanley H. Chan,et al.  Plug-and-Play ADMM for Image Restoration: Fixed-Point Convergence and Applications , 2016, IEEE Transactions on Computational Imaging.

[30]  Hassan Mansour,et al.  Compressive imaging with iterative forward models , 2016, 2017 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP).

[31]  Hassan Mansour,et al.  SEAGLE: Sparsity-Driven Image Reconstruction Under Multiple Scattering , 2017, IEEE Transactions on Computational Imaging.