Imaging and Inverse Problems

• 3D Imaging
  1. A. Fannjiang Toward noisy 1-bit diffraction tomography arXiv: 2310.05571
  2. A. Fannjiang 3D Tomographic Phase Retrieval and Unwrapping Inverse Problems 40(2024) 015015
  3. A. Fannjiang Uniqueness Theorems for Tomographic Phase Retrieval with Few Diffraction Patterns Inverse Problems 38 (2022) 085008
• Superresolution
  1. W. Li, W. Liao & A. Fannjiang Super-resolution limit of the ESPRIT algorithm IEEE Transactions on Information Theory 66 (2020), 4593-4608.
  2. A. Fannjiang Information and Resolution 2017 Asilomar Conference on Signals, Systems, and Computers.
  3. A. Fannjiang Compressive Spectral Estimation with Single-Snapshot ESPRIT: Stability and Resolution arXiv:1607.01827
  4. W. Liao, A. Fannjiang MUSIC for single-snapshot spectral estimation: Stability and super-resolution Applied and Computational Harmonic Analysis 2015.
  5. A. Fannjiang Exact Localization and Superresolution with noisy data and random illumination Inverse Problems 27 (2011) 065012
• Phase retrieval & Ptychography
  1. A. Fannjiang & T. Strohmer The Numerics of Phase Retrieval Acta Numerica , Volume 29 , May 2020 , pp. 125-228
  2. A. Fannjiang and Z. Zhang Fixed point analysis of Douglas-Rachford Splitting for ptychography and phase retrieval SIAM J. Imaging Sci. 13(2), 609-650 (2020).( Download codes)
  3. A. Fannjiang & P. Chen Blind Ptychography: uniqueness and ambiguities Inverse Problems 36 (2020) 045005
  4. A. Fannjiang Raster scan pathology and the cure SIAM Multiscale Modeling & Simulation 2019, Vol. 17, No. 3, pp. 973-995.
  5. P. Chen & A. Fannjiang Coded Aperture Ptychography: Uniqueness and Reconstruction Inverse Problems 34 (2018) 025003.
  6. P. Chen, A. Fannjiang, G. Liu Phase retrieval by linear algebra SIAM J. MATRIX ANAL. APPL (2017) Vol. 38, No. 3, pp. 854 - 868( Download codes) Erratum
  7. P. Chen, A. Fannjiang, G. Liu Phase retrieval with one or two diffraction patterns by alternating projections of the null vector Journal of Fourier Analysis and Applications June 2018, Volume 24, pp 719-758. ( Download codes)
  8. P. Chen and A. Fannjiang FOURIER PHASE RETRIEVAL WITH A SINGLE MASK BY DOUGLAS-RACHFORD ALGORITHM Applied and Computational Harmonic Analysis . Volume 44, Issue 3, May 2018, Pages 665-699.
  9. A. Fannjiang Fourier-Domain Fixed Point Algorithms with Coded Diffraction Patterns arXiv:1406.2742
  10. A. Fannjiang and W. Liao Fourier phasing with phase-uncertain mask Inverse Problems 29(2013) 125001 ( Download codes)
  11. A. Fannjiang and W. Liao Phase retrieval with random phase illumination Journal of Optical Society of America A 29 (2012), 1847-1859. ( Download codes)
  12. A. Fannjiang Absolute uniqueness in phase retrieval with random illumination Inverse Problems 28 (2012) 075008 (20pp)
  13. A. Fannjiang and W. Liao Compressed sensing phase retrieval IEEE Proc. Asilomar conference on signals, systems and computers, 2011.
• Compressive Imaging
  1. A Fannjiang Compressive Sensing Theory for Optical Systems Described by a Continuous Model in Optical Compressive Imaging, Taylor & Francis 2017.
  2. A. Fannjiang, W. Liao Super-resolution by compressive sensing algorithms IEEE Proc. Asilomar conference on signals, systems and computers, 2012.
  3. A. Fannjiang and H Tseng Compressive Radar with off-grid targets Inverse Problems 29 (2013) 054008 (Download codes)
  4. A. Fannjiang TV-min and greedy pursuit for constrained joint sparsity and application to inverse scattering Mathematics and Mechanics of Complex Systems Vol. 1(2013), No. 1, pp.81-104
  5. A. Fannjiang and W. Liao Mismatch and resolution in compressive imaging Wavelets and Sparsity XIV, edited by Manos Papadakis, Dimitri Van De Ville, Vivek K. Goyal, Proc. of SPIE Vol. 8138.
  6. A. Fannjiang & H. Tseng Compressive Imaging of Subwavelength Structures II. Periodic Rough Surfaces Journal of Optical Society of America A 29(4) 617-626 (2012)
  7. A. Fannjiang & W. Liao Coherence-Pattern Guided Compressive Sensing with Unresolved Grids SIAM Journal of Imaging Sciences, Vol. 5, No. 1, pp. 179-202 (2012) (Download codes)
  8. A. Fannjiang Exact Localization and Superresolution with noisy data and random illumination Inverse Problems 27 (2011) 065012
  9. A. Fannjiang The MUSIC algorithm for sparse objects: a compressed sensing analysis Inverse Problems 27 (2011) 035013(32pp)
  10. A. Fannjiang Compressive inverse scattering II. Multi-shot SISO measurements with Born scatterers
      Inverse Problems 26 (2010), 035009
  11. A. Fannjiang Compressive inverse scattering I. high-frequency SIMO/MISO and MIMO measurements
      Inverse Problems 26 (2010), 035008
  12. A. Fannjiang Compressive imaging of subwavelength structures SIAM Journal on Imaging Sciences 2 (2009) 1277-1291.
  13. A. Fannjiang, T. Strohmer and P. Yan: Compressed Remote Sensing of Sparse Object. SIAM Journal on Imaging Sciences 3 (2010) 596-618.
• Imaging in Random Media
  1. A. Fannjiang Introduction to propagation, time reversal and imaging in random media Multi-Scale Phenomena in Complex Fluids - Modeling, Analysis and Numerical Simulation, eds. T.Y Hou, C. Liu and J.G. Liu, World Scientific, 2009.
  2. A. Fannjiang, K. Solna and M. Yan: Synthetic aperture imaging of multiple point targets in Rician fading media
     SIAM Imaging Sciences 2 (2009) 344-366.
  3. A. Fannjiang and Mike Yan: Multi-frequency imaging of multiple targets in Rician fading channels: stability and resolution
     Inverse Problems 23 (2007) 1801-1819
  4. A. Fannjiang and K. Solna: Broadband Resolution Analysis for Imaging with Measurement Noise
     Journal of Optical Society of America A, Vol. 24 (2007) pp. 1623-1632
• Time reversal communications
  1. A. Fannjiang: Information Transfer in Disordered Media by Broadband Time Reversal: Stability, Resolution and Capacity
     Nonlinearity 19 (2006) 2425-2439.
  2. A. Fannjiang: Time Reversal Communication in Rayleigh Fading Broadcast Channels with Pinholes
     Physics Letters A Vol 353/5 (2006) pp 389-397
     
  3. A. Fannjiang: On time reversal mirrors Inverse Problems 25(2009) 095010.
  4. A. Fannjiang and K. Solna: Superresolution and Duality for Time-Reversal of Waves in Random Media
     Physics Letters A Vol 352:1-2 (2005), pp. 22-29.
  5. A. Fannjiang and K. Solna: Time Reversal of Parabolic Waves and Two-Frequency Wigner Distribution
     Discrete and Continuous Time Dynamical Systems. Volume 6, 2006, Pages: 783 - 802
  6. A. Fannjiang and K. Solna: Propagation and Time-reversal of Wave Beams in Atmospheric Turbulence
     SIAM Multiscale Modeling and Simulation 3:3 (2005), pp. 522-558

Radiative Transfer

• Two-frequency analysis
  1. A. Fannjiang: Mutual Coherence of Polarized Light in Disordered Media: Two-Frequency Method Extended
     Journal of Physics A: Math and Theor. 40 No 45 (9 November 2007) 13667-13683, IOP Select (http://Select.iop.org.)
  2. A. Fannjiang: Two-Frequency Radiative Transfer. II: Maxwell Equations in Random Dielectrics
     Journal of Optical Society of America A Vol. 24, Issue 12, pp. 3680-3690, 2007.
  3. A. Fannjiang: Two-frequency radiative transfer and asymptotic solution.
     Journal of Optical Society of America A Vol. 24 (2007), pp. 2248-2256
  4. A. Fannjiang: Self-Averaging Scaling Limits of Two-Frequency Wigner Distribution for Random Paraxial Waves
     J. Phys. A: Math. Theor. 40 (2007) 5025-5044.
  5. A. Fannjiang: Radiative transfer limit of two-frequency Wigner distribution for random parabolic waves: An exact solution
     Comptes Rendus Physique Volume 8, Issue 2 , March 2007, Pages 267-271
  6. A. Fannjiang: White-Noise and Geometrical Optics Limits of Wigner-Moyal Equation for Wave Beams in Turbulent Media II. Two-Frequency Wigner Distribution Formulation.
     Journal of Statistical Physics 120 (2005), 543-586.
  7. A. Fannjiang: Space-frequency correlation of classical waves in disordered media: high-frequency and small-scale asymptotics
     Europhysics Letters Vol 80 (2007) 14005.
• One-frequency analysis
  1. A. Fannjiang: Self-Averaging Radiative Transfer for Parabolic Waves
     Comptes rendus de l'Académie des sciences- Mathematics Volume 342, Issue 2, 15 January 2006, Pages 109-114
  2. A. Fannjiang: Parabolic approximation, radiative transfer and time reversal
     Journal of Physics: Conf. Ser. 7 (2005) 121-137.
  3. A. Fannjiang: Self-Averaging Scaling Limits for Random Parabolic Waves
     Archives of Rational Mechanics and Analysis 175:3 (2005), pp. 343 - 387
  4. A. Fannjiang: White-Noise and Geometrical Optics Limits of Wigner-Moyal Equation for Wave Beams in Turbulent Media.
     Communications in Mathematical Physics. 254:2 (2005), pp. 289-322.
  5. A. Fannjiang and K. Solna: Scaling limits for laser beam propagation in atmospheric turbulence
     Stochastics and Dynamics 4:1(2004), pp. 135-150
  6. G. Bal, A. Fannjiang, G.C Papanicolaou L. Ryzhik Radiative Transport in a Periodic Structure
     J. Stat. Phys. 95:1-2 (1999), pp.479-494.
  7. A. Fannjiang and L. Ryzhik: Radiative Transfer of Sound Waves in a Random Flow: Turbulent Scattering, Straining and Mode-Coupling
     SIAM J. Appl. Math. 61:5(2001), pp. 1545-1577

Nonlinear Waves

1. A. Fannjiang: Phase space models for stochastic nonlinear parabolic waves: wave spread and collapse
   Journal of Physics A.: Math. Gen. Vol 39 (2006), 11383-11398.
2. A. Fannjiang: Nonlinear Schr\"odinger Equation with a White-Noise Potential: Phase-space Approach to Spread and Singularity
   Physica D, Volume 212, Issues 3-4, 2005, Pages 195-204.
3. A. Fannjiang, S. Jin and G. Papanicolaou: High Frequency Behavior of the Focusing Nonlinear Schroedinger Equation with Random Inhomogeneities
   SIAM J. Appl. Math. 63(2003), pp. 1328-1358.
4. A. Fannjiang, A. Kiselev and L. Ryzhik: Quenching of Reaction by Cellular Flows
   Geometrical and Functional Analysis, 16 (2006) 40-69
   

Classical and Quantum Chaos

1. A. Fannjiang, S. Nonnenmacher and L. Wolowski: Relaxation Time of Quantized Toral Maps
   Annales de l'Institut Henri Poincare (C) Non Linear Analysis, 7 (2006), no. 1, 161-198.
2. A. Fannjiang, S. Nonnenmacher and L. Wolowski: Dissipation time and decay of correlations
   Nonlinearity 17 (July 2004) 1481-1508
3. A. Fannjiang and L. Wolowski: Noise-Induced Dissipation in discrete time conservative systems
   Journal of Statistical Physics, 113:112 (2003), pp. 335-378
4. A. Fannjiang: Time Scales in Homogenization of Periodic Flows with Vanishing Molecular Diffusion
   J. Diff. Eq. 179(2002), pp. 433-455.
5. A. Fannjiang: Time Scales in Noisy Conservative Systems
   Lec. Notes Phys 450 (1995), pp. 124-139.

Turbulent Transport

• Small-Scale Relative diffusion
  1. A. Fannjiang: Invariance Principle for Inertial-Scale Behavior of Scalar Field in Kolmogorov-type Turbulence
     Physica D, 179: 3-4 (2003), pp. 161-182.
  2. A. Fannjiang: Convergence of Passive Scalars in Ornstein-Uhlenbeck Flows to Kraichnan's Model
     Journal of Statistical Physics 114:1/2 (2004), 115-135.
  3. A. Fannjiang, L. Ryzhik and G. Papanicolaou: Evolution of Trajectory Correlations in Steady Random Flows
     Proc. Symp. Appl. Math. 54(1998), pp. 105-130.
  4. A. Fannjiang, T. Komorowski and S. Peszat Lagrangian Dynamics for a Passive Tracer in a Class of Gaussian Markovian Flows
     Stoch. Proc. Appl. 97 (2002), pp. 171-198
• Convection-Enhanced Diffusion
  1. A. Fannjiang and G. Papanicolaou: Convection Enhanced Diffusion for Periodic Flows.
     SIAM J. Appl. Math. 54:2(1994), pp. 333-408.
  2. A. Fannjiang and G. Papanicolaou: Convection Enhanced Diffusion for Random Flows
     J. Stat. Phys 88:5-6(1997), pp. 1033-76
• Large-Scale Turbulent Diffusion
  1. A. Fannjiang and G. Papanicolaou: Diffusion in Turbulence
     Probab. Th. Rel. Fields 105 (1996), pp. 279-334.
  2. A. Fannjiang: Boundary Value Problems with Unbounded Random Flows
     J. Diff. Eq. 143:2 (1998), pp. 327-359.
  3. A. Fannjiang and T. Komorowski: A Martingale Approach to Homogenization of Unbounded Random Flows
     Ann. Probab. 25:4(1997), pp. 1872-1894
  4. A. Fannjiang and T. Komorowski: An Invariance Principle for Diffusion in Turbulence
     Ann. Probab. 27:2 (1999), pp. 751-781.
  5. A. Fannjiang and T. Komorowski: Turbulent Diffusion in Markovian Flows
     Ann. Appl. Probab. 9:3 (1999), pp. 591-610.
  6. A. Fannjiang and T. Komorowski: Invariance Principle for a Diffusion in a Markov Field
     Bull. Pol. Acad. Sci. 49(1) (2001).
  7. A. Fannjiang and T. Komorowski: Diffusive and Non-diffusive limits for Transport in Non-Mixing Flows
     SIAM J. Appl. Math. 62:3(2002), pp. 909-923 A. Fannjiang and T. Komorowski: Diffusions in Long-Range Correlated Ornstein-Uhlenbeck Flows
     Electronic Journal of Probability 7(2002), 20
• Phase Diagrams for Anomalous Diffusion
  1. A. Fannjiang: Phase Diagram for Turbulent Transport
     Physica D Vol. 136, Nos. 1-2, pp. 145-174. Erratum Physica D 157(2001), pp. 166-168
  2. A. Fannjiang: Anomalous Diffusion in Random Flows
     IMA Math Appl. 99 (1998), pp. 81-99. A. Fannjiang and T. Komorowski: Limit Theorems for Motions in a Flow with a Nonzero Drift
     Bull. Pol. Acad. Sci. 47:4 (1999), pp. 393-413.
  3. A. Fannjiang and T. Komorowski: Taylor-Kubo Formula for Turbulent Diffusion in a Non-Mixing Flow with Long-Range Correlation
     Bull. Pol. Acad. Sci. 48 (3)(2000), pp 253-275
• Fractional Brownian Motion in Turbulence
  1. A. Fannjiang and T. Komorowski: Fractional Brownian Motion Limit for Turbulent Transport
     Ann. Appl. Probab. 10:4 (2000), pp. 1100-1120.
  2. A. Fannjiang and T. Komorowski: Fractional Brownian Motions and Enhanced Diffusion in a Unidirectional Wave-like Turbulence.
     J. Stat. Phys. 100:5/6(2000), pp. 1071-1095.
  3. A. Fannjiang and T. Komorowski: Frozen Path Approximation for Turbulent Diffusion and Fractional Brownian Motion in Random Flows.
     SIAM Journal on Applied Mathematics, 63:6(2003), pp. 2042-2062

Gradient Elasticity and Fracture

1. Y.-S. Chan, A. Fannjiang, G. Paulino and B.-F. Feng: Finite part integrals and hypersingular kernels Dynamics of Continuous, Discrete and Impulsive Systems A 14 (S2) 264-269 (2007).
2. G.H. Paulino, A. Fannjiang and Y.-S. Chan: Gradient Elasticity Solution for a Mode III Crack in a Functionally Graded Materials
   Materials Science Forum Vols. 308-311 (1999), pp. 971-976.
3. G.H. Paulino, Y.-S. Chan and A. Fannjiang: The crack problem for Nonhomogeneous Materials Under Antiplane Shear Loading - A Displacement Based Formulation
   Int. J. Solids Structures 38:17 (2001), pp. 2989-3005.
4. Y.S. Chan, A. Fannjiang and G. Paulino: Integral Equations with Hypersingular Kernels - Theory and Applications to Fracture Mechanics
   International Journal of Engineering Science 41:7(2003), pp. 683-720
5. A. Fannjiang, Y.S. Chan and G. Paulino: Strain Gradient Elasticity for Anti-Plane Shear Cracks: A Hypersingular Integrodifferential Equation Approach
   SIAM Journal on Applied Mathematics 62:3(2002), pp. 1066-1091
6. Y.-S. Chan, A.C. Fannjiang and G.H. Paulino: Gradient Elasticity Theory for Mode I Crack in Functionally Graded Materials
   Ceramic Transactions 114(2001), pp. 731-738.
7. G. Paulino, A. Fannjiang and Y.-S. Chan: Gradient Elasticity Theory for Mode III Fracture in Functionally Graded Materials - Part I: Crack Perpendicular to the Material Gradient.
   ASME Journal of Applied Mechanics, 70:4(2003), pp. 531-542
8. Y.-S. Chan, G. Paulino and A. Fannjiang: Gradient Elasticity Theory for Mode III Fracture in Functionally Graded Materials - Part II: Crack parallel to the Material Gradation.
   ASME Journal of Applied Mechanics 75:6 (2008) 061015
9. Y.-S. Chan, G. Paulino and A. Fannjiang: Change of Constitutive Relations Due to Interaction between Strain-Gradient Effect and Material Gradation
   ASME Journal of Applied Mechanics - September 2006 - Volume 73, Issue 5, pp. 871-875

Miscellaneous

1. Einstein's religious thought
   Oversea Campus Magazine, No. 62, December, 2003.
   
2. Spinoza's view on religion
   Oversea Campus Magazine, No. 63, February, 2004.
   

• As far as mathematics is certain, it is not true; as far as it is true, it is not certain - Albert Einstein.
• If the true is what is grounded, then the ground is not true, nor yet false - Ludwig Wittgenstein