SAR Image Autofocusing using Wirtinger calculus and Cauchy regularization

In this paper, an optimization model using Cauchy regularization is proposed for simultaneous SAR image reconstruction and autofocusing. A coordinate descent framework in which the desired image and the phase errors are optimized alternatively is designed to solve the model. For the subproblem of estimating the image, we utilize the techniques of Wirtinger calculus to directly minimize the cost function which involves complex variables. We also utilise a state-of-the-art, sparsity-enforcing Cauchy regularizer. The proposed method is demonstrated to give impressive autofocusing results by conducting experiments on both simulated scene and real SAR image.

[1]  Jörn Ostermann,et al.  Backprojection Subimage Autofocus of Moving Ships for Synthetic Aperture Radar , 2019, IEEE Transactions on Geoscience and Remote Sensing.

[2]  M. Çetin,et al.  Autofocused compressive SAR imaging based on the alternating direction method of multipliers , 2017, 2017 IEEE Radar Conference (RadarConf).

[3]  Charles V. Jakowatz,et al.  Phase gradient autofocus-a robust tool for high resolution SAR phase correction , 1994 .

[4]  Joshua M. Kantor.  Polar Format-Based Compressive SAR Image Reconstruction With Integrated Autofocus , 2020, IEEE Transactions on Geoscience and Remote Sensing.

[5]  B. A. D. H. Brandwood.  A complex gradient operator and its applica-tion in adaptive array theory , 1983 .

[6]  Minh N. Do,et al.  SAR Image Autofocus By Sharpness Optimization: A Theoretical Study , 2007, IEEE Transactions on Image Processing.

[7]  Mike E. Davies,et al.  Auto-focus for under-sampled synthetic aperture radar , 2012 .

[8]  Jack Walker,et al.  Range-Doppler Imaging of Rotating Objects , 1980, IEEE Transactions on Aerospace and Electronic Systems.

[9]  Orhan Arikan,et al.  SAR image reconstruction and autofocus by compressed sensing , 2012, Digit. Signal Process..

[10]  J. Kantor.  Minimum entropy autofocus correction of residual range cell migration , 2017, 2017 IEEE Radar Conference (RadarConf).

[11]  J J Miller,et al.  Aberration correction by maximizing generalized sharpness metrics. , 2003, Journal of the Optical Society of America. A, Optics, image science, and vision.

[12]  Müjdat Çetin,et al.  A Sparsity-Driven Approach for Joint SAR Imaging and Phase Error Correction , 2012, IEEE Transactions on Image Processing.

[13]  Alin Achim,et al.  Convergence Guarantees for Non-Convex Optimisation With Cauchy-Based Penalties , 2020, IEEE Transactions on Signal Processing.

[14]  Richard Barrett,et al.  Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods , 1994, Other Titles in Applied Mathematics.

[15]  Alin Achim,et al.  On Solving SAR Imaging Inverse Problems Using Nonconvex Regularization With a Cauchy-Based Penalty , 2021, IEEE Transactions on Geoscience and Remote Sensing.

[16]  Joshua N. Ash,et al.  An Autofocus Method for Backprojection Imagery in Synthetic Aperture Radar , 2012, IEEE Geoscience and Remote Sensing Letters.

[17]  Ken Kreutz-Delgado,et al.  The Complex Gradient Operator and the CR-Calculus ECE275A - Lecture Supplement - Fall 2005 , 2009, 0906.4835.

[18]  P. Berens.  Introduction to Synthetic Aperture Radar (SAR) , 2006 .

[19]  G. Donohoe,et al.  Subaperture autofocus for synthetic aperture radar , 1994 .

[20]  Mujdat Cetin,et al.  An Augmented Lagrangian Method for autofocused Compressed SAR Imaging , 2015, 2015 3rd International Workshop on Compressed Sensing Theory and its Applications to Radar, Sonar and Remote Sensing (CoSeRa).

[21]  Kazuo Ouchi,et al.  Recent Trend and Advance of Synthetic Aperture Radar with Selected Topics , 2013, Remote. Sens..

[22]  I. Hajnsek,et al.  A tutorial on synthetic aperture radar , 2013, IEEE Geoscience and Remote Sensing Magazine.

[23]  Mike E. Davies,et al.  Sparsity-based autofocus for undersampled synthetic aperture radar , 2014, IEEE Transactions on Aerospace and Electronic Systems.