In Search of Robustness and Efficiency via l1− and l2− Regularized Optimization for Physiological Motion Compensation
Compensating physiological motion in the context of minimally invasive cardiac surgery has become an attractive issue since it outperforms traditional cardiac procedures offering remarkable benefits. Owing to space restrictions, computer vision techniques have proven to be the most practical and suitable solution. However, the lack of robustness and efficiency of existing methods make physiological motion compensation an open and challenging problem. This work focusses on increasing robustness and efficiency via exploration of the classes of 1−and 2−regularized optimization, emphasizing the use of explicit regularization. Both approaches are based on natural features of the heart using intensity information. Results pointed out the 1−regularized optimization class as the best since it offered the shortest computational cost, the smallest average error and it proved to work even under complex deformations.
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 J. Livesay, "The benefits of off-pump coronary bypass: A reality or an illusion?” Texas Heart Institute Journal, pp. 258–260, 2003.
 V. Vitiello, K. Kwok, and G. Yang, "Introduction to robot-assisted minimally invasive surgery,” Book Chapter, Medical Robotics Minimally Invasive Surgery, 2012.
 M. L. Koransky, M. L. Tavana, A. Yamaguchi, M. H. Kown, D. N. Miniati, W. Nowlin, and R. C. Robbins, "Quantification of mechanical stabilization for the performance of off-pump coronary artery surgery,” Heart Surg. Forum, vol. 6, pp. 224–231, 2003.
 A. Lemma, A. Mangini, A. Redaelli, and F. Acocella, "Do cardiac stabilizers really stabilize? experimental quantitative analysis of mechanical stabilization,” Interactive CardioVascular and Thoracic Surgery, 2005.
 S. Atashzar, I. Khalaji, M. Shahbazi, A. Talasaz, R. Patel, and M. Naish, "Robot-assisted lung motion compensation during needle insertion,” IEEE International Conference on Robotics and Automation, pp. 1682–1687, 2013.
 J. Gagne, W. Bachta, P. Renaud, P. O., Laroche, and J. Gangloff, "Beating heart surgery: Comparison of two active compensation solutions for minimally invasive coronary artery bypass grafting,” Book Chapter Computational Surgery and Dual Training Computing, Robotics and Imaging, pp. 203–210, 2014.
 L. Hoff, O. Elle, M. Grimnes, S. Halvorsen, H. Alker, and E. Fosse, "Measurements of heart motion using accelerometers,” Proceedings of the 26th Annual International Conference of the IEEE EMBS, pp. 2049–2051, 2004.
 M. Hayashibe, N. Suzuki, and Y. Nakamura, "Laser-scan endoscope system for intraoperative geometry acquisition and surgical robot safety management,” Journal in Medical Image Analysis, pp. 509–519, 2006.
 O. Bebek and M. Cavusoglu, "Whisker sensor design for three dimensional position measurement in robotic assisted beating heart surgery,” IEEE International Conference on Robotics and Automation, pp. 225–231, 2007.
 P. Puangmali, H. Liu, K. Althoefer, and L. Seneviratne, "Optical fiber sensor for soft tissue investigation during minimally invasive surgery,” IEEE International Conference on Robotics and Automation, pp. 2934–2939, 2008.
 W. Hu, H. Zhang, Z. Zhao, Y. Wang, and X. Wang, "Real-time remote vital sign detection using a portable doppler sensor system,” IEEE Sensors Applications Symposium (SAS), pp. 89–93, 2014.
 Y. Nakamura, K. Kishi, and H. Kawakami, "Heartbeat synchronization for robotic cardiac surgery,” International Conference on Robotics and Automation, pp. 2014 – 2019, 2001.
 M. Sauve, A. Noce, P. Poignet, J. Triboulet, and E. Dombre, "Three-dimensional heart motion estimation using endoscopic monocular vision system: From artificial landmarks to texture analysis,” Biomedical Signal Processing and Control, pp. 199 – 207, 2007.
 E. Bogatyrenko, P. Pompey, and U. Hanebeck, "Efficient physics-based tracking of heart surface motion for beating heart surgery robotic systems,” International Journal of Computer Assisted Radiology and Surgery, pp. 387–399, 2011.
 T. Ortmaier, M. Groger, D. Boehm, V. Falk, and G. Hirzinger, "Motion estimation in beating heart surgery,” IEEE Transactions on Biomedical Engineering, pp. 1729–1740, 2005.
 R. Richa, A. B, and P. Poignet, "Towards robust 3d visual tracking for motion compensation in beating heart surgery,” Medical Image Analysis, vol. 15, no. 3, pp. 302 – 315, 2011.
 H. Elhawary and A. Popovic, "Robust feature tracking on the beating heart for a robotic-guided endoscope,” The International Journal of Medical Robotics and computer Assisted Surgery, 2011.
 J. Hadamard, "Lectures on the cauchy problems in linear partial differential equations,” Yale University Press, New Haven, 1923.
 A. Aviles and A. Casals, "Interpolation based deformation model for minimally invasive beating heart surgery,” Book Chapter IFMBE Proceedings vol.41, Springer International Publishing, 2013., 2013.
 A. Sotiras, C. Davatazikosy, and N. Paragios, "Deformable medical image registration: A survey,” Research Report Num. 7919, INRIA, France, 2012.
 M. Unser, A. Aldroubi, and M. Eden, "The l2-polynomial spline pyramid,” IEEE Trans. Patter Anal. Mach. Intell., pp. 364–379, 1993.
 M. Unser, "Splines: A perfect fit for signal and image processing,” IEEE Signal Processing Magazine, vol.16, no.6, pp. 22–38, 1999.
 A. N. Tikhonov and A. V. Y., "Solution of ill-posed problems,” Winston and Sons, Washinton DC, 1977.
 L. Rudin, S. J. Osher, and E. Fatemi, "Nonlinear total variation based noise removal algorithms,” Physica D., 60:259-268, 1992.
 A. Chambolle, M. Caselles, D. Cremers, and T. Pock, "An introduction to total variation for image analysis,” Report number 00437581, pp. 1–87, 2009.
 N. Z. Shor, "Subgradient methods: A survey of soviet research nonsmooth optimization,” Proceedings of the IIASA Workshop, Lemar´echal and R. Mifflin eds. Pergamon Press, 1978.
 D. Bertsekas and S. Mitter, "A descent numerical method for optimization problems with nondifferentiable cost functionals,” SlAM Journal on Control, pp. 637–652, 1973.
 A. Cauchy, "M´ethode g´en´erale pour la r´esolution des syst`ems d equations simultan´ees,” Comp. Rend. Sci. Paris, pp. 46–89, 1847.
 R. Fletcher and C. M. Reeves, "Function minimization by conjugate gradients,” Computer Journal, pp. 149–154, 1964.
 A. Aviles and A. Casals, "On genetic algorithms optimization for heart motion compensation,” Book Section ROBOT2013 Springer International, 2014.
 K. Levenberg, "A method for the solution of certain non-linear problems in least squares,” Quarterly of Applied Mathematics, 1944.
 D. Marquardt, "An algorithm for least-squares estimation of nonlinear parameters,” SIAM Journal on Applied Mathematics, pp. 431–441, 1963.
 M. Powell, "A hybrid method for nonlinear equations,” Numerical Methods for Nonlinear Algebraic Equations, pp. 87–144, 1970.
 D. Stoyanov, G. Mylonas, F. Deligianni, A. Darzi, and G. Yang, "Soft-tissue motion tracking and structure estimation for robotic assisted mis procedures,” In Proceeding Conference on Medical Image Computing and Computer Assisted Intervention, pp. 139–146, 2005.
 A. Talasaz, A. Trejos, and R. Patel, "Effect of force feedback on performance of robotics-assisted suturing,” International Conference on Biomedical Robotics and Biomechatronics, pp. 823–828, 2012.
 P. Boonvisut and M. Cavusoglu, "Estimation of soft tissue mechanical parameters from robotic manipulation data,” IEEE Transactions on Mechatronics, pp. 1602–1611, 2013.
 B. Bickel, M. Bacher, M. Otaduy, W. Matusik, H. Pfister, and M. Gross, "Capture and modeling of non-linear heterogeneous soft tissue,” ACM Transactions on Graphics, 2009.
 A. Aviles, A. Marban, P. Sobrevilla, J. Fernandez, and A. Casals, "A recurrent neural network approach for 3d vision-based force estimation,” To appear in IEEE International Conference on Image Processing Theory, Tools and Applications, 2014