UCSB Engineering

Shivkumar Chandrasekaran

Professor

Electrical & Computer Engineering

Shivkumar Chandrasekaran

Contacts

Department of Electrical and Computer Engineering
University of California, Santa Barbara
Santa Barbara, CA 93106

tel: (805) 893-7542
fax: (805) 893-3262
shiv@ece.ucsb.edu

Research Description

His current research interests include the development of new stable algorithms for the fast updating and downloading of structured systems of linear equations, the development of highly accurate and efficient algorithms for the numerical solution of differential and integral equations, and the development of new accurate and efficient algorithms for inverse scattering and computer vision problems.

Biography

Shiv's Ph.D. thesis involved the design of provably accurate and efficient algorithms for various problems in numerical linear algebra. He classified all then known algorithms for the rank-revealing QR decomposition and showed why they were likely to fail. He then developed the first accurate algorithms to compute this decomposition which would also be efficient in practice. He proposed a new parallelizable variant of the QR algorithm for computing the singular value decomposition. He then developed a provably accurate and efficient version of inverse iteration for computing the eigenvectors of hermitian matrices. This was done after he discovered that existing implementations could fail drastically. He also studied the perturbation behavior of linear and least-squares systems, and eigenvalue and singular value decompositions. This led to the development of sharp perturbation bounds for the components of linear systems. After defending his thesis Shiv worked for a year as a Visiting Instructor at the Mathematics Department of North Carolina State University in Raleigh. At UCSB he developed the first efficient and stable algorithm for the symmetric-definite generalized eigenvalue problem. In collaboration with Prof. Ali H. Sayed (UCLA) he developed the first unconditionally backward stable, fast algorithm for solving nonsymmetric Toeplitz and quasi-Toeplitz systems of linear equations. They also stabilized the fast Schur algorithm for factorizing matrices with displacement structure. In joint work with Prof. Sayed and Prof. Ming Gu (UCLA) they developed the first efficient and stable algorithms for the indefinite least-squares problem and for the diagonally weighted recursive least-squares problem. Also collaborating with Prof. Gene Golub (Stanford University) they developed an efficient algorithm for a new bounded errors-in-variables model of parameter estimation


Awards/Honors

  • Recipient, B.I.T.S Merit Scholarship

Selected Publications

  • Drums, curve descriptors and affine invariant region matching, Image and Vision Computing, Vol. 26, No. 3, 2008, 347-360, Marco Zuliani, Luca Bertelli, Charles S. Kenney, Shivkumar Chandrasekaran, B. S. Manjunath, web link
  • Determining Achievable Rates for Secure, Zero Divergence, Steganography, mage Processing, 2006 IEEE International Conference on 8-11, 2006, 121-124, K. Sullivan, K. Solanki, B.S Manjunath, U. Madhow, S. Chandrasekaran, web link
  • Provably Secure Steganography: Achieving Zero K-L Divergence using Statistical Restoration, Image Processing, 2006 IEEE International Conference on 8-11, 2006, 125-128, Kenneth Sullivan, Kaushal Solanki, B. S. Manjunath, Upamanyu Madhow, Shivkumar Chandrasekaran, web link
  • Modeling the print-scan process for resilient data hiding, Security, Steganography, and Watermarking of Multimedia Contents, 2005, 418-429, Kaushal Solanki, Upamanyu Madhow, B. S. Manjunath, Shivkumar Chandrasekaran
  • Statistical restoration for robust and secure steganography, ICIP IEEE International Conference, Vol. 2, 2005, 1118-1121, Kaushal Solanki, Kenneth Sullivan, Upamanyu Madhow, B. S. Manjunath, Shivkumar Chandrasekaran, web link
  • Steganalysis of spread spectrum data hiding exploiting cover memory, Security, Steganography, and Watermarking of Multimedia Contents, 2005, 38-46, Kenneth Sullivan, Upamanyu Madhow, Shivkumar Chandrasekaran, B. S. Manjunath
  • Estimating and undoing rotation for print-scan resilient data hiding, ICIP, Vol. 1, 2004, 39-42, Kaushal Solanki, Upamanyu Madhow, B. S. Manjunath, Shivkumar Chandrasekaran, web link
  • Robust image-adaptive data hiding using erasure and error correction, IEEE Transactions on Image Processing, Vol. 13, No.12, 2004, 1627-1639, Kaushal Solanki, Noah Jacobsen, Upamanyu Madhow, B. S. Manjunath, Shivkumar Chandrasekaran
  • Steganalysis of quantization index modulation data hiding., ICIP, VOL. 2, 2004, 1165-1168, Kenneth Sullivan, Zhiqiang Bi, Upamanyu Madhow, Shivkumar Chandrasekaran, B. S. Manjunath, web link
  • Toward Real-Time, Physically-Correct Soft Tissue Behavior Simulation, ISBI, 2004, 185-188, Yuan-Fang Wang, Dan Koppel, Shivkumar Chandrasekaran