Research - Jianhan Chen

Research Interests      Current Projects Filter Diagonalization Method (FDM) The Regularized Resolvent Transform (RRT) Novel Liquid NMR Techniques      Publications

Research Interests Signal processing plays a very important role in physical science. In many modern experiments such as NMR and ICR-Mass, time domain signals are often first measured and then transformed to frequency domain spectra to reveal useful information. Time signals also occur in numerical simulations such as quantum dynamic calculations, molecular dynamic simulations (MD). Therefore spectral analysis is a substantial step of these experiments and caliculations. The conventional way to transform the signal is Fourier Transform (FT). FT is a linear method, which is considered fast and reliable. However, it has well-known limitations. For example, the FT resolution is limited by so called FT time-frequency uncertainty principle. In high dimensionality experiments such as multi-dimensional NMR experiments, the signal is typically highly truncated in the indirect dimensions, leading to poor FT resolutions in the corresponding dimensions. Extensive efforts have been spent on developing various alternative methods to Fourier Transform. They are often referred to as so called High-Resolution Methods. To name a few, Linear Prediction (LP), Maximum Entropy, Bayesian Method, Maximum Likelihood, etc. All these methods make use of some additional knowledge of the signals which is not utilized in FT. However, there are a lot of practical difficulties. The signals may not satisfy the model (additional information) very well due to noise, imperfections and others; the signals could be very large and contain many but unknown number of peaks. Therefore, one often end up solving a linear or nonlinear large and ill-condition system, which is both numerically unstable and computationally expensive. My Ph.D. research mainly focuses on developing new nonlinear methods for high resolution spectral analysis and their applications to NMR data processing and quantum dynamics calculations. These methods include the Filter Diagonalization Method (FDM) and Regularized Resolvent Transform (RRT). FDM and RRT can handle both large and complicated data sets very efficently and provide a reliable high-resolution spectral estimation. They really show the promise to be the working methods. Multi-dimensional FDM and RRT are able to process the whole multidimensional data set to pin down the multi-dimensional features and provide superior resolutions in all dimensions. One of the most recent applications of FDM is in processing Constant-Time NMR signals, where there are some special properties of constant-time signals which enable us to obtain really fantastic results. Please read my Ph. D. Dissertation Proposal to know more about my research and progress up to date. (Note: the file is a little blurry on screen, but it prints out fine.) Ongoing projects The Filter Diagonalization Method (FDM) The Regularized Resolvent Transform (RRT) Novel Liquid NMR Techniques Publications Thesis and Reports PhD Thesis: Nonlinear Methods for High Resolution Spectral Estimation and Their Applications in Nuclear Magnetic Resonance Experiments, Department of Chemistry, University of California, Irvine, July 2002. (Download: the Adobe PDF file (6243K) or the zipped postscript file (6012K)) Master Thesis: Filter Diagonalization Method as a High Resolution Spectral Estimator, Department of Chemistry, University of California, Irvine, April 2000. (Download: the Adobe PDF file (6.6M) or the zipped PDF file (1.5M)) Advancement to Ph. D. Candidacy: August 2000   1. Original Proposal: A pseudo Three-Terminal Molecular Device      (Download: Introduction, Proposal, and Appendix).   2. Research Proposal: The Filter Diagonalization Method for the NMR Data Processing.      (Download: the Adobe PDF file (633K)) Journal Papers J. Chen. V. A. Mandelshtam, "Mulit-Scale Filter Diagonalization Method for spectral analysis of noisy data with nolocalized features", J. Chem. Phys. 112, 4429 (2000). J. Chen, V. A. Mandelshtam and A. J. Shaka, "Regularization of the Filter Diagonalization Method: FDM2K", J. Magn. Reson. 146, 368 (2000). J. Chen, A. J. Shaka, V. A. Mandelshtam, "RRT: The Regularized Resolvent Transform for high resolution spectral estimation", J. Magn. Reson. 147, 129 (2000). A. A. De Angelis, J. Chen, V. A. Mandelshtam and A. J. Shaka, "A Method to Obtain High Resolution 13C CT-HSQC Spectra of Proteins with a Short Constant-Time Period", J. Biomol. NMR (submitted). M. A. Smith, J. Chen, and A. J. Shaka, "Small Molecule NOE Difference Spectroscopy for High-Resolution NMR", J. Am. Chem. Soc. in preparation. J. Chen, V. Mandelshtam and D. Neuhauser, "Calculating excited vibrational levels of polyatomic molecules by diffusion Monte Carlo", J. Chem. Phys., in preparation. J. Chen, D. Nietlispach, V. A. Mandelshtam, and A. J. Shaka, "Ultra-high quality HNCO spectra with very short constant times", in preparation. Selected Presentations "A faster Filter Diagonalization Method with fully automated multi-windowing", Poster Presentation, 41st ENC, April 2000. "RRT: The Regularized Resolvent Transform for high resolution spectral estimation", Poster Presentation, 42nd ENC, March 2001. "The Regularized Resolvent Transform and its applications", ACS Annual Meeting, August 2001 (invited talk). "The Filter Diagonalization Method for Spectral Analysis of NMR Data", Washington Area NMR Group, February 2002 (invited talk). "High Resolution Double Constant-Time 3D NMR Spectra by Filter Diagonalization Method", Poster Presentation, 43nd ENC, April 2002.