Blind system identification with application to medical imaging

• Main Author: Yu, Chengpu
• Other Authors: Xie Lihua
• Format: Theses and Dissertations
• Language: English
• Published: 2014
• Subjects: DRNTU::Engineering::Electrical and electronic engineering::Electronic systems::Signal processing
• Online Access: http://hdl.handle.net/10356/55734
• Institution: Nanyang Technological University

Blind system identification is to identify a particular system model using only the system output under some mild conditions on the system input and the system model. It has been intensively explored for a few decades and is still a hot research topic nowadays. In this thesis, we shall investigate the blind identification problem for the following system models: linear time-invariant (LTI) infinite impulse response (IIR) or autoregressive moving average (ARMA) model, Hammerstein model, output-switching model, and single-input multi-output (SIMO) finite impulse response (FIR) system model with quantized outputs. The blind identification of SIMO FIR systems is a well-studied topic; however, it is not the case for SIMO IIR systems. In this thesis, a second-order statistics based identification method is developed for SIMO IIR systems. The proposed method exploits the dynamical autoregressive information of the system contained in the autocorrelation matrices of the system outputs so that the system can be identified using only the lag-0 and lag-1 autocorrelation matrices. Further, the blind identification of single-input single-output (SISO) IIR plants is studied. Using the over-sampling technique, the SISO IIR system is equivalently transformed into an SIMO IIR system so that it can be identified using the proposed second-order statistics based identification method. We also study the blind identification for Hammerstein systems and output-switching systems. Based on the over-sampling technique, deterministic blind identification approaches and sufficient identifiability conditions are provided for the Hammerstein system and the output-switching system. The involved over-sampling rate in the blind identification of the Hammerstein system can be much smaller than the system order of its linear dynamic part as required by other existing methods. For the output-switching system, the design of over-sampling strategy so as to make the system identifiable is deliberately discussed. The difficulty of identifying the output-switching system is that multiple IIR filters are to be identified from a single system output. Next, the blind identification of the SIMO system using quantized observations is investigated. Since the system outputs are nonlinearly distorted and the system inputs are unknown, the identification problem is quite challenging. First, a two-channel SIMO system model with precise observations is transformed into an error-in-variables model, and a maximum likelihood estimator is provided which can obtain consistent estimates of the system parameters. A consistent estimate means that the associated estimation error decays to zero with probability one when the number of observation samples tends to infinity. When only quantized observations are available, an expectation-maximization (EM) like algorithm is then provided. Asymptotic properties of the proposed algorithm are analyzed and the quantization effects on the identification performance are discussed. As the applications of the blind system identification technique, blind deconvolution of ultrasound imaging and blind reconstruction of parallel magnetic resonance imaging (MRI) are studied in this thesis. For the blind deconvolution of ultrasound imaging, an SIMO channel model is introduced to describe the imaging process, in which the ultrasound pulse is the common system input and tissue reflectivity functions are the channel impulse responses. A regularized blind deconvolution model is then proposed based on the prior knowledge that the tissue reflectivity functions are sparse and the spectrum of the ultrasound pulse is smooth. The parallel MRI is an SIMO system with the hydrogen proton density function being the common system input and the multiple coil sensitivity functions being the channel impulse responses. A total variation (TV) regularized model is then provided for the reconstruction of MR images using measurements obtained from arbitrary sampling patterns.