In system identification, the Akaike Information Criterion (AIC) is a well known method to balance the model fit against model complexity. Regularization here acts as a price on model complexity. In statistics and machine learning, regularization has gained popularity due to modeling methods such as Support Vector Machines (SVM), ridge regression and lasso. But also when using a Bayesian approach to modeling, regularization often implicitly shows up and can be associated with the prior knowledge. Regularization has also had a great impact on many applications, and very much so in clinical imaging. In e.g., breast cancer imaging, the number of sensors is physically restricted which leads to long scantimes. Regularization and sparsity can be used to reduce that. In Magnetic Resonance Imaging (MRI), the number of scans is physically limited and to obtain high resolution images, regularization plays an important role. Regularization shows-up in a variety of different situations and is a well known technique to handle ill-posed problems and to control for overfit. We focus on the use of regularization to obtain sparseness and smoothness and discuss novel developments relevant to system identification and signal processing. In regularization for sparsity a quantity is forced to contain elements equal to zero, or to be sparse. The quantity could e.g., be the regression parameter vectorof a linear regression model and regularization would then result in a tool for variable selection. Sparsity has had a huge impact on neighboring disciplines, such as machine learning and signal processing, but rather limited effect on system identification. One of the major contributions of this thesis is therefore the new developments in system identification using sparsity. In particular, a novel method for the estimation of segmented ARX models using regularization for sparsity is presented. A technique for piecewise-affine system identification is also elaborated on as well as several novel applications in signal processing. Another property that regularization can be used to impose is smoothness. To require the relation between regressors and predictions to be a smooth function is a way to control for overfit. We are here particularly interested in regression problems with regressors constrained to limited regions in the regressor-space e.g., a manifold. For this type of systems we develop a new regression technique, Weight Determination by Manifold Regularization (WDMR). WDMR is inspired byapplications in biology and developments in manifold learning and uses regularization for smoothness to obtain smooth estimates. The use of regularization for smoothness in linear system identification is also discussed. The thesis also presents a real-time functional Magnetic Resonance Imaging (fMRI) bio-feedback setup. The setup has served as proof of concept and been the foundation for several real-time fMRI studies.

The research described in this thesis focuses on the biomechanics of cervical spine injury diagnosis and rehabilitation management. This research is particularly relevant to the diagnosis of minor neck injuries that typically arise from motor vehicle accidents and are classified as "whiplash injuries". The diagnosis and treatment of these chronic neck problems has been particularly difficult and frustrating and these difficulties prompted calls for the objective evaluation of the techniques and procedures used in the measurement and assessment of neck dysfunction. The biomechanical aspects of the clinical diagnosis of minor cervical spine injuries were investigated in this work by reconfiguring an existing detailed biomechanical model of the human neck to simulate injuries to particular structures, and to model abnormal muscle activation. The investigation focused on the range of motion assessment and the methods of testing and rehabilitating the function of the deep neck muscles because the model could be applied to provide further insight into these facets of neck injury diagnosis and management. The de Jager detailed head-neck model, available as a research tool from TNO (The Netherlands), was chosen for this study because it incorporated sufficient anatomical detail, but the model required adaptation because it had been developed for impact and crash test dummy simulations. This adaptation significantly broadened the model's field of application to encompass the clinical domain. The facets of the clinical diagnosis of neck dysfunction investigated in this research were range of motion and deep muscle control testing. Range of motion testing was simulated by applying a force to the head to generate the primary motions of flexion/extension, lateral flexion and axial twisting and parametric changes were made to particular structures to determine the effect on the head-neck movement. The main finding from this study of cervical range of motion testing was that while motion can be accurately measured in three dimensions, consideration of the three dimensional nature of the motion can add little to the clinical diagnosis of neck dysfunctions. Given the non-discriminatory nature of range of motion testing, the scientific collection and interpretation of the three dimensional motion patterns cannot be justified clinically. The de Jager head-neck model was then further adapted to model the cranio-cervical flexion test, which is used clinically to test the function of the deep muscle groups of the neck. This simulation provided confirmation of the efficacy of using a pressure bio-feedback unit to provide visual indication of the activation of the deep flexor muscles in the neck. However, investigation of the properties of the pressure bio-feedback unit identified significant differences in the stiffness of the bag for the different levels of inflation that must be accounted for if comparisons are to be made between subjects. Following the identification of the calibration anomalies associated with the pressure bio-feedback unit, the motion of the point of pressure of the head on the headrest and the force at this point of contact during the activation of the deep flexor muscle group were investigated as an alternative source of feedback. This output, however, was found to be subject specific, depending on the posterior shape of the skull that determined the point of contact during the head rolling action. Clinically, an important outcome of the alternative feedback assessment was that the prescribed action to target the deep flexor muscle group will feel different for each individual, ranging from a slide to a roll of the head on the headrest, and this must be accounted for when explaining the action and during rehabilitation management.