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Various improvements which have been made to the vehicle (reduced engine noise, reducedaerodynamic related NVH), have resulted in tire road noise as the dominant source of thevehicle interior noise. Generally, vehicle interior noise has two main sources, 1) travellinglow frequency excitation below 800 Hz from road surface through a structure- borne pathand 2) the high frequency (above 800 Hz) air-borne noise that is caused by air- pumpingnoise caused by tread pattern.The structure-borne waves of the circumference of the tire are generated by excitation atthe contact patch due to the road surface texture and characteristics. These vibrations arethen transferred from the sidewalls of the tire to the rim and then are transmitted throughthe spindle-wheel interface, resulting in high frequency vibration of vehicle body panels andwindows.The focus of this study is to develop several statistical-based models for analyzing the roadsurface and using them to predict the tire-road noise structure-borne component. In order todo this, a new methodology for sensing the road characteristics, such as asperities and roadsurface condition, were developed using virtual sensing and intelligent tire technology. In ad-dition, the spindle forces were used as an indicator to the structure-borne noise of the vehicle.Several data mining and multivariate analysis-based methods were developed to extractfeatures and to develop an empirical model to predict the power of structure-borne noiseunder different operational and road conditions. Finally, multiple data driven models-basedmodels were developed to classify the road types, and conditions and use them for the noisefrequency spectrum prediction. / Doctor of Philosophy / Multiple data driven models were developed in this study to use the vibration of the tirecontact patch as an input to sense some characteristics of road such as asperity, surface type,and the surface condition, and use them to predict the structure-borne noise power. Also,instead of measuring the noise using microphones, forces at wheel spindle were measuredas a metric for the noise power. In other words, a statistical model was developed that bysensing the road, and using the data along with other inputs, one can predict forces at thewheel spindle.

We explore the applicability of local polynomial approximation of signals for noise suppression. In the context of data regression, Savitzky and Golay showed that least-squares approximation of data with a polynomial of fixed order, together with a constant window length, is identical to convolution with a finite impulse response filter, whose characteristics depend entirely on two parameters, namely, the order and window length. Schafer’s recent article in IEEE Signal Processing Magazine provides a detailed account of one-dimensional Savitzky-Golay (SG) filters. Drawing motivation from this idea, we present an elaborate study of two-dimensional SG filters and employ them for image denoising by optimizing the filter response to minimize the mean-squared error (MSE) between the original image and the filtered output. The key contribution of this thesis is a method for optimal selection of order and window length of SG filters for denoising images. First, we apply the denoising technique for images contaminated by additive Gaussian noise. Owing to the absence of ground truth in practice, direct minimization of the MSE is infeasible. However, the classical work of C. Stein provides a statistical method to overcome the hurdle. Based on Stein’s lemma, an estimate of the MSE, namely Stein’s unbiased risk estimator (SURE), is derived, and the two critical parameters of the filter are optimized to minimize the cost. The performance of the technique improves when a regularization term, which penalizes fast variations in the estimate, is added to the optimization cost. In the next three chapters, we focus on non-Gaussian noise models. In Chapter 3, image degradation in the presence of a compound noise model, where images are corrupted by mixed Poisson-Gaussian noise, is addressed. Inspired by Hudson’s identity, an estimate of MSE, namely Poisson unbiased risk estimator (PURE), which is analogous to SURE, is developed. Combining both lemmas, Poisson-Gaussian unbiased risk estimator (PGURE) minimization is performed to obtain the optimal filter parameters. We also show that SG filtering provides better lowpass approximation for a multiresolution denoising framework. In Chapter 4, we employ SG filters for reducing multiplicative noise in images. The standard SG filter frequency response can be controlled along horizontal or vertical directions. This limits its ability to capture oriented features and texture that lie at other angles. Here, we introduce the idea of steering the SG filter kernel and perform mean-squared error minimization based on the new concept of multiplicative noise unbiased risk estimation (MURE). Finally, we propose a method to robustify SG filters, robustness to deviation from Gaussian noise statistics. SG filters work on the principle of least-squares error minimization, and are hence compatible with maximum-likelihood (ML) estimation in the context of Gaussian statistics. However, for heavily-tailed noise such as the Laplacian, where ML estimation requires mean-absolute error minimization in lieu of MSE minimization, standard SG filter performance deteriorates. `1 minimization is a challenge since there is no closed-form solution. We solve the problem by inducing the `1-norm criterion using the iteratively reweighted least-squares (IRLS) method. At every iteration, we solve an l`2 problem, which is equivalent to optimizing a weighted SG filter, but, as iterations progress, the solution converges to that corresponding to `1 minimization. The results thus obtained are superior to those obtained using the standard SG filter.