Linear and synchrosqueezed time–frequency representations revisited:overview, standards of use, resolution, reconstruction, concentration, and algorithms

Time–frequency representations (TFRs) of signals, such as the windowed Fourier transform (WFT), wavelet transform (WT) and their synchrosqueezed versions (SWFT, SWT), provide powerful analysis tools. Here we present a thorough review of these TFRs, summarizing all practically relevant aspects of their use, reconsidering some conventions and introducing new concepts and procedures to advance their applicability and value. Furthermore, a detailed numerical and theoretical study of three specific questions is provided, relevant to the application of these methods, namely: the effects of the window/wavelet parameters on the resultant TFR; the relative performance of different approaches for estimating parameters of the components present in the signal from its TFR; and the advantages/drawbacks of synchrosqueezing. In particular, we show that the higher concentration of the synchrosqueezed transforms does not seem to imply better resolution properties, so that the SWFT and SWT do not appear to provide any significant advantages over the original WFT and WT apart from a more visually appealing pictures. The algorithms and Matlab codes used in this work, e.g. those for calculating (S)WFT and (S)WT, are freely available for download

A Diagnosis Feature Space for Condition Monitoring and Fault Diagnosis of Ball Bearings

The problem of fault diagnosis and condition monitoring of ball bearings is a multidisciplinary subject. It involves research subjects from diverse disciplines of mechanical engineering, electrical engineering and in particular signal processing. In the first step, one should identify the correct method of investigation. The methods of investigation for condition monitoring of ball bearings include acoustic emission measurements, temperature monitoring, electrical current monitoring, debris analysis and vibration signal analysis. In this thesis the vibration signal analysis is employed. Once the method of analysis is selected, then features sensitive to faults should be calculated from the signal. While some of the features may be useful for condition monitoring, some of the calculated features might be extra and may not be helpful. Therefore, a feature reduction module should be employed. Initially, six features are selected as a candidate for the diagnosis feature space. After analyzing the trend of the features, it was concluded that three of the features are not appropriate for fault diagnosis. In this thesis, two problem is investigated. First the problem of identifying the effects of the fault size on the vibration signal is investigated. Also the performance of the feature space is tested in distinguishing the healthy ball bearings from the defective vibration signals

Analytical modeling, performance analysis, and optimization of polarimetric imaging system

Polarized light can provide additional information about a scene that cannot be obtained directly from intensity or spectral images. Rather than treating the optical field as scalar, polarization images seek to obtain the vector nature of the optical field from the scene. Polarimetry thus has been found to be useful in several applications, including material classification and target detection. Recently, optical polarization has been identified as an emerging technique and has shown promising applications in passive remote sensing. Compared with the traditional spectral content of the scene, polarimetric signatures are much more dependent on the scene geometry and the polarimetric bidirectional reflectance distribution function (pBRDF) of the objects. Passive polarimetric scene simulation has been shown to be helpful in better understanding such phenomenology. However, the combined effects of the scene characteristics, the sensor noise and optical imperfections, and the different processing algorithm implementations on the overall system performance have not been systematically studied. To better understand the effects of various system attributes and help optimize the design and use of polarimetric imaging system, an analytical model has been developed to predict the system performance. A detailed introduction of the analytical model is first presented. The model propagates the first and second order statistics of radiance from a scene model to a sensor model, and finally to a processing model. Validation with data collected from a division of time polarimeter show good agreement between model predictions and measurements. It has been shown that the analytical model is able to predict the general polarization behavior and data trends with different scene geometries. Based on the analytical model we then define several system performance metrics to evaluate the polarimetic signatures of different objects as well as target detection performance. Parameter tradeoff studies have been conducted for analysis of potential system performance. Finally based on the analytical model and system performance metrics we investigate optimal filter configurations to sense polarization. We develop an adaptive polarimetric target detector to determine the optimum analyzer orientations for a multichannel polarization-sensitive optical system. Compared with several conventional operation methods, we find that better target detection performance is achieved with our algorithm

Model and Appearance Based Analysis of Neuronal Morphology from Different Microscopy Imaging Modalities

The neuronal morphology analysis is key for understanding how a brain works. This process requires the neuron imaging system with single-cell resolution; however, there is no feasible system for the human brain. Fortunately, the knowledge can be inferred from the model organism, Drosophila melanogaster, to the human system. This dissertation explores the morphology analysis of Drosophila larvae at single-cell resolution in static images and image sequences, as well as multiple microscopy imaging modalities. Our contributions are on both computational methods for morphology quantification and analysis of the influence of the anatomical aspect. We develop novel model-and-appearance-based methods for morphology quantification and illustrate their significance in three neuroscience studies. Modeling of the structure and dynamics of neuronal circuits creates understanding about how connectivity patterns are formed within a motor circuit and determining whether the connectivity map of neurons can be deduced by estimations of neuronal morphology. To address this problem, we study both boundary-based and centerline-based approaches for neuron reconstruction in static volumes. Neuronal mechanisms are related to the morphology dynamics; so the patterns of neuronal morphology changes are analyzed along with other aspects. In this case, the relationship between neuronal activity and morphology dynamics is explored to analyze locomotion procedures. Our tracking method models the morphology dynamics in the calcium image sequence designed for detecting neuronal activity. It follows the local-to-global design to handle calcium imaging issues and neuronal movement characteristics. Lastly, modeling the link between structural and functional development depicts the correlation between neuron growth and protein interactions. This requires the morphology analysis of different imaging modalities. It can be solved using the part-wise volume segmentation with artificial templates, the standardized representation of neurons. Our method follows the global-to-local approach to solve both part-wise segmentation and registration across modalities. Our methods address common issues in automated morphology analysis from extracting morphological features to tracking neurons, as well as mapping neurons across imaging modalities. The quantitative analysis delivered by our techniques enables a number of new applications and visualizations for advancing the investigation of phenomena in the nervous system

A frequency warping approach to speaker normalization

Thesis (M. Eng.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1996.Includes bibliographical references (leaves 63-65).by Li Lee.M.Eng

Measuring aberrations in lithographic projection systems with phase wheel targets

A significant factor in the degradation of nanolithographic image fidelity is optical wavefront aberration. Aerial image sensitivity to aberrations is currently much greater than in earlier lithographic technologies, a consequence of increased resolution requirements. Optical wavefront tolerances are dictated by the dimensional tolerances of features printed, which require lens designs with a high degree of aberration correction. In order to increase lithographic resolution, lens numerical aperture (NA) must continue to increase and imaging wavelength must decrease. Not only do aberration magnitudes scale inversely with wavelength, but high-order aberrations increase at a rate proportional to NA2 or greater, as do aberrations across the image field. Achieving lithographic-quality diffraction limited performance from an optical system, where the relatively low image contrast is further reduced by aberrations, requires the development of highly accurate in situ aberration measurement. In this work, phase wheel targets are used to generate an optical image, which can then be used to both describe and monitor aberrations in lithographic projection systems. The use of lithographic images is critical in this approach, since it ensures that optical system measurements are obtained during the system\u27s standard operation. A mathematical framework is developed that translates image errors into the Zernike polynomial representation, commonly used in the description of optical aberrations. The wavefront is decomposed into a set of orthogonal basis functions, and coefficients for the set are estimated from image-based measurements. A solution is deduced from multiple image measurements by using a combination of different image sets. Correlations between aberrations and phase wheel image characteristics are modeled based on physical simulation and statistical analysis. The approach uses a well-developed rigorous simulation tool to model significant aspects of lithography processes to assess how aberrations affect the final image. The aberration impact on resulting image shapes is then examined and approximations identified so the aberration computation can be made into a fast compact model form. Wavefront reconstruction examples are presented together with corresponding numerical results. The detailed analysis is given along with empirical measurements and a discussion of measurement capabilities. Finally, the impact of systematic errors in exposure tool parameters is measureable from empirical data and can be removed in the calibration stage of wavefront analysis