Introduction to a Transient World. Fourier Kingdom. Discrete Revolution. Time Meets Frequency. Frames. Wavelet Zoom. Wavelet Bases. Wavelet Packet and Local Cosine Bases. An Approximation Tour. Estimations are Approximations. Transform Coding. Appendix A: Mathematical Complements. Appendix B: Software Toolboxes.

http://ahvazdownload.persiangig.com/document/article/39.pdf

A wavelet tour of signal processing

Data Mining Practical Machine Learning Tools and Techniques

/pdf/convex-analysisnoer-san-nojin-zhan-nituite-5dl2rbmoyr.pdf

Convex Analysisの二,三の進展について

1. Introduction and Overview. 2. Detecting Influential Observations and Outliers. 3. Detecting and Assessing Collinearity. 4. Applications and Remedies. 5. Research Issues and Directions for Extensions. Bibliography. Author Index. Subject Index.

Regression Diagnostics: Identifying Influential Data and Sources of Collinearity

The quintessential goal of sensor array signal processing is the estimation of parameters by fusing temporal and spatial information, captured via sampling a wavefield with a set of judiciously placed antenna sensors. The wavefield is assumed to be generated by a finite number of emitters, and contains information about signal parameters characterizing the emitters. A review of the area of array processing is given. The focus is on parameter estimation methods, and many relevant problems are only briefly mentioned. We emphasize the relatively more recent subspace-based methods in relation to beamforming. The article consists of background material and of the basic problem formulation. Then we introduce spectral-based algorithmic solutions to the signal parameter estimation problem. We contrast these suboptimal solutions to parametric methods. Techniques derived from maximum likelihood principles as well as geometric arguments are covered. Later, a number of more specialized research topics are briefly reviewed. Then, we look at a number of real-world problems for which sensor array processing methods have been applied. We also include an example with real experimental data involving closely spaced emitters and highly correlated signals, as well as a manufacturing application example.

Two decades of array signal processing research: the parametric approach

A simple construction of an orthonormal basis starting with a so-called mother wavelet, together with an efficient implementation gained the wavelet decomposition easy acceptance and generated a great research interest in its applications. An orthonormal basis may not, however, always be a suitable representation of a signal, particularly when time (or space) invariance is a required property. The conventional way around this problem is to use a redundant decomposition. We address the time-invariance problem for orthonormal wavelet transforms and propose an extension to wavelet packet decompositions. We show that it,is possible to achieve time invariance and preserve the orthonormality. We subsequently propose an efficient approach to obtain such a decomposition. We demonstrate the importance of our method by considering some application examples in signal reconstruction and time delay estimation.

/pdf/time-invariant-orthonormal-wavelet-representations-4pkfcrgs66.pdf

Time-invariant orthonormal wavelet representations

It is well known that the wavelet transform provides a very effective framework for analysis of multiscale edges. In this paper, we propose a novel approach based on the shearlet transform: a multiscale directional transform with a greater ability to localize distributed discontinuities such as edges. Indeed, unlike traditional wavelets, shearlets are theoretically optimal in representing images with edges and, in particular, have the ability to fully capture directional and other geometrical features. Numerical examples demonstrate that the shearlet approach is highly effective at detecting both the location and orientation of edges, and outperforms methods based on wavelets as well as other standard methods. Furthermore, the shearlet approach is useful to design simple and effective algorithms for the detection of corners and junctions.

https://www.math.uh.edu/~dlabate/shear_edges.pdf

A Shearlet Approach to Edge Analysis and Detection

We propose a best basis algorithm for signal enhancement in white Gaussian noise. The best basis search is performed in families of orthonormal bases constructed with wavelet packets or local cosine bases. We base our search for the "best" basis on a criterion of minimal reconstruction error of the underlying signal. This approach is intuitively appealing, because the enhanced or estimated signal has an associated measure of performance, namely, the resulting mean-square error. Previous approaches in this framework have focused on obtaining the most "compact" signal representations, which consequently contribute to effective denoising. These approaches, however, do not possess the inherent measure of performance which our algorithm provides. We first propose an estimator of the mean-square error, based on a heuristic argument and subsequently compare the reconstruction performance based upon it to that based on the Stein (1981) unbiased risk estimator. We compare the two proposed estimators by providing both qualitative and quantitative analyses of the bias term. Having two estimators of the mean-square error, we incorporate these cost functions into the search for the "best" basis, and subsequently provide a substantiating example to demonstrate their performance.

/pdf/on-denoising-and-best-signal-representation-5570rhqej9.pdf

On denoising and best signal representation

Entropy-based divergence measures have shown promising results in many areas of engineering and image processing. We define a new generalized divergence measure, namely, the Jensen-Renyi (1996, 1976) divergence. Some properties such as convexity and its upper bound are derived. Based on the Jensen-Renyi divergence, we propose a new approach to the problem of image registration. Some appealing advantages of registration by Jensen-Renyi divergence are illustrated, and its connections to mutual information-based registration techniques are analyzed. As the key focus of this paper, we apply Jensen-Renyi divergence for inverse synthetic aperture radar (ISAR) image registration. The goal is to estimate the target motion during the imaging time. Our approach applies Jensen-Renyi divergence to measure the statistical dependence between consecutive ISAR image frames, which would be maximal if the images are geometrically aligned. Simulation results demonstrate that the proposed method is efficient and effective.

Hamid Krim

Papers

Two decades of array signal processing research: the parametric approach

Time-invariant orthonormal wavelet representations

A Shearlet Approach to Edge Analysis and Detection

On denoising and best signal representation

A generalized divergence measure for robust image registration