Search results for "Spline wavelet"
showing 8 items of 8 documents
Block Based Deconvolution Algorithm Using Spline Wavelet Packets
2010
This paper presents robust algorithms to deconvolve discrete noised signals and images. The idea behind the algorithms is to solve the convolution equation separately in different frequency bands. This is achieved by using spline wavelet packets. The solutions are derived as linear combinations of the wavelet packets that minimize some parameterized quadratic functionals. Parameters choice, which is performed automatically, determines the trade-off between the solution regularity and the initial data approximation. This technique, which id called Spline Harmonic Analysis, provides a unified computational scheme for the design of orthonormal spline wavelet packets, fast implementation of the…
<title>Human cell texture analysis with quincunx spline wavelet transform</title>
1999
Wavelet transforms are efficient tools for texture analysis and classification. Separable techniques are classically used but present several drawbacks. First, diagonal coefficients contain poor information. Second, the other coefficients contain useful information only if the texture is oriented in the vertical and horizontal directions. So an approach of texture analysis by non-separable transform is proposed. An improved interscale resolution is allowed by the quincunx scheme and this analysis leads to only one detail image where no particular orientation is favored. New orthogonal isotropic filters for the decomposition are constructed by applying McClellan transform on one dimension B-…
Periodic Polynomial Splines
2018
In this chapter, the spaces of periodic polynomial splines and the Spline Harmonic Analysis (SHA) in these spaces are briefly outlined. The stuff of this chapter is used for the design of periodic discrete-time splines and discrete-time-spline-based wavelets and wavelet packets. For a detailed description of the subject we refer to (Averbuch, Neittaanmaki and Zheludev, Spline and Spline Wavelet Methods with Applications to Signal and Image Processing, Springer, Berlin, 2014) [1]. Periodic polynomial splines provide an example of mixed discrete-continuous circular convolution.
Deconvolution by Regularized Matching Pursuit
2014
In this chapter, an efficient method that restores signals from strongly noised blurred discrete data is presented. The method can be characterized as a Regularized Matching Pursuit (RMP), where dictionaries consist of spline wavelet packets. It combines ideas from spline theory, wavelet analysis and greedy algorithms. The main distinction from the conventional matching pursuit is that different dictionaries are used to test the data and to approximate the solution. In addition, oblique projections of data onto dictionary elements are used instead of orthogonal projections, which are used in the conventional Matching Pursuit (MP). The slopes of the projections and the stopping rule for the …
Periodic Discrete and Discrete-Time Splines
2018
Periodic discrete splines with different periods and spans are introduced in Sect. 3.4 of Volume I (Averbuch, Neittaanmaki and Zheludev, Spline and Spline Wavelet Methods with Applications to Signal and Image Processing, Springer, Berlin, 2014) [2]. In this chapter, we regard periodic discrete splines as a base for the design of periodic discrete-time wavelets, wavelet packets and wavelet frames. Therefore, only the discrete splines whose spans are 2 are outlined. These discrete splines are linear combinations of the discrete B-splines. So also, the so-called discrete-time splines are discussed in the chapter that are linear combinations of the discrete-time B-splines. The discrete-time B-s…
Detection of Incipient Bearing Fault in a Slowly Rotating Machine Using Spline Wavelet Packets
2018
This chapter describes a successful application of spline-based wavelet packet transforms (WPTs) described in Chap. 4 to a complicated problem of detection of incipient defects in rolling element bearings by the analysis of recorded vibration signals. The methodology presented in this chapter is applied to the analysis of vibration data recorded from large bearings working in real unfavorable operation conditions in presence of strong noise and vibrations from multiple internal and external sources. It relies on properties of discrete spline-based wavelet packets such as orthogonality, near-rectangular spectra, transient oscillating shapes of testing waveforms and fast implementation of tra…
Introduction: Periodic Signals and Filters
2018
In this chapter we briefly outline some well-known facts about Discrete-time periodic signals, their transforms and periodic digital filters and filter banks. For details we refer to the classical textbook A. V. Oppenheim and R. W. Schafer (Discrete-Time Signal Processing, Prentice Hall, New York, 2010, [3]) and Volume I of our book (Averbuch, Neittaanmaki and Zheludev, Spline and Spline Wavelet Methods with Applications to Signal and Image Processing, Periodic Splines, vol. 1 (Springer, Berlin, 2014)) [1] Throughout the volume, unless other indicated, \(N=2^{j}, \;j\in \mathbb {N}\).
Block-Based Inversion of the Heat Equations
2014
This chapter presents robust methods, which refine the algorithms, in Sect. 7.2, for inversion of the heat equations. The idea behind the algorithms is to solve the inversion problem separately in different frequency bands. This is achieved by using spline wavelet packets. The solutions that minimize some parameterized quadratic functionals, are derived as linear combinations of the wavelet packets. Choice of parameters, which is performed automatically, determines the trade-off between the solution regularity and the initial data approximation. The Spline Harmonic Analysis (SHA) technique provides a unified computational scheme for the fast implementation of the algorithm and an explicit r…