Search results for "wavelet."
showing 10 items of 327 documents
Automatic screening of cardiac disorders using wavelet analysis of heart sound
2017
Body auscultation is a dominant method for physical examination of human heart using conventional stethoscope. This clinical method is non invasive and efficient but it requires a medical expert to interpret the heart sound for assessment of cardiac disorders. This paper presents analysis of heart sounds in wavelet domain for automated screening of cardiac disorders. Heart sound signal is transformed in wavelet domain to find out discrimination between heart sounds recorded from healthy and anomalous patients. Discriminatory features extracted from wavelet coefficients of heart sound are subjected to machine learning for screening of cardiac disorders automatically. The proposed method for …
Delineation of Malignant Skin Tumors by Hyperspectral Imaging
2018
This chapter outlines a new non-invasive method for delineation of skin lesions such as lentigo maligna and lentigo maligna melanoma. The method is based on the analysis of hyperspectral (HS) images taken in vivo before surgical excision of the lesions. For this, characteristic features of the spectral signatures of diseased pixels and healthy pixels are extracted, which combine the intensities in a few selected wavebands with the coefficients of the wavelet frame transforms of the spectral curves. To reduce dimensionality and to reveal the internal structure of the datasets, the diffusion maps (DM) technique is applied. The averaged Nearest Neighbor and the Classification and Regression Tr…
COLOR MEDICAL IMAGE COMPRESSED USING QUINCUNX WAVELETS AND SPIHT CODING
2013
In the field of medical diagnostics, interested parties have resorted increasingly to color medical imaging. It is well established that the accuracy and completeness of diagnosis are initially connected with the image quality, but the quality of the image is itself dependent on a number of factors including primarily the processing that an image must undergo to enhance its quality. This paper introduces an algorithm for color medical image compression based on the quincunx wavelets coupled with SPÃHT coding algorithm. In order to enhance the compression by our algorithm, we have compared the results obtained with those of other methods containing wavelet transforms. For this reason, we …
Spline-Based Wavelet Transforms
2018
The Lifting Scheme introduced in (Sweldens, Appl. Comput. Harmon. Anal. 3(2), 186–200 (1996) and Sweldens, SIAM J. Math. Anal. 29(2), 511–546 (1997).) [3, 4] is a method that constructs bi-orthogonal wavelet transforms of signals and provides their efficient implementation. The main feature of the lifting scheme is that all the constructions are derived directly in the spatial domain and therefore can be custom designed to more general and irregular settings such as non-uniformly spaced data samples and bounded intervals. In this chapter, we outline the lifting scheme and describe how to use the local quasi-interpolating splines, introduced in Chap. 6, for the construction of wavelet transf…
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…
Wavelet Frames Generated by Spline Based p-Filter Banks
2014
This chapter presents a design scheme to generate tight and so-called semi-tight frames in the space of discrete-time periodic signals. The frames originate from oversampled perfect reconstruction periodic filter banks. The filter banks are derived from discrete-time and discrete periodic splines. Each filter bank comprises one linear phase low-pass filter (in most cases interpolating) and one high-pass filter, whose magnitude response mirrors that of a low-pass filter. In addition, these filter banks comprise a number of band-pass filters. In this chapter, frames generated by four-channel filter banks are briefly outlined (see Chap. 17 in [2] for details) and tight frames generated by six-…
More wavelet-like orthonormal bases for the lowest Landau level: Some considerations
1994
In a previous work, Antoine and I (1994) have discussed a general procedure which 'projects' arbitrary orthonormal bases of L2(R) into orthonormal bases of the lowest Landau level. In this paper, we apply this procedure to a certain number of examples, with particular attention to the spline bases. We also discuss Haar, Littlewood-Paley and Journe bases.
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…
Biorthogonal Wavelet Transforms Originating from Splines
2015
This chapter describes how to design families of biorthogonal wavelet transforms of signals and respective biorthogonal Wavelet bases in the signal space using spline-based prediction filters. Although the designed Wavelets originate from splines, they are not splines themselves. The design and implementation of the biorthogonal Wavelet transforms is done using the Lifting scheme. Most of the filters participating in the expansion of signals over the presented bases have infinite impulse responses and are implemented by recursive filtering whose computational cost is competitive with the FIR filtering cost. Properties of the designed Wavelets, such as symmetry, flat spectra, good time domai…
Quasi-interpolating and Smoothing Local Splines
2015
In this chapter, local quasi-interpolating and smoothing splines are described. Although approximation properties of local spline are similar to properties of the global interpolating and smoothing splines, their design does not require the IIR filtering of the whole data array. The computation of a local spline value at some point utilizes only a few adjacent grid samples. Therefore, local splines can be used for real-time processing of signals and for the design of FIR filter banks generating wavelets and wavelet frames (Chaps. 12 and 14). In the chapter, local splines of different orders are designed and their approximation properties are established which are compared with the propertie…