Spectral analysis is an important step in seismic data processing and interpretation. The frequency contents of seismic traces vary with time due to the fact that the earth is non-stationary medium. Methods were available to improve the temporal and spectral resolution, such as windowed Fourier transform, wavelet transform, S-transform and Matching Pursuit Decomposition, etc. This paper describ...

An accurate time-frequency representation (TFR) can provide useful information in non stationary data analysis and processing. The traditional methods like short-time Fourier transform (STFT) and wavelet transform (WT) based TFR approaches are leads to a tradeoff between time and frequency resolution. A recently proposed synchrosqueezing transform (SST), which is an extension of the WT, has bee...

The wavelet periodogram is hard to smooth because of the low signal-to-noise ratio and non-stationary covariance structure. This article introduces a method for denoising a local wavelet periodogram by applying a Haar-Fisz transform which Gaussianises and stabilizes the variance of the periodogram. Consequently the transformed periodogram is easier to smooth. This article demonstrates the super...

This paper describes the implementation and performance evaluation of three noise estimation algorithms using two different signal decomposition methods: a second-generation wavelet transform and a perceptual wavelet packet transform. These algorithms, which do not require the use of a speech activity detector or signal statistics learning histograms, are: a smoothing-based adaptive technique, ...

The emphasis in this article is on the study of nonstationary two-dimensional (2-D) random fields with wide-sense stationary increments, wide-sense stationary jumps, and 2-D fractional Brownian motion (fBm) fields. The effort made in this work is to develop a realizable method of stationarization provided for nonstationary 2-D random fields. We also present the correlation functions of the disc...

This article addresses the problem of denoising piecewise constant functions by using both an jump-tolerant moving average and Haar wavelet shrinkage. The piecewise constant functions are contaminated with Poissonlike noise and are measurements of perceived itch by human subjects in an experiment to relate perceived itch to blood ow in response to histamine iontophoresis. We show that the trans...

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The Discrete Wavelet Transform (DWT) is a transformation that can be used to analyze the temporal and spectral properties of non-stationary signals. In this paper we describe some applications of the DWT to the problem of extracting information from normal and abnormal arterial pulses. We shall review a feature extraction algorithm of pulse signals, wavelet analysis, with aim of generating the ...

A few different approaches exist for computing undecimated wavelet transform. In this work we construct three undecimated schemes and evaluate their performance for image noise reduction. We use standard wavelet based de-noising techniques and compare the performance of our algorithms with the original undecimated wavelet transform, as well as with the decimated wavelet transform. The experimen...

We present in this paper new multiscale transforms on the sphere, namely the isotropic undecimated wavelet transform, the pyramidal wavelet transform, the ridgelet transform and the curvelet transform. All of these transforms can be inverted i.e. we can exactly reconstruct the original data from its coefficients in either representation. Several applications are described. We show how these tra...