We consider the phase retrieval problem in which one tries to reconstruct a function from the modulus of its wavelet transform. We study the unicity and stability of the reconstruction. In the case where the wavelets are Cauchy wavelets, we prove that the modulus of the wavelet transform uniquely determines the function up to a global phase. We show that the reconstruction operator is continuou...

electrocardiogram (ecg) is one of the most common biological signals which plays a significant role in diagnosis of heart diseases. one of the most important parts of ecg signal processing is interpretation of qrs complex and obtaining its characteristics. r wave is one of the most important sections of this complex which has an essential role in diagnosis of heart rhythm irregularities and als...

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...

Measuring cardiac activity from the chest using an accelerometer is commonly referred to as seismocardiography. Unfortunately, it cannot provide clinically valid data because easily corrupted by motion artefacts. This paper proposes two methods improve peak detection noisy seismocardiography data. They rely on discrete wavelet transform analysis either biorthogonal 3.9 or reverse 3.9. The first...

To evaluate eddy structures of a plane turbulent jet in the dimension of time and scale, the velocity signals were analyzed using the continuous and discrete wavelet transforms in this paper. From the distribution of coefficients of continuous wavelet transform, localized nearly periodic eddy motions with a=64ms, 100ms and 180ms were respectively observed in the shear layer of x/d=8.5 in the ti...

We employ complex continuous wavelet transforms to develop a consistent mathematical framework capable of quantifying both cerebrospinal compensatory reserve and cerebrovascular pressure–reactivity. The wavelet gain ( ) ICP ABP f η , defined as the frequency dependent ratio of time averaged wavelet coefficients of intracranial pressure (ICP) and arterial blood pressure (ABP) fluctuations, chara...

In this article, the continuous wavelet transform is introduced as a signal processing tool for investigating time-varying frequency spectrum characteristics of nonstationary signals. The transform is discussed within the context of Fourier methods and the general problem of time-frequency representation and is compared with the more traditional Gabor method of windowed Fourier transforms. To t...

In this paper, image compression using orthogonal wavelet transforms of Walsh, Cosine, Haar, Kekre, Slant and Sine is studied. Wavelet transform of size N 2 xN 2 is generated using its corresponding orthogonal transform of size NxN. These wavelet transforms are applied on R, G, and B planes of 256x256x3 size colour images separately. In each transformed plane rows/columns are sorted in their de...