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I. Introduction Wavelets are the result of collective efforts that recognized common threads between ideas and concepts that had been independently developed and investigated by distinct research communities. They provide a unifying framework for decompos ...
Microscopy imaging often suffers from limited depth-of-focus. However, the specimen can be “optically sectioned” by moving the object along the optical axis; different areas appear in focus in different images. Extended depth-of-focus is a fusion algorithm ...
Statistical Parametric Mapping (SPM) is a widely deployed tool for detecting and analyzing brain activity from fMRI data. One of SPM's main features is smoothing the data by a Gaussian filter to increase the SNR. The subsequent statistical inference is bas ...
Musical and audio signals in general form a major part of the large amount of data exchange taking place in our information-based society. Transmission of high quality audio signals through narrow-band channels, such as the Internet, requires refined metho ...
We present complex rotation-covariant multiresolution families aimed for image analysis. Since they are complex-valued functions, they provide the important phase information, which is missing in the discrete wavelet transform with real wavelets. Our basis ...
Complex wavelet transforms offer the opportunity to perform directional and coherent processing based on the local magnitude and phase of signals and images. Although denoising, segmentation, and image enhancement are significantly improved using complex w ...
We continue the analysis of the continuous wavelet transform on the 2-sphere, introduced in a previous paper. After a brief review of the transform, we define and discuss the notion of directional spherical wavelet, i.e., wavelets on the sphere that are se ...
Microscopy imaging often suffers from limited depth-of-field. However, the specimen can be “optically sectioned” by moving the object along the optical axis. Then different areas appear in focus in different images. Extended depth-of-field is a fusion algo ...
The ridgelet transform (Candès and Donoho, 1999) was introduced as a sparse expansion for functions on continuous spaces that are smooth away from discontinuities along lines. In this paper, we propose an or- thonormal version of the ridgelet transform for ...
In 1983, Burt and Adelson introduced the Laplacian pyramid (LP) as a multiresolution representation for images. We study the LP using the frame theory, and this reveals that the usual reconstruction is suboptimal. We show that the LP with orthogonal filter ...
