Surgery of spline-type and molecular frames

We prove a result about producing new frames for general spline-type spaces by piecing together portions of known frames. Using spline-type spaces as models for the range of certain integral transforms, we obtain results for time-frequency decompositions and sampling.Comment: 34 pages. Corrected typo

Characterization of coorbit spaces with phase-space covers

We show that coorbit spaces can be characterized in terms of arbitrary phase-space covers, which are families of phase-space multipliers associated with partitions of unity. This generalizes previously known results for time-frequency analysis to include time-scale decompositions. As a by-product, we extend the existing results for time-frequency analysis to an irregular setting.Comment: 31 pages. Revised version (title slightly changed). Typos fixe

Multitaper estimation on arbitrary domains

Multitaper estimators have enjoyed significant success in estimating spectral densities from finite samples using as tapers Slepian functions defined on the acquisition domain. Unfortunately, the numerical calculation of these Slepian tapers is only tractable for certain symmetric domains, such as rectangles or disks. In addition, no performance bounds are currently available for the mean squared error of the spectral density estimate. This situation is inadequate for applications such as cryo-electron microscopy, where noise models must be estimated from irregular domains with small sample sizes. We show that the multitaper estimator only depends on the linear space spanned by the tapers. As a result, Slepian tapers may be replaced by proxy tapers spanning the same subspace (validating the common practice of using partially converged solutions to the Slepian eigenproblem as tapers). These proxies may consequently be calculated using standard numerical algorithms for block diagonalization. We also prove a set of performance bounds for multitaper estimators on arbitrary domains. The method is demonstrated on synthetic and experimental datasets from cryo-electron microscopy, where it reduces mean squared error by a factor of two or more compared to traditional methods.Comment: 28 pages, 11 figure

Open Source Virtual Worlds and Low Cost Sensors for Physical Rehab of Patients with Chronic Diseases

For patients with chronic diseases, exercise is a key part of rehab to deal better with their illness. Some of them do rehabilitation at home with telemedicine systems. However, keeping to their exercising program is challenging and many abandon the rehabilitation. We postulate that information technologies for socializing and serious games can encourage patients to keep doing physical exercise and rehab. In this paper we present Virtual Valley, a low cost telemedicine system for home exercising, based on open source virtual worlds and utilizing popular low cost motion controllers (e.g. Wii Remote) and medical sensors. Virtual Valley allows patient to socialize, learn, and play group based serious games while exercising