We give specific examples of the spectral decomposition self-adjoint operators in application to establish sharp inequalities for their powers.

Abstract We consider the problem of recovering three-dimensional atomic structure a flexible macromolecule from heterogeneous cryogenic electron microscopy (cryo-EM) dataset. The dataset contains noisy tomographic projections electrostatic potential macromolecule, taken different viewing directions, and in case, each cryo-EM image corresponds to conformation macromolecule. Under assumption that...

Spectral analysis is an important signal processing tool for seismic data. The transformation of a seismogram into the frequency domain is the basis for a significant number of processing algorithms and interpretive methods. However, for seismograms whose frequency content vary with time, a simple 1-D (Fourier) frequency transformation is not sufficient. Improved spectral decomposition in frequ...

Clinical successes with dual energy CT, aggressive development of energy discriminating x-ray detectors, and novel, target-specific, nanoparticle contrast agents promise to establish spectral CT as a powerful functional imaging modality. Common to all of these applications is the need for a material decomposition algorithm which is robust in the presence of noise. Here, we develop such an algor...

Detector-based spectral computed tomography is a novel dual-energy CT technology that employs two layers of detectors to simultaneously collect low- and high-energy data in all patients using standard CT protocols. In addition to the conventional polyenergetic images created for each patient, projection-space decomposition is used to generate spectral basis images (photoelectric and Compton sca...