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Time-frequency super-resolution with superlets.

ABSTRACT: Due to the Heisenberg-Gabor uncertainty principle, finite oscillation transients are difficult to localize simultaneously in both time and frequency. Classical estimators, like the short-time Fourier transform or the continuous-wavelet transform optimize either temporal or frequency resolution, or find a suboptimal tradeoff. Here, we introduce a spectral estimator enabling time-frequency super-resolution, called superlet, that uses sets of wavelets with increasingly constrained bandwidth. These are combined geometrically in order to maintain the good temporal resolution of single wavelets and gain frequency resolution in upper bands. The normalization of wavelets in the set facilitates exploration of data with scale-free, fractal nature, containing oscillation packets that are self-similar across frequencies. Superlets perform well on synthetic data and brain signals recorded in humans and rodents, resolving high frequency bursts with excellent precision. Importantly, they can reveal fast transient oscillation events in single trials that may be hidden in the averaged time-frequency spectrum by other methods.

SUBMITTER: Moca VV

PROVIDER: S-EPMC7803992 | biostudies-literature | 2021 Jan

REPOSITORIES: biostudies-literature

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Time-frequency super-resolution with superlets.

Moca Vasile V VV Bârzan Harald H Nagy-Dăbâcan Adriana A Mureșan Raul C RC

Nature communications 20210112 1

Due to the Heisenberg-Gabor uncertainty principle, finite oscillation transients are difficult to localize simultaneously in both time and frequency. Classical estimators, like the short-time Fourier transform or the continuous-wavelet transform optimize either temporal or frequency resolution, or find a suboptimal tradeoff. Here, we introduce a spectral estimator enabling time-frequency super-resolution, called superlet, that uses sets of wavelets with increasingly constrained bandwidth. These ...[more]

PMID: 33436585

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Project description:X-ray diffraction plays a pivotal role in the understanding of biological systems by revealing atomic structures of proteins, nucleic acids and their complexes, with much recent interest in very large assemblies like the ribosome. As crystals of such large assemblies often diffract weakly (resolution worse than 4 A), we need methods that work at such low resolution. In macromolecular assemblies, some of the components may be known at high resolution, whereas others are unknown: current refinement methods fail as they require a high-resolution starting structure for the entire complex. Determining the structure of such complexes, which are often of key biological importance, should be possible in principle as the number of independent diffraction intensities at a resolution better than 5 A generally exceeds the number of degrees of freedom. Here we introduce a method that adds specific information from known homologous structures but allows global and local deformations of these homology models. Our approach uses the observation that local protein structure tends to be conserved as sequence and function evolve. Cross-validation with R(free) (the free R-factor) determines the optimum deformation and influence of the homology model. For test cases at 3.5-5 A resolution with known structures at high resolution, our method gives significant improvements over conventional refinement in the model as monitored by coordinate accuracy, the definition of secondary structure and the quality of electron density maps. For re-refinements of a representative set of 19 low-resolution crystal structures from the Protein Data Bank, we find similar improvements. Thus, a structure derived from low-resolution diffraction data can have quality similar to a high-resolution structure. Our method is applicable to the study of weakly diffracting crystals using X-ray micro-diffraction as well as data from new X-ray light sources. Use of homology information is not restricted to X-ray crystallography and cryo-electron microscopy: as optical imaging advances to subnanometre resolution, it can use similar tools.

Dataset Information

Time-frequency super-resolution with superlets.

Publications

Time-frequency super-resolution with superlets.

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