Designing Gabor windows using convex optimization

Perraudin, Nathanaël; Holighaus, Nicki; Søndergaard, Peter; Balázs, Péter

doi:10.1016/j.amc.2018.01.035

Cited by 22 publications

(11 citation statements)

References 81 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…We developed scprep efficiently process single-cell data, and graphtools was developed for construction and manipulation of graphs built on data. Fourier analysis and Chebyshev approximations are implemented using functions from the pygsp toolbox [77].…”

Section: Summary Of the Ees Algorithmmentioning

confidence: 99%

Quantifying the effect of experimental perturbations at single-cell resolution

Burkhardt¹,

Stanley

Tong

et al. 2019

Preprint

103

View full text Add to dashboard Cite

4Single-cell RNA-sequencing (scRNA-seq) is a powerful tool to quantify transcriptional states in 5 thousands to millions of cells. It is increasingly common for scRNA-seq data to be collected in 6 multiple experimental conditions, yet quantifying differences between scRNA-seq datasets re-7 mains an analytical challenge. Previous efforts at quantifying such differences focus on discrete 8 regions of the transcriptional state space such as clusters of cells. Here, we describe a contin-9 uous measure of the effect of an experiment across the transcriptomic space. First, we use the 10 manifold assumption to model the cellular state space as a graph (or network) with cells as nodes 11 and edges connecting cells with similar transcriptomic profiles. Next, we create an Enhanced 12 Experimental Signal (EES) that estimates the likelihood of observing cells from each condition 13 at every point in the manifold. We show that the EES has useful properties and information that 14 can be extracted. The EES can be used to identify how gene expression is affected by a given 15 perturbation, including identifying non-monotonic changes from only two conditions. We also 16 show that we can use both the magnitude and frequency of the EES, using an algorithm we 17 call vertex frequency clustering, to derive subsets of cells at appropriate levels of granularity 18 (tailored to areas that change) that are enriched in the experimental or control conditions or that 19 are unaffected between conditions. We demonstrate both algorithms using a combination of 20 biological and synthetic datasets. Implementations are provided in the MELD Python package, 21 which is available at https://github.com/KrishnaswamyLab/MELD. 22As single-cell RNA-sequencing (scRNA-seq) has become more accessible, the design of single-cell exper-24 iments has become increasingly complex. Researchers regularly use scRNA-seq to quantify the effect of 25 a drug, gene knockout, or other experimental perturbation on a biological system. However, quantifying 26 the compositional differences between single-cell datasets collected from multiple experimental conditions 27 1 remains an analytical challenge [1] because of the heterogeneity and noise in both the data and the effects 28 of a given perturbation. 29 Previous work has shown the utility of modelling the transcriptomic state space as a continuous low-30 dimensional manifold, or set of manifolds, to characterize cellular heterogeneity and dynamic biological 31 processes [2][3][4][5][6][7][8]. In the manifold model, the biologically valid combinations of gene expression are rep-32 resented as a smooth, low-dimensional surface in a high dimensional space, such as a two-dimensional 33 sheet embedded in three dimensions. The main challenge in developing tools to quantify compositional 34 differences between single-cell datasets is that each dataset comprises several intrinsic structures of hetero-35 geneous cells, and the effect of the experimental condition could be diffuse or isolated to particular areas 36 of...

show abstract

Section: Summary Of the Ees Algorithmmentioning

confidence: 99%

Quantifying the effect of experimental perturbations at single-cell resolution

Burkhardt¹,

Stanley

Tong

et al. 2019

Preprint

103

View full text Add to dashboard Cite

show abstract

“…Gegenüber Basen gibt es mehr Freiheiten, Rahmen mit besonderen Eigenschaften zu konstruieren, und falls bei einer möglichen Datenübertragung eine Komponente verrauscht ist oder verloren geht, ist ein Teil der Information immer noch in anderen Koeffizienten enthalten [7]. Darüber hinaus erlaubt die Redundanz mehr als einen dualen Rahmen, der eine verlustfreie Wiederherstellung garantiert, was etwa in der Resynthese auch wieder mehr Optionen ermöglicht [18]. [15], welche dann in der Akustik eingesetzt werden, etwa für die Signaltrennung [27].…”

Section: Rahmenunclassified

Application of frame multipliers for the extraction of curve squeals from train signals

Balázs

Kasess

Kreuzer

et al. 2021

Elektrotech. Inftech.

Self Cite

View full text Add to dashboard Cite

ZusammenfassungFür viele Anwendungen in der Akustik ist es notwendig, Signale und Funktionen mithilfe von zeitvarianten Filtern zu bearbeiten, z. B. um Komponenten aus einem Signal zu entfernen, deren Frequenzverlauf sich über die Zeit ändert. Es wird eine Methode vorgestellt, die auf einer Darstellung des Signals durch Rahmen (engl. Frames) basiert, und mit deren Hilfe Filter auf der Zeit-Frequenz-Ebene definiert werden können. Nach einer kurzen Beschreibung des theoretischen Hintergrunds von Rahmen wird ihre Anwendung anhand eines Beispiels aus der Lärmforschung erläutert. Mithilfe einer einfachen grafischen Oberfläche wird aus einer Aufnahme einer Kurvenfahrt eines Zugs eine durch den Dopplereffekt zeitvariante Komponente (Kurvenquietschen) herausgeschnitten und in ein zweites Signal eingefügt. Auf diese Art und Weise lassen sich kontrollierte Signale generieren, die dann zur Lärmbewertung eingesetzt werden können.

show abstract

“…1 for the download URL). When DGT is redundant, there exist infinitely many dual windows corresponding to a single window w. Therefore, many attempts to design a dual window with some desirable properties have been made [8][9][10][11]. A window is called tight when itself is proportional to its dual window, and its useful properties in signal processing have been studied [11][12][13][14].…”

Section: Inversion and Related Topics On Dgtmentioning

confidence: 99%

“…In contrast, the phasecorrected spectrogram on the bottom left is smooth along time. 10 Here, frequencies are considered in the unit of index. 11 The reason for using cumulative sum of the relative instantaneous frequency ½m; n ¼ P n k¼1 D t Eq(7) ½m; k is that D t Eq(7) only represents the adjacent (local) relation, while the phase correction is based on the global relation ½m; n given for all m; n.…”

Section: Pcmentioning

confidence: 99%

Representation of complex spectrogram via phase conversion

Yatabe

Masuyama

Kusano

et al. 2019

Acoust. Sci. & Tech.

View full text Add to dashboard Cite

As importance of the phase of complex spectrogram has been recognized widely, many techniques have been proposed for handling it. However, several definitions and terminologies for the same concept can be found in the literature, which has confused beginners. In this paper, two major definitions of the short-time Fourier transform and their phase conventions are summarized to alleviate such complication. A phase-aware signal-processing scheme based on phase conversion is also introduced with a set of executable MATLAB functions (https://doi.org/10/c3qb).

show abstract

Designing Gabor windows using convex optimization

Cited by 22 publications

References 81 publications

Quantifying the effect of experimental perturbations at single-cell resolution

Quantifying the effect of experimental perturbations at single-cell resolution

Application of frame multipliers for the extraction of curve squeals from train signals

Representation of complex spectrogram via phase conversion

Contact Info

Product

Resources

About