There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

다중혈관 관상동맥 환자에서 y-문합을 이용하여 양쪽 내흉동맥만을 사용한 우회술의 조기 성적

In this work, we are interested in generalizing convolutional neural networks (CNNs) from low-dimensional regular grids, where image, video and speech are represented, to high-dimensional irregular domains, such as social networks, brain connectomes or words' embedding, represented by graphs. We present a formulation of CNNs in the context of spectral graph theory, which provides the necessary mathematical background and efficient numerical schemes to design fast localized convolutional filters on graphs. Importantly, the proposed technique offers the same linear computational complexity and constant learning complexity as classical CNNs, while being universal to any graph structure. Experiments on MNIST and 20NEWS demonstrate the ability of this novel deep learning system to learn local, stationary, and compositional features on graphs.

Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering

/pdf/convolutional-neural-networks-on-graphs-with-fast-localized-1rjlnh7c4h.pdf

Convolutional neural networks on graphs with fast localized spectral filtering

We explore in this chapter questions of existence and uniqueness for solutions to stochastic differential equations and offer a study of their properties. This endeavor is really a study of diffusion processes. Loosely speaking, the term diffusion is attributed to a Markov process which has continuous sample paths and can be characterized in terms of its infinitesimal generator.

Stochastic Differential Equations

Pearson Correlation Coefficient

Noise spectrum estimation is a fundamental component of speech enhancement and speech recognition systems. We present an improved minima controlled recursive averaging (IMCRA) approach, for noise estimation in adverse environments involving nonstationary noise, weak speech components, and low input signal-to-noise ratio (SNR). The noise estimate is obtained by averaging past spectral power values, using a time-varying frequency-dependent smoothing parameter that is adjusted by the signal presence probability. The speech presence probability is controlled by the minima values of a smoothed periodogram. The proposed procedure comprises two iterations of smoothing and minimum tracking. The first iteration provides a rough voice activity detection in each frequency band. Then, smoothing in the second iteration excludes relatively strong speech components, which makes the minimum tracking during speech activity robust. We show that in nonstationary noise environments and under low SNR conditions, the IMCRA approach is very effective. In particular, compared to a competitive method, it obtains a lower estimation error, and when integrated into a speech enhancement system achieves improved speech quality and lower residual noise.

/pdf/noise-spectrum-estimation-in-adverse-environments-improved-k9jxzivyvw.pdf

Noise spectrum estimation in adverse environments: improved minima controlled recursive averaging

Noise spectrum estimation is a fundamental component of speech enhancement and speech recognition systems. In this paper, we present an Improved Minima Con- trolled Recursive Averaging (IMCRA) approach, for noise es- timation in adverse environments involving non-stationary noise, weak speech components, and low input signal-to- noise ratio (SNR). The noise estimate is obtained by av- eraging past spectral power values, using a time-varying frequency-dependent smoothing parameter that is adjusted by the signal presence probability. The speech presence probability is controlled by the minima values of a smoothed periodogram. The proposed procedure comprises two iter- ations of smoothing and minimum tracking. The rst it- eration provides a rough voice activity detection in each frequency band. Then, smoothing in the second iteration excludes relatively strong speech components, which makes the minimum tracking during speech activity robust. We show that in non-stationary noise environments and under low SNR conditions, the IMCRA approach is very eectiv e. In particular, compared to a competitive method, it obtains a lower estimation error, and when integrated into a speech enhancement system achieves improved speech quality and lower residual noise.

/pdf/noise-spectrum-estimation-in-adverse-environments-improved-2p8w9t313q.pdf

Noise Spectrum Estimation in Adverse Environments: Improved Minima Controlled

In this letter, we introduce a minima controlled recursive averaging (MCRA) approach for noise estimation. The noise estimate is given by averaging past spectral power values and using a smoothing parameter that is adjusted by the signal presence probability in subbands. The presence of speech in subbands is determined by the ratio between the local energy of the noisy speech and its minimum within a specified time window. The noise estimate is computationally efficient, robust with respect to the input signal-to-noise ratio (SNR) and type of underlying additive noise, and characterized by the ability to quickly follow abrupt changes in the noise spectrum.

/pdf/noise-estimation-by-minima-controlled-recursive-averaging-230nb4wkob.pdf

Noise estimation by minima controlled recursive averaging for robust speech enhancement

https://webee.technion.ac.il/Sites/People/IsraelCohen/Publications/sp_Nov2001.pdf

Israel Cohen

Papers

Pearson Correlation Coefficient

Noise spectrum estimation in adverse environments: improved minima controlled recursive averaging

Noise Spectrum Estimation in Adverse Environments: Improved Minima Controlled

Noise estimation by minima controlled recursive averaging for robust speech enhancement

Speech enhancement for non-stationary noise environments