Separable Complex-Valued Graph Filter Banks for Graph Signals

2021 ◽  
Author(s):  
Chunxu Guo ◽  
Yulong Qiao
Keyword(s):  
Filter Banks ◽  
Valued Graph ◽  
Complex Valued

Complex-valued linear-phase paraunitary filter banks

2000 ◽  
Vol 36 (10) ◽  
pp. 917 ◽  
Author(s):  
L. Chen ◽  
K.P. Chan ◽  
T.Q. Nguyen
Keyword(s):  
Filter Banks ◽  
Linear Phase ◽  
Paraunitary Filter Banks ◽  
Complex Valued

Phase Watermarking of Images with Complex-Valued Linear-Phase Subband Filter Banks

2013 ◽  
Vol 339 ◽  
pp. 275-280
Author(s):  
Li Chen ◽  
Rong Hua Peng
Keyword(s):  
Frequency Band ◽  
Filter Banks ◽  
Low Frequency ◽  
Linear Phase ◽  
Time Frequency ◽  
Frequency Spread ◽  
Phase Filter ◽  
Dct Domain ◽  
Dct Coefficients ◽  
Complex Valued

A new algorithm is proposed for digital watermarking by applying complex-valued linear-phase filter banks to low frequency-band coefficients of images in the DCT domain. The watermark is conveyed in the phase spectrum of the subband coefficients. The robustness of the algorithm is examined in JPEG encoding with different qualities and compared with the DFT-based approach. Because only low frequency-band DCT coefficients are applied to complex-valued filter banks, the computational load introduced by the complex-valued filter banks is kept low. The watermark decoding is only accessible to users with the key information, i.e., impulse responses of the complex-valued linear-phase filter banks that designed with time-frequency spread property.

scholarly journals Emergence of Canonical Functional Networks from the Structural Connectome

2020 ◽  
Author(s):  
Xihe Xie ◽  
Pablo F. Damasceno ◽  
Chang Cai ◽  
Srikantan Nagarajan ◽  
Ashish Raj
Keyword(s):  
Spatial Patterns ◽  
Linear Models ◽  
Signal Transmission ◽  
Functional Networks ◽  
Inference Procedure ◽  
Linear Superposition ◽  
Structural Connectome ◽  
Complex Laplacian ◽  
Valued Graph ◽  
Complex Valued

AbstractHow do functional brain networks emerge from the underlying wiring of the brain? We examine how resting-state functional activation patterns emerge from the underlying connectivity and length of white matter fibers that constitute its “structural connectome”. By introducing realistic signal transmission delays along fiber projections, we obtain a complex-valued graph Laplacian matrix that depends on two parameters: coupling strength and oscillation frequency. This complex Laplacian admits a complex-valued eigen-basis in the frequency domain that is highly tunable and capable of reproducing the spatial patterns of canonical functional networks without requiring any detailed neural activity modeling. Specific canonical functional networks can be predicted using linear superposition of small subsets of complex eigenmodes. Using a novel parameter inference procedure we show that the complex Laplacian outperforms the real-valued Laplacian in predicting functional networks. The complex Laplacian eigenmodes therefore constitute a tunable yet parsimonious substrate on which a rich repertoire of realistic functional patterns can emerge. Although brain activity is governed by highly complex nonlinear processes and dense connections, our work suggests that simple extensions of linear models to the complex domain effectively approximate rich macroscopic spatial patterns observable on BOLD fMRI.

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