Journal ArticleDOI
Design of Time---Frequency Localized Filter Banks: Transforming Non-convex Problem into Convex Via Semidefinite Relaxation Technique
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TLDR
The design examples demonstrate that reasonably smooth wavelets can be designed from the proposed filter banks and the performance of optimal filter banks has been found better in terms of joint time–frequency localization.Abstract:
We present a method for designing optimal biorthogonal wavelet filter banks (FBs). Joint time---frequency localization of the filters has been chosen as the optimality criterion. The design of filter banks has been cast as a constrained optimization problem. We design the filter either with the objective of minimizing its frequency spread (variance) subject to the constraint of prescribed time spread or with the objective of minimizing the time spread subject to the fixed frequency spread. The optimization problems considered are inherently non-convex quadratic constrained optimization problems. The non-convex optimization problems have been transformed into convex semidefinite programs (SDPs) employing the semidefinite relaxation technique. The regularity constraints have also been incorporated along with perfect reconstruction constraints in the optimization problem. In certain cases, the relaxed SDPs are found to be tight. The zero duality gap leads to the global optimal solutions. The design examples demonstrate that reasonably smooth wavelets can be designed from the proposed filter banks. The optimal filter banks have been compared with popular filter banks such as Cohen---Daubechies---Feauveau biorthogonal wavelet FBs, time---frequency optimized half-band pair FBs and maximally flat half-band pair FBs. The performance of optimal filter banks has been found better in terms of joint time---frequency localization.read more
Citations
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Journal ArticleDOI
A new approach to characterize epileptic seizures using analytic time-frequency flexible wavelet transform and fractal dimension
TL;DR: It appears that a system is in place to assist clinicians to diagnose seizures accurately in less time as the proposed model achieves perfect 100% classification sensitivity and is found to be outperforming all existing models in terms of classification sensitivity (CSE).
Journal ArticleDOI
An automatic detection of focal EEG signals using new class of time–frequency localized orthogonal wavelet filter banks
Manish Sharma,Abhinav Dhere,Ram Bilas Pachori,U. Rajendra Acharya,U. Rajendra Acharya,U. Rajendra Acharya +5 more
TL;DR: A novel class of orthogonal wavelet filter banks which are localized in time–frequency domain to detect FC and NFC EEG signals automatically and help in localization of the affected brain area which needs to undergo surgery is employed.
Journal ArticleDOI
Time–frequency localized three-band biorthogonal wavelet filter bank using semidefinite relaxation and nonlinear least squares with epileptic seizure EEG signal classification
TL;DR: The designed three-band filter banks and multi-layer perceptron neural network (MLPNN) are further used together to implement a signal classifier that provides classification accuracy better than the recently reported results for epileptic seizure EEG signal classification.
Journal ArticleDOI
An automated diagnosis of depression using three-channel bandwidth-duration localized wavelet filter bank with EEG signals
Manish Sharma,P.V. Achuth,Dipankar Deb,Subha D. Puthankattil,U. Rajendra Acharya,U. Rajendra Acharya,U. Rajendra Acharya +6 more
TL;DR: A computer aided depression diagnosis system using newly designed bandwidth-duration localized (BDL) three-channel orthogonal wavelet filter bank and EEG signal for the detection of depression and attained the perfect value of 1 for area under the curve (AUC) of receiver’s operating characteristics (ROC) using seven features.
Journal ArticleDOI
A novel approach to detect epileptic seizures using a combination of tunable-q wavelet transform and fractal dimension
Manish Sharma,Ram Bilas Pachori +1 more
TL;DR: A new machine learning and signal processing-based automated system that can detect epileptic episodes accurately and is expected to assist clinicians in analyzing seizures accurately in less time without any error is proposed.
References
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Journal ArticleDOI
Semidefinite programming
Lieven Vandenberghe,Stephen Boyd +1 more
TL;DR: A survey of the theory and applications of semidefinite programs and an introduction to primaldual interior-point methods for their solution are given.
Journal ArticleDOI
Improved approximation algorithms for maximum cut and satisfiability problems using semidefinite programming
TL;DR: This algorithm gives the first substantial progress in approximating MAX CUT in nearly twenty years, and represents the first use of semidefinite programming in the design of approximation algorithms.
Journal ArticleDOI
Semidefinite Relaxation of Quadratic Optimization Problems
TL;DR: This article has provided general, comprehensive coverage of the SDR technique, from its practical deployments and scope of applicability to key theoretical results, and showcased several representative applications, namely MIMO detection, B¿ shimming in MRI, and sensor network localization.
Journal ArticleDOI
Biorthogonal bases of compactly supported wavelets
TL;DR: In this paper, it was shown that under fairly general conditions, exact reconstruction schemes with synthesis filters different from the analysis filters give rise to two dual Riesz bases of compactly supported wavelets.