Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: The magnitude squared coherence (MSC) spectrum is an often used frequency-dependent measure for the linear dependency beten two stationary processes, and the recent literature contain several contributions on how to form high-resolution data-dependent and adaptive MSC estimators, and on the efficient implementation of such estimators. In this work,  further this development with the presentation of computationally efficient implementations of the recent iterative adaptive approach (IAA) estimator, present a novel sparse learning via iterative minimization (SLIM) algorithm, discuss extensions to two-dimensional data sets, examining both the case of complete data sets and when some of the observations are missing. The algorithms further the recent development of exploiting the estimators' inherently low displacement rank of the necessary products of Toeplitz-like matrices, extending these formulations to the coherence estimation using IAA and SLIM formulations. The performance of the proposed algorithms and implementations are illustrated both with theoretical complexity measures and with numerical simulations. Highlights? Computationally efficient IAA and SLIM based MSC methods are proposed. ? Complete and incomplete, one and two dimensional data sets are considered. ? Low displacement rank representations of Toeplitz matrix products are derived. ? Fast evaluation of data dependent trigonometric polynomials is proposed. ? Several orders of magnitude faster than the straightforward implementations.
['Kostas Angelopoulos', 'George-Othan Glentis', 'Andreas Jakobsson']
I am writing a research paper on a idea Computationally efficient sparsity-inducing coherence spectrum estimation of complete and non-complete data sets
[{"from": "human", "value": "I am writing a research paper on a idea Computationally efficient sparsity-inducing coherence spectrum estimation of complete and non-complete data sets"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: The magnitude squared coherence (MSC) spectrum is an often used frequency-dependent measure for the linear dependency beten two stationary processes, and the recent literature contain several contributions on how to form high-resolution data-dependent and adaptive MSC estimators, and on the efficient implementation of such estimators. In this work,  further this development with the presentation of computationally efficient implementations of the recent iterative adaptive approach (IAA) estimator, present a novel sparse learning via iterative minimization (SLIM) algorithm, discuss extensions to two-dimensional data sets, examining both the case of complete data sets and when some of the observations are missing. The algorithms further the recent development of exploiting the estimators' inherently low displacement rank of the necessary products of Toeplitz-like matrices, extending these formulations to the coherence estimation using IAA and SLIM formulations. The performance of the proposed algorithms and implementations are illustrated both with theoretical complexity measures and with numerical simulations. Highlights? Computationally efficient IAA and SLIM based MSC methods are proposed. ? Complete and incomplete, one and two dimensional data sets are considered. ? Low displacement rank representations of Toeplitz matrix products are derived. ? Fast evaluation of data dependent trigonometric polynomials is proposed. ? Several orders of magnitude faster than the straightforward implementations."}]