Second-order finite-time and fixed-time systems for sparse recovery and dynamic sparse recovery

Authors: Yihua Huang
Primary area: optimization
Keywords: frame of defining penalty functions, noise, accelerated distributed generalized reweighted noise filtering consensus algorithm, accelerated distributed robust generalized reweighted denoise consensus algorithm, $l_p$-norm minimization, multi-target tracking

Abstract:
In the rapidly advancing field of healthcare, efficient processing of sparse data is essential for applications such as medical imaging and personalized medicine.
This paper introduces innovative second-order finite-time and fixed-time systems
tailored for sparse recovery in healthcare data, incorporating control laws into
the second-order derivative. We validate the stability and convergence of these
systems within finite and fixed times using the Lyapunov method. Furthermore,
we examine the tracking performance and assess both practical finite-time and
fixed-time convergence. The effectiveness of our systems is highlighted through
comparative analyses with existing methods, with numerical experiments demonstrating superior accuracy and dynamic tracking capabilities of sparse biomedical
signals.

Decision: reject

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