arXiv subjects

Ilker Bayram

Publications and source records attributed to Ilker Bayram.

5 recordsLinked to original sources

arXiv2025

Classification Filtering

We consider a streaming signal in which each sample is linked to a latent class. We assume that multiple classifiers are available, each providing class probabilities with varying degrees of accuracy. These classifiers are employed following a straightforward and fixed policy. In this setting, we consider the problem of fusing the output of the classifiers while incorporating the temporal aspect to improve classification accuracy. We propose a state-space model and develop a filter tailored for realtime execution. We demonstrate the effectiveness of the proposed filter in an activity classification application based on inertial measurement unit (IMU) data from a wearable device.

eess.SP↗

arXiv2024

Interbeat Interval Filtering

A number of inhibitory and excitatory factors regulate the beating of the heart. Consequently, the inter-beat intervals (IBIs) are not constant but vary around a mean value, even in the absence of external factors like exercise or stress. Various statistics have been proposed to capture the heart rate variability (HRV) to provide a glimpse into this balance. These statistics usually require accurate estimation of IBIs as a first step. However, estimating IBIs accurately can be challenging in practice, especially for signals recorded in ambulatory conditions. We propose a lightweight state-space filter that models the IBIs as samples of an inverse Gaussian distribution with time-varying parameters. We make the filter robust against outliers by adapting the probabilistic data association filter to the setup. We demonstrate that the resulting filter can accurately identify outliers and the parameters of the tracked distribution can be used to compute a specific HRV statistic (standard deviation of normal-to-normal intervals) without further analysis.

eess.SP↗

arXiv2020

An Exploratory Method for Smooth/Transient Decomposition

We consider a separation problem where the observation consists of the sum of a high amplitude smooth signal and a low amplitude transient signal. We propose a method for decomposition that relies on solving instances of a `constrained filtering problem', which is posed as a convex minimization problem. We provide a fast algorithm for solving the minimization problem, and demonstrate the effectiveness of the scheme for a vital signs monitoring experiment using radar.

eess.SP↗

arXiv2015

On the Convergence of the Iterative Shrinkage/Thresholding Algorithm With a Weakly Convex Penalty

We consider the iterative shrinkage/thresholding algorithm (ISTA) applied to a cost function composed of a data fidelity term and a penalty term. The penalty is non-convex but the concavity of the penalty is accounted for by the data fidelity term so that the overall cost function is convex. We provide a generalization of the convergence result for ISTA viewed as a forward-backward splitting algorithm. We also demonstrate experimentally that for the current setup, using large stepsizes in ISTA can accelerate convergence more than existing schemes proposed for the convex case, like TwIST or FISTA.

math.OC↗

arXiv2014

Sparse Signal Estimation by Maximally Sparse Convex Optimization

This paper addresses the problem of sparsity penalized least squares for applications in sparse signal processing, e.g. sparse deconvolution. This paper aims to induce sparsity more strongly than L1 norm regularization, while avoiding non-convex optimization. For this purpose, this paper describes the design and use of non-convex penalty functions (regularizers) constrained so as to ensure the convexity of the total cost function, F, to be minimized. The method is based on parametric penalty functions, the parameters of which are constrained to ensure convexity of F. It is shown that optimal parameters can be obtained by semidefinite programming (SDP). This maximally sparse convex (MSC) approach yields maximally non-convex sparsity-inducing penalty functions constrained such that the total cost function, F, is convex. It is demonstrated that iterative MSC (IMSC) can yield solutions substantially more sparse than the standard convex sparsity-inducing approach, i.e., L1 norm minimization.

cs.LG↗