arXiv subjects

İlker Bayram

Publications and source records attributed to İlker Bayram.

5 recordsLinked to original sources

arXiv2021

Time-Series Estimation from Randomly Time-Warped Observations

We consider the problem of estimating a signal from its warped observations. Such estimation is commonly performed by altering the observations through some inverse-warping, or solving a computationally demanding optimization formulation. While these may be unavoidable if observations are few, when large amounts of warped observations are available, the cost of running such algorithms can be prohibitive. We consider the scenario where we have many observations, and propose a computationally simple algorithm for estimating the function of interest. We demonstrate the utility of the algorithm on streaming biomedical signals.

eess.SP↗

arXiv2017

Sparsity Within and Across Overlapping Groups

Recently, penalties promoting signals that are sparse within and across groups have been proposed. In this letter, we propose a generalization that allows to encode more intricate dependencies within groups. However, this complicates the realization of the threshold function associated with the penalty, which hinders the use of the penalty in energy minimization. We discuss how to sidestep this problem, and demonstrate the use of the modified penalty in an energy minimization formulation for an inverse problem.

math.OC↗

arXiv2017

Multichannel Linear Prediction for Blind Reverberant Audio Source Separation

A class of methods based on multichannel linear prediction (MCLP) can achieve effective blind dereverberation of a source, when the source is observed with a microphone array. We propose an inventive use of MCLP as a pre-processing step for blind source separation with a microphone array. We show theoretically that, under certain assumptions, such pre-processing reduces the original blind reverberant source separation problem to a non-reverberant one, which in turn can be effectively tackled using existing methods. We demonstrate our claims using real recordings obtained with an eight-microphone circular array in reverberant environments.

cs.SD↗

arXiv2016

A Penalty Function Promoting Sparsity Within and Across Groups

We introduce a new weakly-convex penalty function for signals with a group behavior. The penalty promotes signals with a few number of active groups, where within each group, only a few high magnitude coefficients are active. We derive the threshold function associated with the proposed penalty and study its properties. We discuss how the proposed penalty/threshold function can be useful for signals with isolated non-zeros, such as audio with isolated harmonics along the frequency axis, or reflection functions in exploration seismology where the non-zeros occur on the boundaries of subsoil layers. We demonstrate the use of the proposed penalty/threshold functions in a convex denoising and a non-convex deconvolution formulation. We provide convergent algorithms for both formulations and compare the performance with state-of-the-art methods.

math.NA↗

arXiv2015

The Douglas-Rachford Algorithm for Weakly Convex Penalties

The Douglas-Rachford algorithm is widely used in sparse signal processing for minimizing a sum of two convex functions. In this paper, we consider the case where one of the functions is weakly convex but the other is strongly convex so that the sum is convex. We provide a condition that ensures the convergence of the same Douglas-Rachford iterations, provided that the strongly convex function is smooth. We also present a modified Douglas-Rachford algorithm that does not impose a smoothness condition for the convex function. We then provide a discussion on the convergence speed of the two types of algorithms and demonstrate the discussion with numerical experiments.

math.OC↗