Ender M. Eksioglu

RLS Algorithm With Convex Regularization

In this letter, the RLS adaptive algorithm is considered in the system identification setting. The RLS algorithm is regularized using a general convex function of the system impulse response estimate. The normal equations corresponding to the convex regularized cost function are derived, and a recursive algorithm for the update of the tap estimates is established. We also introduce a closed-form expression for selecting the regularization parameter. With this selection of the regularization parameter, we show that the convex regularized RLS algorithm performs as well as, and possibly better than, the regular RLS when there is a constraint on the value of the convex function evaluated at the true weight vector. Simulations demonstrate the superiority of the convex regularized RLS with automatic parameter selection over regular RLS for the sparse system identification setting.

K-SVD Meets Transform Learning: Transform K-SVD

Recently there has been increasing attention directed towards the analysis sparsity models. Consequently, there is a quest for learning the operators which would enable analysis sparse representations for signals in hand. Analysis operator learning algorithms such as the Analysis K-SVD have been proposed. Sparsifying transform learning is a paradigm which is similar to the analysis operator learning, but they differ in some subtle points. In this paper, we propose a novel transform operator learning algorithm called as the Transform K-SVD, which brings the transform learning and the K-SVD based analysis dictionary learning approaches together. The proposed Transform K-SVD has the important advantage that the sparse coding step of the Analysis K-SVD gets replaced with the simple thresholding step of the transform learning framework. We show that the Transform K-SVD learns operators which are similar both in appearance and performance to the operators learned from the Analysis K-SVD, while its computational complexity stays much reduced compared to the Analysis K-SVD.

RLS adaptive filtering with sparsity regularization

We propose a new algorithm for the adaptive identification of sparse systems. The algorithm is based on the minimization of the RLS cost function when regularized by adding a sparsity inducing ℓ1 norm penalty. The resulting recursive update equations for the system impulse response estimate are in a similar form to the regular RLS. However, they include novel terms which account for the sparsity prior. The proposed, ℓ1 relaxation based RLS algorithm emphasizes sparsity during the adaptive filtering process and allows for faster convergence when the system under consideration is sparse. Computer simulations comparing the performance of the proposed algorithm to conventional RLS and other adaptive algorithms are provided. Simulations demonstrate that the new algorithm exploits the inherent sparse structure effectively.

Decoupled Algorithm for MRI Reconstruction Using Nonlocal Block Matching Model: BM3D-MRI

The block matching 3D (BM3D) is an efficient image model, which has found few applications other than its niche area of denoising. We will develop a magnetic resonance imaging (MRI) reconstruction algorithm, which uses decoupled iterations alternating over a denoising step realized by the BM3D algorithm and a reconstruction step through an optimization formulation. The decoupling of the two steps allows the adoption of a strategy with a varying regularization parameter, which contributes to the reconstruction performance. This new iterative algorithm efficiently harnesses the power of the nonlocal, image-dependent BM3D model. The MRI reconstruction performance of the proposed algorithm is superior to state-of-the-art algorithms from the literature. A convergence analysis of the algorithm is also presented.

Online dictionary learning algorithm with periodic updates and its application to image denoising

We introduce a coefficient update procedure into existing batch and online dictionary learning algorithms. We first propose an algorithm which is a coefficient updated version of the Method of Optimal Directions (MOD) dictionary learning algorithm (DLA). The MOD algorithm with coefficient updates presents a computationally expensive dictionary learning iteration with high convergence rate. Secondly, we present a periodically coefficient updated version of the online Recursive Least Squares (RLS)-DLA, where the data is used sequentially to gradually improve the learned dictionary. The developed algorithm provides a periodical update improvement over the RLS-DLA, and we call it as the Periodically Updated RLS Estimate (PURE) algorithm for dictionary learning. The performance of the proposed DLAs in synthetic dictionary learning and image denoising settings demonstrates that the coefficient update procedure improves the dictionary learning ability.

OVERCOMPLETE SPARSIFYING TRANSFORM LEARNING ALGORITHM USING A CONSTRAINED LEAST SQUARES APPROACH

Analysis sparsity and the accompanying analysis operator learning problem provide an important framework for signal modeling. Very recently, sparsifying transform learning has been put forward as an effective and new formulation for the analysis operator learning problem. In this study, we develop a new sparsifying transform learning algorithm by using the uniform normalized tight frame constraint. The new algorithm bypasses the computationally expensive analysis sparse coding step of the standard analysis operator learning algorithms. The resulting minimization problem is solved by alternating between two steps. The first step is the operator update, which comprises a least squares solution followed by a projection, and the second step is the sparse code update realized by a simple thresholding procedure. Simulation results indicate that the proposed algorithm provides improved analysis operator recovery performance when compared to a recent analysis operator learning algorithm from the literature, which uses the same uniform normalized tight frame constraint.

Transform learning MRI with global wavelet regularization

Sparse regularization of the reconstructed image in a transform domain has led to state of the art algorithms for magnetic resonance imaging (MRI) reconstruction. Recently, new methods have been proposed which perform sparse regularization on patches extracted from the image. These patch level regularization methods utilize synthesis dictionaries or analysis transforms learned from the patch sets. In this work we jointly enforce a global wavelet domain sparsity constraint together with a patch level, learned analysis sparsity prior. Simulations indicate that this joint regularization culminates in MRI reconstruction performance exceeding the performance of methods which apply either of these terms alone.

Reliability analysis of the complex mode indicator function and Hilbert Transform techniques for operational modal analysis

This study presents application of the CMIF and the Hilbert Transform techniques onto simulated response data obtained using a numerical model of a typical school building from Turkey. White noise is added to the data in order to achieve a noise to signal ratio of 5%. 100 Monte Carlo analysis sequences are carried out and the modal parameters (the frequencies, the mode shapes and the damping ratios) are identified at each Monte Carlo run for both techniques. The results are compared with the identifications obtained from the simulated data using stochastic subspace based system identification technique. The overall results of the study show that the mode shapes are clearly identified the best by using the CMIF technique. The damping ratios are estimated better by using the stochastic subspace based system identification technique whereas the frequencies are best determined by the CMIF. The results also show that both the CMIF and the Hilbert Transform techniques are sensitive to the type of window used as well as the averaging and the decimation process. It is apparent that the CMIF technique is as robust as the frequently used stochastic subspace based system identification technique and can be confidently used for modal parameter estimation of stiff low to mid rise reinforced concrete structures.

A compressive sensing framework for multirate signal estimation

This paper develops a novel compressive sensing setting for the multirate signal estimation problem. The multirate signal estimation task consists of estimating the values for a source signal when observed through several measurement channels sampled at different sampling rates. We demonstrate that this formulation can be recast in a compressive sensing setup. Reformulating the multirate signal estimation problem in a compressive sensing framework, enables us to infuse the sparse signal estimation and reconstruction methodologies into this multirate setting in a novel manner. We show that for sparse signals sampled through a multirate multichannel system, the compressive sensing signal reconstruction paradigm fits in effectively. Simulations are provided demonstrating that compressive sensing based signal reconstruction for multirate signal estimation is a viable and effective alternative.

Adaptive multirate signal estimation with lattice orthogonalization

In this paper, we address the signal estimation problem in statistical multirate systems. We propose an adaptive least squares lattice filter which is sequential and periodically time varying (PTV) with the multirate system period. Furthermore, we consider the elimination of redundant mathematical operations due to sequential processing of multirate observations. Experimental results show that our multirate lattice filter is fast convergent and it has lower order computational complexity when compared with the transversal structure.