• The Pure and Applied Mathematics
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• v.28 no.4
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• pp.315-328
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• 2021

A characterization of frame operators of finite Gabor frames is presented here. Regularity aspects of Gabor frames in 𝑙²(ℤ_N) are discussed by introducing associated semi-frame operators. Gabor type frames in finite dimensional Hilbert spaces are also introduced and discussed.

• Korean Journal of Mathematics
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• v.28 no.4
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• pp.877-888
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• 2020

In this paper we discuss about the image of Gabor frame under a unitary operator and derive a sufficient condition under which a unitary operator from L²(ℝ) to 𝑙²(ℤ) maps Gabor frame in L²(ℝ) to a Gabor frame in 𝑙²(ℤ).

• The Pure and Applied Mathematics
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• v.29 no.4
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• pp.321-334
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• 2022

We introduce a special class of structured frames having single generators in finite dimensional Hilbert spaces. We call them as pseudo B-Gabor like frames and present a characterisation of the frame operators associated with these frames. The concept of Gabor semi-frames is also introduced and some significant properties of the associated semi-frame operators are discussed.

• Journal of the Korean Mathematical Society
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• v.51 no.5
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• pp.897-918
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• 2014

This paper addresses multi-window Gabor frames with rational time-frequency product. Such issue was considered by Zibulski and Zeevi (Appl. Comput. Harmonic Anal. 4 (1997), 188-221) in terms of Zak transform matrix (so-called Zibuski-Zeevi matrix), and by many others. In this paper, we introduce of a new Zak transform matrix. It is different from Zibulski-Zeevi matrix, but more direct and convenient for our purpose. Using such Zak transform matrix we characterize rational time-frequency multi-window Gabor frames (Riesz bases and orthonormal bases), and Gabor duals for a Gabor frame. Some examples are also provided, which show that our Zak transform matrix method is efficient.

• The KIPS Transactions:PartB
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• v.9B no.5
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• pp.653-662
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• 2002

Fingerprint recognition is a task to find a matching pattern in a database for a specific persons fingerprint. To accomplish this task, preprocessing, classification, and matching steps are taken for a large-scale fingerprint database but only the matching step is taken without classification for a small-scale database. The primary matching method is based on minutiae (ridge ending point, bifurcation). This matching method, however, requires a very complex computation to extract minutiae and match minutiae-to-minutiae accurately due to translation, rotation, nonlinear deformation of fingerprint and occurrence of spurious minutiae. In addition, this method requires a laborious preprocessing step in order to improve the quality of fingerprint Images. This paper proposes a new simple method to eliminate these problems. With this method, Gabor variance is used instead of minutiae for fingerprint recognition. The Gabor variance is computed from Gabor features that result from filtering a fingerprint image through Gabor filter. In this paper, this method is described and its test result is shown, demonstrating the potential of using this new method for fingerprint recognition.

• Bulletin of the Korean Mathematical Society
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• v.50 no.6
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• pp.1841-1846
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• 2013

In this paper we establish some new results on sums of Hilbert space frames and Riesz bases. We also provide a correction to some recently established results in [2].

• Journal of Communications and Networks
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• v.12 no.4
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• pp.289-307
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• 2010

The problem of model selection arises in a number of contexts, such as subset selection in linear regression, estimation of structures in graphical models, and signal denoising. This paper studies non-asymptotic model selection for the general case of arbitrary (random or deterministic) design matrices and arbitrary nonzero entries of the signal. In this regard, it generalizes the notion of incoherence in the existing literature on model selection and introduces two fundamental measures of coherence-termed as the worst-case coherence and the average coherence-among the columns of a design matrix. It utilizes these two measures of coherence to provide an in-depth analysis of a simple, model-order agnostic one-step thresholding (OST) algorithm for model selection and proves that OST is feasible for exact as well as partial model selection as long as the design matrix obeys an easily verifiable property, which is termed as the coherence property. One of the key insights offered by the ensuing analysis in this regard is that OST can successfully carry out model selection even when methods based on convex optimization such as the lasso fail due to the rank deficiency of the submatrices of the design matrix. In addition, the paper establishes that if the design matrix has reasonably small worst-case and average coherence then OST performs near-optimally when either (i) the energy of any nonzero entry of the signal is close to the average signal energy per nonzero entry or (ii) the signal-to-noise ratio in the measurement system is not too high. Finally, two other key contributions of the paper are that (i) it provides bounds on the average coherence of Gaussian matrices and Gabor frames, and (ii) it extends the results on model selection using OST to low-complexity, model-order agnostic recovery of sparse signals with arbitrary nonzero entries. In particular, this part of the analysis in the paper implies that an Alltop Gabor frame together with OST can successfully carry out model selection and recovery of sparse signals irrespective of the phases of the nonzero entries even if the number of nonzero entries scales almost linearly with the number of rows of the Alltop Gabor frame.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.13 no.1
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• pp.333-342
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• 2012

This paper presents a vowel onset point (VOP) detection method based on the human auditory system. This method maps the "perceptual" frequency scale, i.e. Mel scale onto a linear acoustic frequency, and then establishes a series of Triangular Mel-weighted Filter Bank simulate the function of band pass filtering in human ear. This nonlinear critical-band filter bank helps greatly reduce the data dimensionality, and eliminate the effect of harmonic waves to make the formants more prominent in the nonlinear spaced Mel spectrum. The sum of mel spectrum peaks energy is extracted as feature for each frame, and the instinct at which the energy amplitude starts rising sharply is detected as VOP, by convolving with Gabor window. For the single-word database which contains 12 vowels articulated with different kinds of consonants, the experimental results showed a good average detection rate of 72.73%, higher than other vowel detection methods based on short-time energy and zero-crossing rate.

• Journal of the Korean Physical Society
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• v.73 no.9
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• pp.1269-1278
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• 2018

Using the thawed Gaussian wave packets [E. J. Heller, J. Chem. Phys. 62, 1544 (1975)] and the adaptive reinitialization technique employing the frame operator [L. M. Andersson et al., J. Phys. A: Math. Gen. 35, 7787 (2002)], a trajectory-based Gaussian wave packet method is introduced that can be applied to scattering and time-dependent problems. This method does not require either the numerical multidimensional integrals for potential operators or the inversion of nearly-singular matrices representing the overlap of overcomplete Gaussian basis functions. We demonstrate a possibility that the method can be a promising candidate for the time-dependent $Schr{\ddot{o}}dinger$ equation solver by applying to tunneling, high-order harmonic generation, and above-threshold ionization problems in one-dimensional model systems. Although the efficiency of the method is confirmed in one-dimensional systems, it can be easily extended to higher dimensional systems.

• Journal of Korea Multimedia Society
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• v.16 no.6
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• pp.764-781
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• 2013

In this paper, we propose a highly precise vehicle detection method with low false alarm using billboard sweep stereo matching and multi-stage hypothesis generation. First, we capture stereo images from cameras established in front of the vehicle and obtain the disparity map in which the regions of ground plane or background are removed using billboard sweep stereo matching algorithm. And then, we perform the vehicle detection and tracking on the labeled disparity map. The vehicle detection and tracking consists of three steps. In the learning step, the SVM(support vector machine) classifier is obtained using the features extracted from the gabor filter. The second step is the vehicle detection which performs the sobel edge detection in the image of the left camera and extracts candidates of the vehicle using edge image and billboard sweep stereo disparity map. The final step is the vehicle tracking using template matching in the next frame. Removal process of the tracking regions improves the system performance in the candidate region of the vehicle on the succeeding frames.