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Eksik Veri Temininde Shearlet Dönüşümünün Asimptotik Analizi

Supply of missing data, also known as inpainting, is an important application of image processing. Wavelets are commonly used for inpainting algorithms. Shearlet transform which is an affine transformation is the improvement of the wavelet transform. An asymptotic analysis may help to evaluate the performance of an algorithm. In this article we compare the asymptotical analysis for wavelet and shearlet transforms in the case of inpainting where the missing data is shaped like a rectangle.

Makine öğrenmesi algoritmaları ve dalgacık dönüşümü ile EKG sinyalinden özellik çıkarımı

Gunumuzde biyomedikal sinyallerin analizinde dalgacik donusumunun kullanilmasi oldukca yaygin olup elde edilen sonuclar etkileyicidir. Bu calismada, biyomedikal sinyallerden elektrokardiyogram (EKG) sinyallerinde QRS zirvesi belirleme hedeflenmis ve daha iyi sonuclar almak icin oncelikle EKG sinyallerindeki zemin gezinme gurultusunun giderilmesi ve yuksek frekansli gurultunun temizlenmesi amaciyla dalgacik analizi kullanilmistir. Daubechies 10 (db10) dalgacik donusumu uygulanan sinyalin 10. seviye yaklasim katsayisi ve 10. seviye detay katsayisi cikartilarak sinyaldeki zemin gezinmesi problemi giderilmistir. Yuksek frekans gurultusunun giderilmesi icin ise zemin gezinmesi problemi giderilmis olan sinyale dalgacik gurultu temizleme uygulanmistir. Gurultusu temizlenen sinyalde QRS zirvelerini belirlemek icin sinyalin 1. turev ve 2. turev bilgileri ele alinarak Destek Vektor Makineleri ve Naive Bayes algoritmalari kullanilmistir. QRS zirvelerinin bulunmasinda, MIT-BIH aritmi veri tabaninda verilen QRS zirvelerinin konum bilgileri kullanilmistir. QRS zirvelerini dogru belirlemede Destek Vektor Makineleri algoritmasi Naive Bayes algoritmasindan daha yavas sonuc vermesine ragmen %99.46 duyarlilik, %100 secicilik ve %0.54 hata degerlerine ulasmistir.

The Solution of Initial Boundary Value Problem with Time and Space-Fractional Diffusion Equation via a Novel Inner Product

The main goal of this study is to find the solution of initial boundary value problem for the one-dimensional time and space-fractional diffusion equation which is a very intriguing topic for many researchers. With the aim of newly defined inner product, which is the main contribution of this study, the analytic solution of the boundary value problem is obtained. The time and space-fractional derivatives are defined in the Caputo sense which is more suitable than Riemann-Liouville sense. We apply the separation of variables method to reduce the problem to two separate fractional ODEs. The generalized solution is constructed/formed in the form of a Fourier series with respect to the eigenfunctions of a certain eigenvalue problem. In order to obtain the coefficients of the Fourier series for the solution, we define a new inner product which is the key point of study.

Wavelet transform based noise removal from ECG signal for accurate heart rate detection using ECG

Use of wavelet transform for the analysis of bioelectric signals has gained momentum and effective results have been obtained through this method. In this study, we have applied the wavelet analysis to the electrocardiogram (ECG) signal for the better detection of heart rate. Wavelet analysis is used for the elimination of baseline wandering and elimination of the highfrequency noise. Heart rate detection is performed on this final signal through simple R peak determination. The data used in this study is taken from the MIT-BIH arrhythmia database which is chosen because of the labelled the R-peaks of the QRS complexes. When the raw data were analyzed for the R -peaks, detection average rate of R peaks was 94.87%. In the algorithm, the ECG signal was first decomposed up to 4th level through wavelet analysis. The fourth level approximation coefficient was subtracted from the ECG signal to eliminate the baseline wandering. The new signal was again passed through wavelet packet filters up to 2nd level. The detail coefficient at the 2nd level was subtracted from this signal for the elimination of high frequency noise. For the Daubechies 4 (db4), Daubechies 10 (db10) and Coiflet 4 (coif4) wavelet families, average detection rate of R peaks exceeded 99%. Selection of db10 for the wavelet filters in the algorithm gave the best results with detection rate of 99.76%.

A correction for computing matrix-valued Nevanlinna-Pick interpolation problem

The Nevanlinna-Pick interpolation theorems and their matrix generalizations have proved to be very useful in solving engineering problems, in particular, in circuit theory [7] and for control theory problems involving an H∞ - criterion. This development led to a new field of research, in which the emphasis is on interpolants that are rational matrix functions and on the search for explicit formulas and efficient algorithms for the construction of interpolants in a form which is suitable for engineering applications. In 1994, Chen and Koc developed an algorithm based on Delsarte et als paper to solve this problem in the unit disc[5]. The Proposed algorithm in [5] has a mathematical mistake at the formulation stage. In this study this was pointed out. An application of the algorithm for some data is included as well.

An image denoising application using shearlets

Medical imaging is a multidisciplinary field related to computer science, electrical/electronic engineering, physics, mathematics and medicine. There has been dramatic increase in variety, availability and resolution of medical imaging devices for the last half century. For proper medical imaging highly trained technicians and clinicians are needed to pull out clinically pertinent information from medical data correctly. Artificial systems must be designed to analyze medical data sets either in a partially or even a fully automatic manner to fulfil the need. For this purpose there has been numerous ongoing research for finding optimal representations in image processing and computer vision [1, 18]. Medical images almost always contain artefacts and it is crucial to remove these artefacts to obtain healthy results. Out of many methods for denoising images, in this paper, two denoising methods, wavelets and shearlets, have been applied to mammography images. Comparing these two methods, shearlets give bette...

On analysis of electroencephalogram by multiresolution-based energetic approach

Epilepsy is a common brain disorder where the normal neuronal activity gets affected. Electroencephalography (EEG) is the recording of electrical activity along the scalp produced by the firing of neurons within the brain. The main application of EEG is in the case of epilepsy. On a standard EEG some abnormalities indicate epileptic activity. EEG signals like many biomedical signals are highly non-stationary by their nature. For the investigation of biomedical signals, in particular EEG signals, wavelet analysis have found prominent position in the study for their ability to analyze such signals. Wavelet transform is capable of separating the signal energy among different frequency scales and a good compromise between temporal and frequency resolution is obtained. The present study is an attempt for better understanding of the mechanism causing the epileptic disorder and accurate prediction of occurrence of seizures. In the present paper following Magossos work [12], we identify typical patterns of energ...