Browsing by Author "Koç, A."

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Open Access
Efficient computation of quadratic-phase integrals in optics
(Optical Society of America, 2006) Özaktaş, H. M.; Koç, A.; Sarı, I.; Kutay, M. A.
Received June 29, 2005; revised manuscript received August 22, 2005; accepted September 12, 2005 We present a fast N log N time algorithm for computing quadratic-phase integrals. This three-parameter class of integrals models propagation in free space in the Fresnel approximation, passage through thin lenses, and propagation in quadratic graded-index media as well as any combination of any number of these and is therefore of importance in optics. By carefully managing the sampling rate, one need not choose N much larger than the space–bandwidth product of the signals, despite the highly oscillatory integral kernel. The only deviation from exactness arises from the approximation of a continuous Fourier transform with the discrete Fourier transform. Thus the algorithm computes quadratic-phase integrals with a performance similar to that of the fast-Fourier-transform algorithm in computing the Fourier transform, in terms of both speed and accuracy. © 2006 Optical Society of America
Open Access
Fast algorithms for digital computation of linear canonical transforms
(Springer, New York, 2016) Koç, A.; Oktem, F. S.; Özaktaş, Haldun M.; Kutay, M. A.; Healy, J. J.; Kutay, M. A.; Özaktaş, Haldun M.; Sheridan, J. T.
Fast and accurate algorithms for digital computation of linear canonical transforms (LCTs) are discussed. Direct numerical integration takes O.N2/ time, where N is the number of samples. Designing fast and accurate algorithms that take O.N logN/ time is of importance for practical utilization of LCTs. There are several approaches to designing fast algorithms. One approach is to decompose an arbitrary LCT into blocks, all of which have fast implementations, thus obtaining an overall fast algorithm. Another approach is to define a discrete LCT (DLCT), based on which a fast LCT (FLCT) is derived to efficiently compute LCTs. This strategy is similar to that employed for the Fourier transform, where one defines the discrete Fourier transform (DFT), which is then computed with the fast Fourier transform (FFT). A third, hybrid approach involves a DLCT but employs a decomposition-based method to compute it. Algorithms for two-dimensional and complex parametered LCTs are also discussed.
Open Access
Fast and accurate algorithms for quadratic phase integrals in optics and signal processing
(SPIE, 2011) Koç, A.; Özaktaş, Haldun M.; Hesselink L.
The class of two-dimensional non-separable linear canonical transforms is the most general family of linear canonical transforms, which are important in both signal/image processing and optics. Application areas include noise filtering, image encryption, design and analysis of ABCD systems, etc. To facilitate these applications, one need to obtain a digital computation method and a fast algorithm to calculate the input-output relationships of these transforms. We derive an algorithm of NlogN time, N being the space-bandwidth product. The algorithm controls the space-bandwidth products, to achieve information theoretically sufficient, but not redundant, sampling required for the reconstruction of the underlying continuous functions. © 2011 SPIE.
Open Access
Fast and accurate linear canonical transform algorithms
(IEEE, 2015) Özaktaş, Haldun M.; Koç, A.
Linear canonical transforms are encountered in many areas of science and engineering. Important transformations such as the fractional Fourier transform and the ordinary Fourier transform are special cases of this transform family. This family of transforms is especially important for the modelling of wave propagation. It has many applications such as noise removal, image encryption, and analysis of optical systems. Here we discuss algorithms for fast and accurate computation of these transforms. These algorithms can achieve the same accuracy and speed as fast Fourier transform algorithms, so that they can be viewed as optimal algorithms. Efficient sampling of signals plays an important part in the development of these algorithms.
Open Access
Generating semantic similarity atlas for natural languages
(IEEE, 2018-12) Şenel, Lütfi Kerem; Utlu, İhsan; Yücesoy, V.; Koç, A.; Çukur, Tolga
Cross-lingual studies attract a growing interest in natural language processing (NLP) research, and several studies showed that similar languages are more advantageous to work with than fundamentally different languages in transferring knowledge. Different similarity measures for the languages are proposed by researchers from different domains. However, a similarity measure focusing on semantic structures of languages can be useful for selecting pairs or groups of languages to work with, especially for the tasks requiring semantic knowledge such as sentiment analysis or word sense disambiguation. For this purpose, in this work, we leverage a recently proposed word embedding based method to generate a language similarity atlas for 76 different languages around the world. This atlas can help researchers select similar language pairs or groups in cross-lingual applications. Our findings suggest that semantic similarity between two languages is strongly correlated with the geographic proximity of the countries in which they are used.
Open Access
Learning traffic congestion by contextual bandit problems for optimum localization
(IEEE, 2017) Şahin, Ümitcan; Yücesoy, V.; Koç, A.; Tekin, Cem
Optimum localization problem, which has a wide range of application areas in real life such as emergency services, command and control systems, warehouse localization, shipment planning, aims to find the best location to minimize the arrival, response or return time which might be vital in some applications. In most of the cases, uncertainty in traffic is the most challenging issue and in the literature generally it is assumed to obey a priori known stochastic distribution. In this study, problem is defined as the optimum localization of ambulances for emergency services and traffic is modeled to be Markovian to generate context data. Unlike the solution methods in the literature, there exists no mutual information transfer between the model and solution of the problem; thus, a contextual multi-armed bandit learner tries to determine the underlying traffic with simple assumptions. The performance of the bandit algorithm is compared with the performance of a classical estimation method in order to show the effectiveness of the learning approach on the solution of the optimum localization problem.
Open Access
Measuring cross-lingual semantic similarity across European languages
(IEEE, 2017) Şenel, Lütfü Kerem; Yücesoy, V.; Koç, A.; Çukur, Tolga
This paper studies cross-lingual semantic similarity (CLSS) between five European languages (i.e. English, French, German, Spanish and Italian) via unsupervised word embeddings from a cross-lingual lexicon. The vocabulary in each language is projected onto a separate high-dimensional vector space, and these vector spaces are then compared using several different distance measures (i.e., correlation, cosine etc.) to measure their pairwise semantic similarities between these languages. A substantial degree of similarity is observed between the vector spaces learned from corpora of the European languages. Null hypothesis testing and bootstrap methods (by resampling without replacement) are utilized to verify the results.
Open Access
Resolution enhancement of wide-field interferometric microscopy by coupled deep autoencoders
(OSA - The Optical Society, 2018) Işıl, Ç.; Yorulmaz, M.; Solmaz, B.; Turhan, Adil Burak; Yurdakul, C.; Ünlü, S.; Özbay, Ekmel; Koç, A.
Wide-field interferometric microscopy is a highly sensitive, label-free, and low-cost biosensing imaging technique capable of visualizing individual biological nanoparticles such as viral pathogens and exosomes. However, further resolution enhancement is necessary to increase detection and classification accuracy of subdiffraction-limited nanoparticles. In this study, we propose a deep-learning approach, based on coupled deep autoencoders, to improve resolution of images of L-shaped nanostructures. During training, our method utilizes microscope image patches and their corresponding manual truth image patches in order to learn the transformation between them. Following training, the designed network reconstructs denoised and resolution-enhanced image patches for unseen input.
Open Access
Semantic similarity between Turkish and European languages using word embeddings
(IEEE, 2017) Şenel, Lütfü Kerem; Yücesoy, V.; Koç, A.; Çukur, Tolga
Representation of words coming from vocabulary of a language as real vectors in a high dimensional space is called as word embeddings. Word embeddings are proven to be successful in modelling semantic relations between words and numerous natural language processing applications. Although developed mainly for English, word embeddings perform well for many other languages. In this study, semantic similarity between Turkish (two different corpora) and five basic European languages (English, German, French, Spanish, Italian) is calculated using word embeddings over a fixed vocabulary, obtained results are verified using statistical testing. Also, the effect of using different corpora, and additional preprocess steps on the performance of word embeddings on similarity and analogy test sets prepared for Turkish is studied.