Browsing by Subject "Convolution"

Now showing 1 - 7 of 7

Open Access
A transformer-based real-time focus detection technique for wide-field interferometric microscopy
(IEEE - Institute of Electrical and Electronics Engineers, 2023-08-28) Polat, Can; Güngör, A.; Yorulmaz, M.; Kızılelma, B.; Çukur, Tolga
Wide-field interferometric microscopy (WIM) has been utilized for visualization of individual biological nanoparticles with high sensitivity. However, the image quality is highly affected by the focusing of the image. Hence, focus detection has been an active research field within the scope of imaging and microscopy. To tackle this issue, we propose a novel convolution and transformer based deep learning technique to detect focus in WIM. The method is compared to other focus detecton techniques and is able to obtain higher precision with less number of parameters. Furthermore, the model achieves real-time focus detection thanks to its low inference time.
Open Access
Convexity in source separation: Models, geometry, and algorithms
(Institute of Electrical and Electronics Engineers Inc., 2014) McCoy, M. B.; Cevher, V.; Dinh, Q. T.; Asaei, A.; Baldassarre, L.
Source separation, or demixing, is the process of extracting multiple components entangled within a signal. Contemporary signal processing presents a host of difficult source separation problems, from interference cancellation to background subtraction, blind deconvolution, and even dictionary learning. Despite the recent progress in each of these applications, advances in high-throughput sensor technology place demixing algorithms under pressure to accommodate extremely high-dimensional signals, separate an ever larger number of sources, and cope with more sophisticated signal and mixing models. These difficulties are exacerbated by the need for real-time action in automated decision-making systems. © 1991-2012 IEEE.
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
Fractional free space, fractional lenses, and fractional imaging systems
(OSA - The Optical Society, 2003) Sümbül, U.; Özaktaş, Haldun M.
Continuum extensions of common dual pairs of operators are presented and consolidated, based on the fractional Fourier transform. In particular, the fractional chirp multiplication, fractional chirp convolution, and fractional scaling operators are defined and expressed in terms of their common nonfractional special cases, revealing precisely how they are interpolations of their conventional counterparts. Optical realizations of these operators are possible with use of common physical components. These three operators can be interpreted as fractional lenses, fractional free space, and fractional imaging systems, respectively. Any optical system consisting of an arbitrary concatenation of sections of free space and thin lenses can be interpreted as a fractional imaging system with spherical reference surfaces. As a special case, a system departing from the classical single-lens imaging condition can be interpreted as a fractional imaging system. © 2003 Optical Society of America.
Open Access
On possible deterioration of smoothness under the operation of convolution
(1996) Uludağ, A. Muhammed
We show that the convolution of two probability densities which are restrictions to R of entire functions can possess infinite essential supremuin on each interval. We also present several sufficient conditions of deterioration of smoothness under the operation of convolution.
Open Access
Optimal filtering in fractional Fourier domains
(Institute of Electrical and Electronics Engineers, 1997-05) Kutay, M. A.; Özaktaş, Haldun M.; Arıkan, Orhan
For time-invariant degradation models and stationary signals and noise, the classical Fourier domain Wiener filter, which can be implemented in O(N log N) time, gives the minimum mean-square-error estimate of the original undistorted signal. For time-varying degradations and nonstationary processes, however, the optimal linear estimate requires O(N/sup 2/) time for implementation. We consider filtering in fractional Fourier domains, which enables significant reduction of the error compared with ordinary Fourier domain filtering for certain types of degradation and noise (especially of chirped nature), while requiring only O(N log N) implementation time. Thus, improved performance is achieved at no additional cost. Expressions for the optimal filter functions in fractional domains are derived, and several illustrative examples are given in which significant reduction of the error (by a factor of 50) is obtained.
Open Access
Structured least squares problems and robust estimators
(IEEE, 2010-10-22) Pilanci, M.; Arıkan, Orhan; Pinar, M. C.
A novel approach is proposed to provide robust and accurate estimates for linear regression problems when both the measurement vector and the coefficient matrix are structured and subject to errors or uncertainty. A new analytic formulation is developed in terms of the gradient flow of the residual norm to analyze and provide estimates to the regression. The presented analysis enables us to establish theoretical performance guarantees to compare with existing methods and also offers a criterion to choose the regularization parameter autonomously. Theoretical results and simulations in applications such as blind identification, multiple frequency estimation and deconvolution show that the proposed technique outperforms alternative methods in mean-squared error for a significant range of signal-to-noise ratio values.