Bilgisayar Mühendisliği Bölümü Yayın Koleksiyonu
https://hdl.handle.net/11494/296
2024-03-28T12:35:49ZA parameter-uniform weak Galerkin finite element method for a coupled system of singularly perturbed reaction-diffusion equations
https://hdl.handle.net/11494/4868
A parameter-uniform weak Galerkin finite element method for a coupled system of singularly perturbed reaction-diffusion equations
Toprakseven, Şuayip; Zhu, Peng
The aim of this paper to investigate a weak Galerkin finite element method (WG-FEM) for
solving a system of coupled singularly perturbed reaction-diffusion equations. Each equation in the system
has perturbation parameter of different magnitude and thus, the solutions will exhibit two distinct but
overlapping boundary layers near each boundary of the domain. The proposed method is applied to the
coupled system on Shishkin mesh to solve the problem theoretically and numerically. Elimination of the
interior unknowns efficiently from the discrete solution system reduces the degrees of freedom and, thus
the number of unknown in the discrete solution is comparable with the standard finite element scheme. The
stability and error analysis of the proposed method on the Shishkin mesh are presented. We show that the
method convergences of order O(N−k
lnk N) in the energy norm, uniformly with respect to the perturbation
parameter. Moreover, the optimal convergence rate of O(N−(k+1)) in the L
2
-norm and the superconvergence
rate of O((N−2k
ln2k N) in the discrete L
∞-norm is observed numerically. Finally, some numerical experiments
are carried out to verify numerically theory.
2023-01-01T00:00:00Z3D-CNN and autoencoder-based gas detection in hyperspectral images
https://hdl.handle.net/11494/4719
3D-CNN and autoencoder-based gas detection in hyperspectral images
Özdemir, Okan Bilge; Koz, Alper
The detection of gas emission levels is a crucial problem for ecology and human health. Hyperspectral image analysis offers many advantages over traditional gas detection systems with its detection capability from safe distances. Observing that the existing hyperspectral gas detection methods in the thermal range neglect the fact that the captured radiance in the longwave infrared (LWIR) spectrum is better modeled as a mixture of the radiance of background and target gases, we propose a deep learning-based hyperspectral gas detection method in this article, which combines unmixing and classification. The proposed method first converts the radiance data to luminance-temperature data. Then, a 3-D convolutional neural network (CNN) and autoencoder-based network, which is specially designed for unmixing, is applied to the resulting data to acquire abundances and endmembers for each pixel. Finally, the detection is achieved by a three-layer fully connected network to detect the target gases at each pixel based on the extracted endmember spectra and abundance values. The superior performance of the proposed method with respect to the conventional hyperspectral gas detection methods using spectral angle mapper and adaptive cosine estimator is verified with LWIR hyperspectral images including methane and sulfur dioxide gases. In addition, the ablation study with respect to different combinations of the proposed structure including direct classification and unmixing methods has revealed the contribution of the proposed system.
2023-01-01T00:00:00ZUphill resampling for particle filter and its implementation on graphics processing unit
https://hdl.handle.net/11494/4706
Uphill resampling for particle filter and its implementation on graphics processing unit
Dülger, Özcan; Oğuztüzün, Halit; Demirekler, Mübeccel
We introduce a new resampling method, named Uphill, that is free from numerical instability and suitable for
parallel implementation on graphics processing unit (GPU). Common resampling algorithms such as Systematic
suffer from numerical instability when single precision floating point numbers are used. This is due to
cumulative summation over the weights of particles when the weights differ widely or the number of particles is
large. The Metropolis and Rejection resampling algorithms do not suffer from numerical instability as they only
calculate the ratios of weights pairwise rather than perform collective operations over the weights. They are
more suitable for the GPU implementation of the particle filter. However, they undergo non-coalesced global
memory access patterns which cause their speed deteriorate rapidly as the number of particles gets large. Uphill
also does not suffer from numerical instability but, experiences the same non-coalesced global memory access
problem with Metropolis and Rejection. We introduce its faster version named Uphill-Fast which eliminates
this problem. We make comparisons of Uphill and Uphill-Fast with the Systematic, Metropolis, Metropolis-C2
and Rejection resampling methods with respect to quality and speed. We also compare them on a highly
non-linear system. Uphill-Fast runs faster and attains similar quality, in terms of RMSE, in comparison with
Metropolis and Rejection when the number of particles is very large. Uphill-Fast runs with roughly same speed
as Metropolis-C2 with better variance and MSE when the number of particles is very large.
2023-01-01T00:00:00ZDeepSR: a deep learning tool for image super resolution
https://hdl.handle.net/11494/4607
DeepSR: a deep learning tool for image super resolution
Temiz, Hakan
An open source tool is introduced that provides a versatile environment to meet the needs of re-
searchers in developing deep learning (DL) algorithms for single image super-resolution reconstruction
(SISR). The processes of SISR were carefully studied, unified and integrated to create software that can
be used by the community for any type of imaging method such as aerial, medical, optical, etc. DeepSR
allows easy implementation of SISR application with rapidly prototyped DL models, and detailed
reporting and recording of the results. The entire experiment can be done with simple command
line scripts. It can be easily extended by user-defined metrics, augmentations, callbacks, etc.
2023-01-01T00:00:00Z