Matematik Mühendisliği

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http://hdl.handle.net/11527/18049

Gözat

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  • Öge
    A novel image denoising technique with Caputo type space–time fractional operators
    (Springer, 2024) Tanrıöver, Evren ; Kiriş, Ahmet ; Tunga, Burcu ; Tunga, M. Alper ; 0000-0003-4098-3155 ; 0000-0002-3687-6640 ; 0000-0001-7318-964X ; 0000-0003-3551-4549 ; Matematik Mühendisliği
    A novel image denoising model, namely Full Fractional Total Variation (TVFF), based on the Rudin-Osher-Fatemi (ROF) and the fractional total variation models is presented. The leading advantage of TVFF model is that it uses fractional derivatives with length scale parameters instead of ordinary derivatives with respect to both time and spatial variables in the diffusion equation. The Riesz–Caputo fractional derivative operator is used to disperse nonlocal influence throughout all directions, whereas the Caputo fractional derivative concept is employed for time fractional derivatives. Therefore, the influence of neighboring pixels is given greater weight compared to those situated farther away and this reflects the consideration behind denoising process better. Moreover, the numerical approach is constructed, and its stability and convergence properties are thoroughly examined. To show the superiority of our model, the denoised images are subjected to visual and numerical comparisons using metrics such as the Signal-to-Noise Ratio (SNR), the Structural Similarity Index Measure (SSIM) and the Edge-Retention Ratio (ERR). The performance of the TVFF method is evaluated under various types of noise, including Poisson, Speckle, and Salt & Pepper, and the results are compared with those obtained using Gauss and Median Filters. Furthermore, the proposed method is applied to both blind and synthetic images, thereby showcasing its versatility and applicability across diverse datasets. The outcomes showcase the substantial potential of our enhanced model as a versatile and efficient tool for image denoising.
  • Öge
    Machine learning based tomographic image reconstruction technique to detect hollows in wood
    (Springer, 2024) Yıldızcan, Ecem Nur ; Arı, Mehmet Erdi ; Tunga, Burcu ; Gelir, Ali ; Kurul, Fatih ; As, Nusret ; Dündar, Türker ; 0000-0001-6511-5587 ; 0000-0001-7659-6742 ; 0000-0001-7318-964X ; 0000-0001-6534-2253 ; Matematik Mühendisliği
    A new technique based on machine learning algorithms was introduced to detect internal wood defects. This technique relies on analyzing segmented propagation rays of stress waves and successfully generates the tomographic images of the defects by using the stress wave velocity. Utilizing a dual-stage methodology, the initial phase involves ray segmentation for the precise delineation of stress wave propagation, while the subsequent stage integrates advanced classification and clustering algorithms to facilitate the generation of tomographic images. This approach effectively tackles the inherent challenges associated with accurate segmentation and classification of stress wave velocity rays. The effectiveness of the proposed method was evaluated using both synthetic and experimental data. The results showed that the proposed method, when compared with some state-of-the-art methods, has a superior ability to accurately detect defective regions in the wood. The success of the proposed method is evaluated with four different evaluation metrics. It determined that over 90% success is achieved for all metrics. In comparison with related studies, it determined that the results are improved by 7–22% compared to the literature.