Image filtering techniques have numerous potential applications in biomedical imaging and image processing. The design of filters largely depends on the a priori, knowledge about the type of noise corrupting the image. This makes the standard filters application specific. Widely used filters such as average, Gaussian, and Wiener reduce noisy artifacts by smoothing. However, this operation normally results in smoothing of the edges as well. On the other hand, sharpening filters enhance the high-frequency details, making the image nonsmooth. An integrated general approach to design a finite impulse response filter based on Hebbian learning is proposed for optimal image filtering. This algorithm exploits the interpixel correlation by updating the filter coefficients using Hebbian learning. The algorithm is made iterative for achieving efficient learning from the neighborhood pixels. This algorithm performs optimal smoothing of the noisy image by preserving high-frequency as well as low-frequency features. Evaluation results show that the proposed finite impulse response filter is robust under various noise distributions such as Gaussian noise, salt-and-pepper noise, and speckle noise. Furthermore, the proposed approach does not require any a priori knowledge about the type of noise. The number of unknown parameters is few, and most of these parameters are adaptively obtained from the processed image. The proposed filter is successfully applied for image reconstruction in a positron emission tomography imaging modality. The images reconstructed by the proposed algorithm are found to be superior in quality compared with those reconstructed by existing PET image reconstruction methodologies.
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