Suppression of ringing artifacts in images is a well-known image restoration problem. Gibbs-ringing artifacts occur when, in the process of magnetic resonance imaging, the source data from the frequency domain are mapped onto the spatial domain by using the discrete Fourier transform. The artifacts are caused by the incompleteness of these data, which, in turn, is due to cutting off the high frequencies of the Fourier spectrum. In this paper, we propose a hybrid method for Gibbs-ringing artifact suppression in magnetic resonance images that combines a deep learning model and a classical non-machine-learning algorithm for Gibbs-ringing artifact suppression based on optimal subvoxel shifts.

A way to improve the quality of magnetic resonance image processing using the Kolmogorov–Arnold networks for deep feature filtering in the convolutional neural network is studied. Recently proposed Kolmogorov–Arnold networks are inspired by the representation theorem of the same name from real analysis and approximation theory. It states that every multivariate continuous function on a compact set can be represented as a superposition of continuous single-variable functions. However, the need to use gradient descent while training the network imposes restrictions on the parameterization of such single-variable functions—they must be at least differentiable; for this reason, in practice, they are searched in a linear span of B‑Splines or some other differentiable basis functions. In this study, we propose an adaptive method for the selection of basis functions by the model itself during training thus mitigating the rule of thumb choice of the basis functions. The method is based on the self-attention mechanism successfully used in state-of-the-art transformer networks. The proposed approach is tested on magnetic resonance image enhancement for images taken from IXI dataset; and it demonstrates better average PSNR and TV values over the synthetic testing dataset. Without loss of generality, the system of basis functions included B-splines, Chebyshev polynomials and Hermite functions.

Gibbs-ringing artifact is a common artifact in medical image processing. It is usually caused by image enhancement procedures, like image deblurring, or physically caused in magnetic resonance imaging (MRI), where the k-space is a finite sampling of underlying signals. Under-sampling in Fourier space is often employed to reduce imaging time for real-time applications. In addition, ringing effect is regularly accompanied by noise boosting due to a low-grade sensor, resulting in lowering image quality to a large extent. In this work we propose hybrid approach for suppressing the stated artifacts, which utilizes recently proposed deep learning Fourier Neural Operator over the classical solvers: Perona-Malik diffusion and Kellner algorithm.

Gibbs-ringing artifact is a common artifact in MRI image processing. As MRI raw data is taken in a frequency domain, 2D in- verse discrete Fourier transform is applied to visualize data. Inability to take inverse Fourier transform of full spectrum (full k-space) leads to the insufficient sampling of the high frequency data and results in a well-known Gibbs phenomenon. It is worth to notice that truncation of high frequency information generates a significant blur, thus some techniques from other image restoration problems (for example, image deblur task) can be successfully used. We propose attention-based convolutional neural network for Gibbs-ringing reduction which is the extension of recently proposed GAS-CNN (Gibbs-ringing Artifact Suppression Convolutional Neural Network). Proposed method includes simplified non-linear mapping, amended by LRNN (Layer Recurrent Neural Network) refinement block with feature attention module, controlling the correlation between input and output tensors of the refinement unit. The research shows that the proposed post-processing refinement construction considerably simplifies the non-linear mapping.

The paper deals with problem of optimal input scale search for deep classification neural networks. It is shown that state-of-the-art deep neural networks are not stable to input image scale, leading to quality degradation. The paper demonstrates relevance of the topic on classical image classification DL-pipeline. Unlike previous researchers, who aim to build entire complex invariant neural nets, we claim that computing optimal input transformations (e.g. scale) is a more perspective way for successful neural networks real-life applications. Thus, a new scale search algorithm for DL image classification is proposed in the paper, based on empirical hierarchical analysis of activation values.

Preparation of input data for an artificial neural network is a key step to achieve a high accuracy of its predictions. It is well known that convolutional neural models have low invariance to changes in the scale of input data. For instance, processing multiscale whole-slide histological images by convolutional neural networks naturally poses a problem of choosing an optimal processing scale. In this paper, this problem is solved by iterative analysis of distances to a separating hyperplane that are generated by a convolutional classifier at different input scales. The proposed method is tested on the DenseNet121 deep architecture pre-trained on PATH-DT-MSU data, which implements patch classification of whole-slide histological images.