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Blind inpainting algorithms based on deep learning architectures have shown a remarkable performance in recent years, typically outperforming model-based methods both in terms of image quality and run time. However, neural network strategies typically lack a theoretical explanation, which contrasts with the well-understood theory underlying model-based methods. In this work, we leverage the advantages of both approaches by integrating theoretically founded concepts from transform domain methods and sparse approximations into a CNN-based approach for blind image inpainting. To this end, we present a novel strategy to learn convolutional kernels that applies a specifically designed filter dictionary whose elements are linearly combined with trainable weights. Numerical experiments demonstrate the competitiveness of this approach. Our results show not only an improved inpainting quality compared to conventional CNNs but also significantly faster network convergence within a lightweight network design. Our code is available at https://github.com/cv-stuttgart/SDPF_Blind-Inpainting. 

The axon initial segment (AIS) is a highly regulated subcellular domain required for neuronal firing. Changes in the AIS protein composition and distribution are a form of structural plasticity, which powerfully regulates neuronal activity and may underlie several neuropsychiatric and neurodegenerative disorders. Despite its physiological and pathophysiological relevance, the signaling pathways mediating AIS protein distribution are still poorly studied. Here, we used confocal imaging and whole-cell patch clamp electrophysiology in primary hippocampal neurons to study how AIS protein composition and neuronal firing varied in response to selected kinase inhibitors targeting the AKT/GSK3 pathway, which has previously been shown to phosphorylate AIS proteins. Image-based features representing the cellular pattern distribution of the voltage-gated Na+ (Nav) channel, ankyrin G, βIV spectrin, and the cell-adhesion molecule neurofascin were analyzed, revealing βIV spectrin as the most sensitive AIS protein to AKT/GSK3 pathway inhibition. Within this pathway, inhibition of AKT by triciribine has the greatest effect on βIV spectrin localization to the AIS and its subcellular distribution within neurons, a phenotype that Support Vector Machine classification was able to accurately distinguish from control. Treatment with triciribine also resulted in increased excitability in primary hippocampal neurons. Thus, perturbations to signaling mechanisms within the AKT pathway contribute to changes in βIV spectrin distribution and neuronal firing that may be associated with neuropsychiatric and neurodegenerative disorders. 

Abstract We present a new method for the stable reconstruction of a class of binary images from a small number of measurements. The images we consider are characteristic functions of algebraic domains, that is, domains defined as zero loci of bivariate polynomials, and we assume to know only a finite set of uniform samples for each image. The solution to such a problem can be set up in terms of linear equations associated to a set of image moments. However, the sensitivity of the moments to noise makes the numerical solution highly unstable. To derive a robust image recovery algorithm, we represent algebraic polynomials and the corresponding image moments in terms of bivariate Bernstein polynomials and apply polynomial-generating, refinable sampling kernels. This approach is robust to noise, computationally fast and simple to implement. We illustrate the performance of our reconstruction algorithm from noisy samples through extensive numerical experiments. Our code is released open source and freely available. 

Water turbidity is a frequent impediment for achieving satisfactory imaging clarity in underwater video and inhibits the extraction of information concerning the condition of submerged structures. Ports, rivers, lakes, and inland waterways are notoriously difficult spots for camera inspections, in particular for hull inspections in lieu of dry-docking. This complex problem motivated us to study methods to extract a cleaner image /video footage from the acquired one. The purpose of this paper is to describe a novel mathematical model for the degradation of images due to underwater turbidity caused by suspended silt particulates and algae organisms and to propose methods to improve image and video clarity using multiscale non-linear transforms.