The Use of Features Extracted from Noisy Samples for Image Restoration Purposes

An important feature of neural networks is the ability they have to learn from their environment, and, through learning to improve performance in some sense. In the following we restrict the development to the problem of feature extracting unsupervised neural networks derived on the base of the biologically motivated Hebbian self-organizing principle which is conjectured to govern the natural neural assemblies and the classical principal component analysis (PCA) method used by statisticians for almost a century for multivariate data analysis and feature extraction. The research work reported in the paper aims to propose a new image reconstruction method based on the features extracted from the noise given by the principal components of the noise covariance matrix.feature extraction, PCA, Generalized Hebbian Algorithm, image restoration, wavelet transform, multiresolution support set

Sequences and series involving the sequence of composite numbers

Denoting by pn and cn the nth prime number and the nth composite number, respectively, we prove that both the sequence (xn)n≥1, defined by xn=∑k=1n (ck+1−ck) / k−pn / n, and the series ∑n=1∞ (pcn−cpn) / npn are convergent

Denoising Techniques Based on the Multiresolution Representation

So far, considerable research efforts have been invested in the are of using statistical methods for image processing purposes yielding to a significant amount of models that aim to improve as much as possible the still existing and currently used processing techniques, some of them being based on using wavelet representation of images. Among them the simplest and the most attractive one use the Gaussian assumption about the distribution of the wavelet coefficients. This model has been successfully used in image denoising and restoration. The limitation comes from the fact that only the first-order statistics of wavelet coefficients are taking into account and the higher-order ones are ignored. The dependencies between wavelet coefficients can be formulated explicitly, or implicitly. The multiresolution representation is used to develop a class of algorithms for noise removal in case of normal models. The multiresolution algorithms perform the restoration tasks by combining, at each resolution level, according to a certain rule, the pixels of a binary support image. The values of the support image pixels are either 1 or 0 depending on their significance degree. At each resolution level, the contiguous areas of the support image corresponding to 1-value pixels are taken as possible objects of the image. Our work reports two attempts in using the multiresolution based algorithms for restoration purposes in case of normally distributed noise. Several results obtained using our new restoration algorithm are presented in the final sections of the paper.multiresolution support, wavelet transform, filtering techniques, statistically significant wavelet coefficients

Enhancing Cognitive Performance and Monitoring through a Mobile App: Insights from the Rodi Study

The prevalence of neurocognitive disorders has led to increased interest in mobile health applications (mHealth apps) for detection and training. However, there’s a need for apps that integrate comprehensive cognitive training, assessment, and monitoring in personalized contexts. The RODI app was meticulously developed with the objective of catering to individuals with deficits as well as healthy adults. In this study, 11 participants without diagnosed impairments used the app twice weekly for eight weeks. Results show a consistent enhancement in cognitive performance within the app over time. Notably, a discernible divergence is observed, with the rate of improvement appearing to be comparatively slower in the younger age group in contrast to their older counterparts. Furthermore, the study assesses the reliability of the application using the intraclass correlation coefficient (ICC), confirming its consistent performance across repeated administrations. Finally, the app’s capacity to monitor participants’ cognitive status across various domains is investigated, unveiling controlled variations that indicate foreseeable outcomes within defined parameters. These findings underscore RODI’s potential for cognitive enhancement and monitoring, offering insights into user needs and the broader significance of mobile app interventions for cognitive well-being and future research in this field