We propose tabular two-dimensional correlation analysis for extracting features from multifaceted characterization data, essential for understanding material properties. This method visualizes similarities and phase lags in structural parameter changes through heatmaps, combining hierarchical clustering and asynchronous correlations. We applied the proposed method to datasets of carbon nanotube (CNTs) films annealed at various temperatures and revealed the complexity of their hierarchical structures, which include elements like voids, bundles, and amorphous carbon. Our analysis addresses the challenge of attempting to understand the sequence of structural changes, especially in multifaceted characterization data where 11 structural parameters derived from 8 characterization methods interact with complex behavior. The results show how phase lags (asynchronous changes from stimuli) and parameter similarities can illuminate the sequence of structural changes in materials, providing insights into phenomena like the removal of amorphous carbon and graphitization in annealed CNTs. This approach is beneficial even with limited data and holds promise for a wide range of material analyses, demonstrating its potential in elucidating complex material behaviors and properties.

A screenshot of Neurogrow, which tests a patient's memory and reaction time as an experimental treatment for cognitive decline. A screenshot of Neurogrow, which tests a patient's memory and reaction time as an experimental treatment for cognitive decline. The neurologist said Pam Stevens' cognitive impairment couldn't be treated. She and her husband, Pete Stevens, were told to give up hope. "On two separate occasions, over a two-year period, the neurologist said there was nothing we could do," said Pete Stevens.

Deep neural networks, in particular generative adversarial networks by [Goodfellow et al., 2014] have been recently used to produce generative models for real world data that can capture very complex structures. This is especially true for natural images (see for instance [Nguyen et al., 2016]). Those generative priors have been successfully used to efficiently solve classical inverse problems in signal processing, like super resolution ([Johnson et al., 2016]) and compressed sensing ([Bora et al., 2017]). The latter numerically demonstrates that the generative prior can be exploited to solve the compressed sensing problem with ten times fewer measurements than the classic compressed sensing theory requires. Followup work by [Hand and Voroninski, 2017] recently explained the success of local methods (namely empirical risk minimization) in the compressed sensing task by assuming a generative model of a multi-layer neural network with random weights and ReLU activation functions. The aim of this paper is to propose a theoretical framework that will allow us to analyze neural networks in the context of another classical inverse problem in signal processing: signal denoising.