Bilevel Parameter Learning for Higher-Order Total Variation Regularisation Models.

We consider a bilevel optimisation approach for parameter learning in higher-order total variation image reconstruction models. Apart from the least squares cost functional, naturally used in bilevel learning, we propose and analyse an alternative cost based on a Huber-regularised TV seminorm. Differentiability properties of the solution operator are verified and a first-order optimality system is derived. Based on the adjoint information, a combined quasi-Newton/semismooth Newton algorithm is proposed for the numerical solution of the bilevel problems. Numerical experiments are carried out to show the suitability of our approach and the improved performance of the new cost functional. Thanks to the bilevel optimisation framework, also a detailed comparison between TGV 2 and ICTV is carried out, showing the advantages and shortcomings of both regularisers, depending on the structure of the processed images and their noise level.King Abdullah University of Science and Technology (KAUST) (Grant ID: KUKI1-007-43), Engineering and Physical Sciences Research Council (Grant IDs: Nr. EP/J009539/1 “Sparse & Higher-order Image Restoration” and Nr. EP/M00483X/1 “Efficient computational tools for inverse imaging problems”), Escuela Politécnica Nacional de Quito (Grant ID: PIS 12-14, MATHAmSud project SOCDE “Sparse Optimal Control of Differential Equations”), Leverhulme Trust (project on “Breaking the non-convexity barrier”), SENESCYT (Ecuadorian Ministry of Higher Education, Science, Technology and Innovation) (Prometeo Fellowship)This is the final version of the article. It first appeared from Springer via http://dx.doi.org/10.1007/s10851-016-0662-

Dynamic sampling schemes for optimal noise learning under multiple nonsmooth constraints

We consider the bilevel optimisation approach proposed by De Los Reyes, Sch\"onlieb (2013) for learning the optimal parameters in a Total Variation (TV) denoising model featuring for multiple noise distributions. In applications, the use of databases (dictionaries) allows an accurate estimation of the parameters, but reflects in high computational costs due to the size of the databases and to the nonsmooth nature of the PDE constraints. To overcome this computational barrier we propose an optimisation algorithm that by sampling dynamically from the set of constraints and using a quasi-Newton method, solves the problem accurately and in an efficient way

Learning optimal spatially-dependent regularization parameters in total variation image denoising

We consider a bilevel optimization approach in function space for the choice of spatially dependent regularization parameters in TV image denoising models. First- and second-order optimality conditions for the bilevel problem are studied when the spatially-dependent parameter belongs to the Sobolev space H1(Ω). A combined Schwarz domain decomposition-semismooth Newton method is proposed for the solution of the full optimality system and local superlinear convergence of the semismooth Newton method is verified. Exhaustive numerical computations are finally carried out to show the suitability of the approach

Learning filter functions in regularisers by minimising quotients

Learning approaches have recently become very popular in the field of inverse problems. A large variety of methods has been established in recent years, ranging from bi-level learning to high-dimensional machine learning techniques. Most learning approaches, however, only aim at fitting parametrised models to favourable training data whilst ignoring misfit training data completely. In this paper, we follow up on the idea of learning parametrised regularisation functions by quotient minimisation as established in [3]. We extend the model therein to include higher-dimensional filter functions to be learned and allow for fit- and misfit-training data consisting of multiple functions. We first present results resembling behaviour of well-established derivative-based sparse regularisers like total variation or higher-order total variation in one-dimension. Our second and main contribution is the introduction of novel families of non-derivative-based regularisers. This is accomplished by learning favourable scales and geometric properties while at the same time avoiding unfavourable ones

Perceptions of Problem Behavior in Adolescents’ Families: Perceiver, Target, and Family Effects

Considerable research has focused on the reliability and validity of informant reports of family behavior, especially maternal reports of adolescent problem behavior. None of these studies, however, has based their orientation on a theoretical model of interpersonal perception. In this study we used the social relations model (SRM) to examine family members’ reports of each others’ externalizing and internalizing problem behavior. Two parents and two adolescents in 69 families rated each others’ behavior within a round-robin design. SRM analysis showed that within-family perceptions of externalizing and internalizing behaviors are consistently due to three sources of variance; perceiver, target, and family effects. A family/contextual effect on informant reports of problem behavior has not been previously reported

Genome-wide gene expression analysis supports a developmental model of low temperature tolerance gene regulation in wheat (Triticum aestivum L.)

<p>Abstract</p> <p>Background</p> <p>To identify the genes involved in the development of low temperature (LT) tolerance in hexaploid wheat, we examined the global changes in expression in response to cold of the 55,052 potentially unique genes represented in the Affymetrix Wheat Genome microarray. We compared the expression of genes in winter-habit (winter Norstar and winter Manitou) and spring-habit (spring Manitou and spring Norstar)) cultivars, wherein the locus for the vernalization gene <it>Vrn-A1 </it>was swapped between the parental winter Norstar and spring Manitou in the derived near-isogenic lines winter Manitou and spring Norstar. Global expression of genes in the crowns of 3-leaf stage plants cold-acclimated at 6°C for 0, 2, 14, 21, 38, 42, 56 and 70 days was examined.</p> <p>Results</p> <p>Analysis of variance of gene expression separated the samples by genetic background and by the developmental stage before or after vernalization saturation was reached. Using gene-specific ANOVA we identified 12,901 genes (at <it>p </it>< 0.001) that change in expression with respect to both genotype and the duration of cold-treatment. We examined in more detail a subset of these genes (2,771) where expression was highly influenced by the interaction between these two main factors. Functional assignments using GO annotations showed that genes involved in transport, oxidation-reduction, and stress response were highly represented. Clustering based on the pattern of transcript accumulation identified genes that were up or down-regulated by cold-treatment. Our data indicate that the cold-sensitive lines can up-regulate known cold-responsive genes comparable to that of cold-hardy lines. The levels of expression of these genes were highly influenced by the initial rate and the duration of the gene's response to cold. We show that the <it>Vrn-A1 </it>locus controls the duration of gene expression but not its initial rate of response to cold treatment. Furthermore, we provide evidence that <it>Ta.Vrn-A1 </it>and <it>Ta.Vrt1 </it>originally hypothesized to encode for the same gene showed different patterns of expression and therefore are distinct.</p> <p>Conclusion</p> <p>This study provides novel insight into the underlying mechanisms that regulate the expression of cold-responsive genes in wheat. The results support the developmental model of LT tolerance gene regulation and demonstrate the complex genotype by environment interactions that determine LT adaptation in winter annual cereals.</p

How young can children reliably and validly self-report their health-related quality of life?: An analysis of 8,591 children across age subgroups with the PedsQL™ 4.0 Generic Core Scales

BACKGROUND: The last decade has evidenced a dramatic increase in the development and utilization of pediatric health-related quality of life (HRQOL) measures in an effort to improve pediatric patient health and well-being and determine the value of healthcare services. The emerging paradigm shift toward patient-reported outcomes (PROs) in clinical trials has provided the opportunity to further emphasize the value and essential need for pediatric patient self-reported outcomes measurement. Data from the PedsQL™ Database(SM )were utilized to test the hypothesis that children as young as 5 years of age can reliably and validly report their HRQOL. METHODS: The sample analyzed represented child self-report age data on 8,591 children ages 5 to 16 years from the PedsQL™ 4.0 Generic Core Scales Database(SM). Participants were recruited from general pediatric clinics, subspecialty clinics, and hospitals in which children were being seen for well-child checks, mild acute illness, or chronic illness care (n = 2,603, 30.3%), and from a State Children's Health Insurance Program (SCHIP) in California (n = 5,988, 69.7%). RESULTS: Items on the PedsQL™ 4.0 Generic Core Scales had minimal missing responses for children as young as 5 years old, supporting feasibility. The majority of the child self-report scales across the age subgroups, including for children as young as 5 years, exceeded the minimum internal consistency reliability standard of 0.70 required for group comparisons, while the Total Scale Scores across the age subgroups approached or exceeded the reliability criterion of 0.90 recommended for analyzing individual patient scale scores. Construct validity was demonstrated utilizing the known groups approach. For each PedsQL™ scale and summary score, across age subgroups, including children as young as 5 years, healthy children demonstrated a statistically significant difference in HRQOL (better HRQOL) than children with a known chronic health condition, with most effect sizes in the medium to large effect size range. CONCLUSION: The results demonstrate that children as young as the 5 year old age subgroup can reliably and validly self-report their HRQOL when given the opportunity to do so with an age-appropriate instrument. These analyses are consistent with recent FDA guidelines which require instrument development and validation testing for children and adolescents within fairly narrow age groupings and which determine the lower age limit at which children can provide reliable and valid responses across age categories

Quantitative image analysis for the characterization of microbial aggregates in biological wastewater treatment : a review

Quantitative image analysis techniques have gained an undeniable role in several fields of research during the last decade. In the field of biological wastewater treatment (WWT) processes, several computer applications have been developed for monitoring microbial entities, either as individual cells or in different types of aggregates. New descriptors have been defined that are more reliable, objective, and useful than the subjective and time-consuming parameters classically used to monitor biological WWT processes. Examples of this application include the objective prediction of filamentous bulking, known to be one of the most problematic phenomena occurring in activated sludge technology. It also demonstrated its usefulness in classifying protozoa and metazoa populations. In high-rate anaerobic processes, based on granular sludge, aggregation times and fragmentation phenomena could be detected during critical events, e.g., toxic and organic overloads. Currently, the major efforts and needs are in the development of quantitative image analysis techniques focusing on its application coupled with stained samples, either by classical or fluorescent-based techniques. The use of quantitative morphological parameters in process control and online applications is also being investigated. This work reviews the major advances of quantitative image analysis applied to biological WWT processes.The authors acknowledge the financial support to the project PTDC/EBB-EBI/103147/2008 and the grant SFRH/BPD/48962/2008 provided by Fundacao para a Ciencia e Tecnologia (Portugal)