Low Complexity Regularization of Linear Inverse Problems

Inverse problems and regularization theory is a central theme in contemporary signal processing, where the goal is to reconstruct an unknown signal from partial indirect, and possibly noisy, measurements of it. A now standard method for recovering the unknown signal is to solve a convex optimization problem that enforces some prior knowledge about its structure. This has proved efficient in many problems routinely encountered in imaging sciences, statistics and machine learning. This chapter delivers a review of recent advances in the field where the regularization prior promotes solutions conforming to some notion of simplicity/low-complexity. These priors encompass as popular examples sparsity and group sparsity (to capture the compressibility of natural signals and images), total variation and analysis sparsity (to promote piecewise regularity), and low-rank (as natural extension of sparsity to matrix-valued data). Our aim is to provide a unified treatment of all these regularizations under a single umbrella, namely the theory of partial smoothness. This framework is very general and accommodates all low-complexity regularizers just mentioned, as well as many others. Partial smoothness turns out to be the canonical way to encode low-dimensional models that can be linear spaces or more general smooth manifolds. This review is intended to serve as a one stop shop toward the understanding of the theoretical properties of the so-regularized solutions. It covers a large spectrum including: (i) recovery guarantees and stability to noise, both in terms of $\ell^2$-stability and model (manifold) identification; (ii) sensitivity analysis to perturbations of the parameters involved (in particular the observations), with applications to unbiased risk estimation ; (iii) convergence properties of the forward-backward proximal splitting scheme, that is particularly well suited to solve the corresponding large-scale regularized optimization problem

Virtual Ontogeny of Cortical Growth Preceding Mental Illness

Background: Morphology of the human cerebral cortex differs across psychiatric disorders, with neurobiology and developmental origins mostly undetermined. Deviations in the tangential growth of the cerebral cortex during pre/perinatal periods may be reflected in individual variations in cortical surface area later in life. Methods: Interregional profiles of group differences in surface area between cases and controls were generated using T1-weighted magnetic resonance imaging from 27,359 individuals including those with attention-deficit/hyperactivity disorder, autism spectrum disorder, bipolar disorder, major depressive disorder, schizophrenia, and high general psychopathology (through the Child Behavior Checklist). Similarity of interregional profiles of group differences in surface area and prenatal cell-specific gene expression was assessed. Results: Across the 11 cortical regions, group differences in cortical area for attention-deficit/hyperactivity disorder, schizophrenia, and Child Behavior Checklist were dominant in multimodal association cortices. The same interregional profiles were also associated with interregional profiles of (prenatal) gene expression specific to proliferative cells, namely radial glia and intermediate progenitor cells (greater expression, larger difference), as well as differentiated cells, namely excitatory neurons and endothelial and mural cells (greater expression, smaller difference). Finally, these cell types were implicated in known pre/perinatal risk factors for psychosis. Genes coexpressed with radial glia were enriched with genes implicated in congenital abnormalities, birth weight, hypoxia, and starvation. Genes coexpressed with endothelial and mural genes were enriched with genes associated with maternal hypertension and preterm birth. Conclusions: Our findings support a neurodevelopmental model of vulnerability to mental illness whereby prenatal risk factors acting through cell-specific processes lead to deviations from typical brain development during pregnancy

Development Of An Analytical Method For Cholesterol Determination In Feed For Ruminants Using Factorial Experimental Design [desenvolvimento De Metodologia Analítica Para Determinaç ão De Colesterol Em Ração Para Ruminantes Através De Planejamento Experimental Fatorial]

A chromatographic method was developed for cholesterol determination in feed for ruminants using response surface methodology. Among the five approaches of sample preparation methods tested, the saponification of the sample without heating presented less interference in the gas chromatography. The method presented a relative standard deviation (RSD) of 4.3%, recoveries between 84 and 87% and detection limit of 0.001 mg of cholesterol per g of feed.31614221426+S1Piironen, V., Lindsay, D.G., Miettinen, T.A., Toivo, J., Lampi, A.M., (2000) J. Sci. Food Agric, 80, p. 939Volin, P., (2001) J. Chromatogr., A, 935, p. 125Van Elswyk, M.E., Schake, L.S., Hargis, P.S., (1991) Poultry Sci, 70, p. 1258Bragagnolo, N., Rodriguez-Amaya, D.B., (2003) J. Food Comp. Anal, 16, p. 147Behrman, E.J., Gopalan, V., (2005) J. Chem. Educ, 82, p. 1791Saldanha, T., Mazalli, M.R., Bragagnolo, N., (2004) Ciênc. Tecnol. Aliment, 24, p. 109Folch, J., Less, M., Stanley, S., (1957) J. Biol. Chem, 226, p. 497Bohac, C.E., Rhee, K.S., Cross, H.R., Ono, K., (1988) J. Food Sci, 5, p. 1642Diemair, W., (1963) Laboratoriumsbuch fur Lebensmittelchemiker, , 8 th ed, Verlag Von Theodor Steinkopff: DresdenRios, A.O., Mercadante, A.Z., (2004) Food Addit. Contam, 21, p. 125Mariutti, L.R.B., Nogueira, G.C., Bragagnolo, N., J. Agric. Food Chem, , no preloMazalli, M.R., Sawaya, A.C.H.F., Eberlin, M.N., Bragagnolo, N., (2006) Lipids, 41, p. 615Box, G.E.P., Hunter, W.G., Hunter, J.S., (1978) Statistics for Experiments: An Introduction to Designs, Data Analysis and Model Building, , Wiley: New YorkDirectiva 2002/657/CE de 12 de agosto de 2002(2002) J. Off. Comun. Europ, L 221, p. 8. , Comissão da União Européia;Ahmida, H.S.M., Bertucci, P., Franzo, L., Massoud, R., Cortese, C., Lala, A., Federici, G., (2006) J. Chromatogr., B: Anal. Technol. Biomed. Life Sci, 842, p. 43Dutta, P.C., Normém, L., (1998) J. Chromatogr., A, 816, p. 177Phillips, K.M., Ruggio, D.M., Bailey, J.A., (1999) J. Chromatogr., B: Anal. Technol. Biomed. Life Sci, 732, p. 17Phillips, K.M., Ruggio, D.M., Toivo, J.I., Swank, M.A., Simpkins, A.H., (2002) J. Food Comp. Anal, 15, p. 123Frega, N., Bocci, F., Lercker, G., (1992) J. Am. Oil Chem. Soc, 69, p. 447Rodriguez-Estrada, M.T., Frega, N., Lercker, G., (2002) Grasas Aceites, 53, p. 76Lagarda, M.J., García-Llatas, G., Farré, R., (2006) J. Pharm. Biomed. Anal, 41, p. 1486Ferrari, A.M., Santos, J., (2005) Ciên. Tecnol. Aliment, 25, p. 132Rossell, J.B., (1991) Analysis of oilseeds, fats and fatty foods, , Elsevier: Londo