No abstract

Sparse modeling is a powerful framework for data analysis and processing. Traditionally, encoding in this framework is performed by solving an 1-regularized linear regression problem, commonly referred to as Lasso or Basis Pursuit. In this work we combine the sparsity-inducing property of the Lasso at the individual feature level, with the block-sparsity property of the Group Lasso, where sparse groups of features are jointly encoded, obtaining a sparsity pattern hierarchically structured. This results in the Hierarchical Lasso (HiLasso), which shows important practical advantages. We then extend this approach to the collaborative case, where a set of simultaneously coded signals share the same sparsity pattern at the higher (group) level, but not necessarily at the lower (inside the group) level, obtaining the collaborative HiLasso model (C-HiLasso). Such signals then share the same active groups, or classes, but not necessarily the same active set. This model is very well suited for applications such as source identification and separation. An efficient optimization procedure, which guarantees convergence to the global optimum, is developed for these new models. The underlying presentation of the framework and optimization approach is complemented by experimental examples and theoretical results regarding recovery guarantees.

The power of sparse signal modeling with learned over-complete dictionaries has been demonstrated in a variety of applications and fields, from signal processing to statistical inference and machine learning. However, the statistical properties of these models, such as under-fitting or over-fitting given sets of data, are still not well characterized in the literature. As a result, the success of sparse modeling depends on hand-tuning critical parameters for each data and application. This work aims at addressing this by providing a practical and objective characterization of sparse models by means of the Minimum Description Length (MDL) principle -a well established informationtheoretic approach to model selection in statistical inference. The resulting framework derives a family of efficient sparse coding and dictionary learning algorithms which, by virtue of the MDL principle, are completely parameter free. Furthermore, such framework allows to incorporate additional prior information to existing models, such as Markovian dependencies, or to define completely new problem formulations, including in the matrix analysis area, in a natural way. These virtues will be demonstrated with parameter-free algorithms for the classic image denoising and classification problems, and for low-rank matrix recovery in video applications.

The neotropical parasitoid Conura annulifera (Walker) (Hymenoptera: Chalcididae) is known to parasitize birdparasitic flies in the genus Philornis (Diptera: Muscidae) including P. downsi (Dodge and Aitken), a species that has invaded the Gal apagos islands and is negatively impacting populations of Darwin's finches. We report here some aspects of the life history, field ecology, and host specificity of C. annulifera. We collected puparia of four Philornis species in 13 bird nests during 2015 and 2016 in western mainland Ecuador and found that C. annulifera and three other parasitoid species emerged from those puparia. This is the first record of C. annulifera in Ecuador. Rearing records and dissections of parasitized puparia revealed that C. annulifera is a solitary pupal ectoparasitoid, placing its eggs in the gap between host pupa and puparium. Laboratory studies of host specificity involving P. downsi and pupae from five other dipteran, three lepidopteran, and one hymenopteran species found that C. annulifera only produced progeny when presented with P. downsi pupae. Pupae of P. downsi that had been exposed to C. annulifera also failed to emerge more often than expected by chance compared with no-parasitoid controls, suggesting that the parasitoids can cause developmental mortality through means other than successful parasitism. These studies constitute the first steps in evaluating C. annulifera as a potential biological control agent of P. downsi in the Gal apagos Islands.

Image denosing, impulse noise, discrete universal denoising, dudeWe present an extension of the Discrete Universal DEnoiser (DUDE) specialized for the denoising of grayscale images. The original DUDE is a low-complexity algorithm aimed at recovering discrete sequences corrupted by discrete memoryless noise of known statistical characteristics. It is universal, in the sense of asymptotically achieving, without access to any information on the statistics of the clean sequence, the same performance as the best denoiser that does have access to such information. The denoising performance of the DUDE, however, is poor on grayscale images of practical size. The difficulty lies in the fact that one of the DUDE's key components is the determination of conditional empirical probability distributions of image samples, given the sample values in their neighborhood. When the alphabet is moderately large (as is the case with grayscale images), even for a small-sized neighborhood, the required distributions would be estimated from a large collection of sparse statistics, resulting in poor estimates that would cause the algorithm to fall significantly short of the asymptotically optimal performance. The present work enhances the basic DUDE scheme by incorporating statistical modeling tools that have proven successful in addressing similar issues in lossless image compression. The enhanced framework is tested on additive and non-additive noise, and shown to yield powerful denoisers that significantly surpass the state of the art in the case of non-additive noise, and perform well for Gaussian noise. AbstractWe present an extension of the Discrete Universal DEnoiser (DUDE) specialized for the denoising of grayscale images. The original DUDE is a low-complexity algorithm aimed at recovering discrete sequences corrupted by discrete memoryless noise of known statistical characteristics. It is universal, in the sense of asymptotically achieving, without access to any information on the statistics of the clean sequence, the same performance as the best denoiser that does have access to such information. The denoising performance of the DUDE, however, is poor on grayscale images of practical size. The difficulty lies in the fact that one of the DUDE's key components is the determination of conditional empirical probability distributions of image samples, given the sample values in their neighborhood.When the alphabet is moderately large (as is the case with grayscale images), even for a small-sized neighborhood, the required distributions would be estimated from a large collection of sparse statistics, resulting in poor estimates that would cause the algorithm to fall significantly short of the asymptotically optimal performance. The present work enhances the basic DUDE scheme by incorporating statistical modeling tools that have proven successful in addressing similar issues in lossless image compression. The enhanced framework is tested on additive and non-additive noise, and shown to yield powerful denoisers that significantly su...