Minimization of multi-penalty functionals by alternating iterative thresholding and optimal parameter choices

Inspired by several recent developments in regularization theory, optimization, and signal processing, we present and analyze a numerical approach to multi-penalty regularization in spaces of sparsely represented functions. The sparsity prior is motivated by the largely expected geometrical/structured features of high-dimensional data, which may not be well-represented in the framework of typically more isotropic Hilbert spaces. In this paper, we are particularly interested in regularizers which are able to correctly model and separate the multiple components of additively mixed signals. This situation is rather common as pure signals may be corrupted by additive noise. To this end, we consider a regularization functional composed by a data-fidelity term, where signal and noise are additively mixed, a non-smooth and non-convex sparsity promoting term, and a penalty term to model the noise. We propose and analyze the convergence of an iterative alternating algorithm based on simple iterative thresholding steps to perform the minimization of the functional. By means of this algorithm, we explore the effect of choosing different regularization parameters and penalization norms in terms of the quality of recovering the pure signal and separating it from additive noise. For a given fixed noise level numerical experiments confirm a significant improvement in performance compared to standard one-parameter regularization methods. By using high-dimensional data analysis methods such as Principal Component Analysis, we are able to show the correct geometrical clustering of regularized solutions around the expected solution. Eventually, for the compressive sensing problems considered in our experiments we provide a guideline for a choice of regularization norms and parameters.Comment: 32 page

A survey of spiders (Araneae) inhabiting the euedaphic soil stratum and the superficial underground compartment in Bulgaria

In 2005 a team of Bulgarian zoologists started a project aiming to study the invertebrates inhabiting the deeper soil stratum (euedaphon) and the Superficial Underground Compartment (SUC) in Bulgaria. In the course of a four-year sampling, a total of 52 species of spiders were caught from 19 collecting sites and 9 geographical regions. They belong to the following families: Scytodidae (1), Segestriidae (1), Dysderidae (8), Nesticidae (1), Anapidae (1), Theridiidae (1), Linyphiidae (20), Agelenidae (3), Cybaeidae (1), Dictynidae (2), Amaurobiidae (2), Liocranidae (3), Corinnidae (1), Zodariidae (1), Gnaphosidae (5), and Salticidae (1). The family Anapidae, with the species Zangherella relicta (Kratochvíl, 1935) is recorded from three sites in the Pirin and Slavyanka mountains, and this represents the first record of the family, genus and species in Bulgaria. In spite of the active investigations of the epigean and cave spiders in these regions over the years Z. relicta was not found and it seems it occurs only in deeper subterranean habitats and nowhere else. Comparative study of almost topotypic specimens of Z. relicta from Montenegro with those collected from Bulgaria showed no variation in the shape of palp and female vulvae. Until the true identity of Z. apuliae (Caporiacco, 1949) from Italy is revealed, it remains unclear whether Z. relicta and Z. apuliae are conspecific, as it remains unclear whether the older records of Z. apuliae from the Balkan Peninsula refer to this species or to Z. relicta. Pelecopsis mengei (Simon, 1884) (Linyphiidae) and Scotolathys simplex Simon, 1884 (Dictynidae) are also reported from Bulgaria for the first time, the latter being also new to FYR of Macedonia. A faunistic overview of the spiders found in these underground environments is made, along with remarks on the distribution and ecology of some rare and interesting species. The presence of cave-dwelling and superficial spiders in the sampled sites indicates that SUC and euedaphon are inhabited by different ecotypes, e.g. litter-(tanathostromic), soil-(edaphic) and cave-(troglobitic) which at some places co-occur

Oleksandr Dovzhenko, Ivan Kavaleridze, Leonid Skrypnyk: The avant-garde and philosophical explorations of Ukrainian filmmakers of the 1920s

The filmmakers Oleksandr Dovzhenko and Ivan Kavaleridze created bold avant-garde works at the time when Ukrainian cinema was being established, at the end of the 1920s and early 1930s. In effect, the works of these two directors shaped the defining features of Ukrainian cinema. This article discusses the creative methods used by Dovzhenko in his three films Zvenyhora (1927), Arsenal (1929) and Earth (1930), which clearly depict Ukrainian worldviews and mentality. Kavaleridze’s approach is considered in the light of two of his films, Downpour (1929) and Perekop (1930). Already a recognized sculptor at the time, Kavaleridze sought unique forms of expression in film. The approaches these directors took towards framing scenes, montage, lighting and rhythm underpinned the theoretical propositions of their contemporary, Ukrainian film theorist Leonid Skrypnyk. The author suggests that this testifies to a deliberate and comprehensive search for new means of expression in all phases of filmmaking.The filmmakers Oleksandr Dovzhenko and Ivan Kavaleridze created bold avant-garde works at the time when Ukrainian cinema was being established, at the end of the 1920s and early 1930s. In effect, the works of these two directors shaped the defining features of Ukrainian cinema. This article discusses the creative methods used by Dovzhenko in his three films Zvenyhora (1927), Arsenal (1929) and Earth (1930), which clearly depict Ukrainian worldviews and mentality. Kavaleridze’s approach is considered in the light of two of his films, Downpour (1929) and Perekop (1930). Already a recognized sculptor at the time, Kavaleridze sought unique forms of expression in film. The approaches these directors took towards framing scenes, montage, lighting and rhythm underpinned the theoretical propositions of their contemporary, Ukrainian film theorist Leonid Skrypnyk. The author suggests that this testifies to a deliberate and comprehensive search for new means of expression in all phases of filmmaking