PENDANTSS: PEnalized Norm-ratios Disentangling Additive Noise, Trend and Sparse Spikes

Denoising, detrending, deconvolution: usual restoration tasks, traditionally decoupled. Coupled formulations entail complex ill-posed inverse problems. We propose PENDANTSS for joint trend removal and blind deconvolution of sparse peak-like signals. It blends a parsimonious prior with the hypothesis that smooth trend and noise can somewhat be separated by low-pass filtering. We combine the generalized quasi-norm ratio SOOT/SPOQ sparse penalties $\ell_p/\ell_q$ with the BEADS ternary assisted source separation algorithm. This results in a both convergent and efficient tool, with a novel Trust-Region block alternating variable metric forward-backward approach. It outperforms comparable methods, when applied to typically peaked analytical chemistry signals. Reproducible code is provided

Spectral unmixing of multiply stained fluorescence samples T

The widespread use of fluorescence microscopy along with the vast library of available fluorescent stains and staining methods has been extremely beneficial to researchers in many fields, ranging from material sciences to plant biology. In clinical diagnostics, the ability to combine different markers in a given sample allows the simultaneous detection of the expression of several different molecules, which in turn provides a powerful diagnostic tool for pathologists, allowing a better classification of the sample at hand. The correct detection and separation of multiple stains in a sample is achieved not only by the biochemical and optical properties of the markers, but also by the use of appropriate hardware and software tools. In this chapter, we will review and compare these tools along with their advantages and limitations

Cool core remnants in galaxy clusters

X ray clusters are conventionally divided into two classes: "cool core" (CC) and "non cool core" (NCC) objects, on the basis of the observational properties of their central regions. Recent results have shown that the cluster population is bimodal (Cavagnolo et al. 2009). We want to understand whether the observed distribution of clusters is due to a primordial division into two distinct classes rather than to differences in how these systems evolve across cosmic time. We systematically search the ICM of NCC clusters in a subsample of the B55 flux limited sample of clusters for regions which have some characteristics typical of cool cores, namely low entropy gas and high metal abundance We find that most NCC clusters in our sample host regions reminiscent of CC, i. e. characterized by relative low entropy gas (albeit not as low as in CC systems) and a metal abundance excess. We have dubbed these structures "cool core remnants", since we interpret them as what remains of a cool core after a heating event (AGN giant outbursts in a few cases and more commonly mergers). We infer that most NCC clusters have undergone a cool core phase during their life. The fact that most cool core remnants are found in dynamically active objects provides strong support to scenarios where cluster core properties are not fixed "ab initio" but evolve across cosmic time.Comment: Accepted for publication in Astronomy & Astrophysics. Version with full resolution figures available at: http://www.iasf-milano.inaf.it/~rossetti/public/CCR/rossetti.pd