Error analysis for filtered back projection reconstructions in Besov spaces

Filtered back projection (FBP) methods are the most widely used reconstruction algorithms in computerized tomography (CT). The ill-posedness of this inverse problem allows only an approximate reconstruction for given noisy data. Studying the resulting reconstruction error has been a most active field of research in the 1990s and has recently been revived in terms of optimal filter design and estimating the FBP approximation errors in general Sobolev spaces. However, the choice of Sobolev spaces is suboptimal for characterizing typical CT reconstructions. A widely used model are sums of characteristic functions, which are better modelled in terms of Besov spaces $\mathrm{B}^{\alpha,p}_q(\mathbb{R}^2)$. In particular $\mathrm{B}^{\alpha,1}_1(\mathbb{R}^2)$ with $\alpha \approx 1$ is a preferred model in image analysis for describing natural images. In case of noisy Radon data the total FBP reconstruction error $$\|f-f_L^\delta\| \le \|f-f_L\|+ \|f_L - f_L^\delta\|$$ splits into an approximation error and a data error, where $L$ serves as regularization parameter. In this paper, we study the approximation error of FBP reconstructions for target functions $f \in \mathrm{L}^1(\mathbb{R}^2) \cap \mathrm{B}^{\alpha,p}_q(\mathbb{R}^2)$ with positive $\alpha \not\in \mathbb{N}$ and $1 \leq p,q \leq \infty$. We prove that the $\mathrm{L}^p$-norm of the inherent FBP approximation error $f-f_L$ can be bounded above by \begin{equation*} \|f - f_L\|_{\mathrm{L}^p(\mathbb{R}^2)} \leq c_{\alpha,q,W} \, L^{-\alpha} \, |f|_{\mathrm{B}^{\alpha,p}_q(\mathbb{R}^2)} \end{equation*} under suitable assumptions on the utilized low-pass filter's window function $W$. This then extends by classical methods to estimates for the total reconstruction error.Comment: 32 pages, 8 figure

Bayesian view on the training of invertible residual networks for solving linear inverse problems

Learning-based methods for inverse problems, adapting to the data's inherent structure, have become ubiquitous in the last decade. Besides empirical investigations of their often remarkable performance, an increasing number of works addresses the issue of theoretical guarantees. Recently, [3] exploited invertible residual networks (iResNets) to learn provably convergent regularizations given reasonable assumptions. They enforced these guarantees by approximating the linear forward operator with an iResNet. Supervised training on relevant samples introduces data dependency into the approach. An open question in this context is to which extent the data's inherent structure influences the training outcome, i.e., the learned reconstruction scheme. Here we address this delicate interplay of training design and data dependency from a Bayesian perspective and shed light on opportunities and limitations. We resolve these limitations by analyzing reconstruction-based training of the inverses of iResNets, where we show that this optimization strategy introduces a level of data-dependency that cannot be achieved by approximation training. We further provide and discuss a series of numerical experiments underpinning and extending the theoretical findings

Invertible residual networks in the context of regularization theory for linear inverse problems

Learned inverse problem solvers exhibit remarkable performance in applications like image reconstruction tasks. These data-driven reconstruction methods often follow a two-step scheme. First, one trains the often neural network-based reconstruction scheme via a dataset. Second, one applies the scheme to new measurements to obtain reconstructions. We follow these steps but parameterize the reconstruction scheme with invertible residual networks (iResNets). We demonstrate that the invertibility enables investigating the influence of the training and architecture choices on the resulting reconstruction scheme. For example, assuming local approximation properties of the network, we show that these schemes become convergent regularizations. In addition, the investigations reveal a formal link to the linear regularization theory of linear inverse problems and provide a nonlinear spectral regularization for particular architecture classes. On the numerical side, we investigate the local approximation property of selected trained architectures and present a series of experiments on the MNIST dataset that underpin and extend our theoretical findings

Pelvic tenderness is not limited to the prostate in chronic prostatitis/chronic pelvic pain syndrome (CPPS) type IIIA and IIIB: comparison of men with and without CP/CPPS

Background: We wished to determine if there were differences in pelvic and non-pelvic tenderness between men with chronic prostatitis/chronic pelvic pain syndrome (CP/CPPS) Type III and men without pelvic pain. Methods: We performed the Manual Tender Point Survey (MTPS) as described by the American College of Rheumatology on 62 men with CP/CPPS Type IIIA and IIIB and 98 men without pelvic pain. We also assessed tenderness of 10 external pelvic tender points (EPTP) and of 7 internal pelvic tender points (IPTP). All study participants completed the National Institutes of Health Chronic Prostatitis Symptom Inventory (NIH CPSI). Results: We found that men with CPPS were significantly more tender in the MTPS, the EPTPS and the IPTPS. CPSI scores correlated with EPTP scale but not with IPTP scale or prostate tenderness. Prostatic tenderness was present in 75% of men with CPPS and in 50% of men without CPPS. Expressed prostatic fluid leukocytosis was not associated with prostatic tenderness. Conclusion: Men with CP/CPPS have more tenderness compared to men without CPPS. Tenderness in men with CPPS is distributed throughout the pelvis and not specific to the prostate

Prognostic impact of vitamin B6 metabolism in lung cancer

Patients with non-small cell lung cancer (NSCLC) are routinely treated with cytotoxic agents such as cisplatin. Through a genome-wide siRNA-based screen, we identified vitamin B6 metabolism as a central regulator of cisplatin responses in vitro and in vivo. By aggravating a bioenergetic catastrophe that involves the depletion of intracellular glutathione, vitamin B6 exacerbates cisplatin-mediated DNA damage, thus sensitizing a large panel of cancer cell lines to apoptosis. Moreover, vitamin B6 sensitizes cancer cells to apoptosis induction by distinct types of physical and chemical stress, including multiple chemotherapeutics. This effect requires pyridoxal kinase (PDXK), the enzyme that generates the bioactive form of vitamin B6. In line with a general role of vitamin B6 in stress responses, low PDXK expression levels were found to be associated with poor disease outcome in two independent cohorts of patients with NSCLC. These results indicate that PDXK expression levels constitute a biomarker for risk stratification among patients with NSCLC.publishedVersio

Parasitic, bacterial, viral, immune-mediated, metabolic, and nutritional factors associated with Nodding syndrome

Nodding syndrome is a neglected, disabling and potentially fatal epileptic disorder of unknown aetiology affecting thousands of individuals mostly confined to Eastern sub-Saharan Africa. Previous studies have identified multiple associations – including O. volvulus, antileiomodin-1 antibodies, vitamin B6 deficiency, and measles virus infection – yet none is proven causal. We conducted a case-control study of children with early-stage Nodding syndrome (symptom onset <1 year). Cases and controls were identified through a household survey in the Greater Mundri area in South Sudan. A wide range of parasitic, bacterial, viral, immune-mediated, metabolic, and nutritional risk factors was investigated using conventional and state-of-the-art untargeted assays. Associations were examined by multiple logistic regression analysis and a hypothetical causal model was constructed using structural equation modelling. From 607 children with Nodding syndrome, 72 with early-stage disease were included as cases and matched to 65 household- and 44 community controls. Mansonella perstans infection (odds ratio [OR] 7.04, 95% confidence interval [CI] 2.28-21.7), Necator americanus infection (OR 2.33, 95% CI 1.02-5.3), higher antimalarial seroreactivity (OR 1.75, 95% CI 1.20-2.57), higher vitamin E concentration (OR 1.53 per standard deviation [SD] increase, 95% CI 1.07-2.19) and lower vitamin B12 concentration (OR 0.56 per SD increase, 95% CI 0.36-0.87) were associated with higher odds of NS. In a structural equation model, we hypothesized that M. perstans infection, higher vitamin E concentration and fewer viral exposures increased the risk of Nodding syndrome while lower vitamin B12 concentration, N. americanus and malaria infections resulted from having Nodding syndrome. We found no evidence that O. volvulus, antileiomodin-1 antibodies, vitamin B6 and other factors were associated with Nodding syndrome. Our results argue against several previous causal hypotheses including O. volvulus. Instead, Nodding syndrome may be caused by a complex interplay between multiple pathogens and nutrient levels. Further studies need to confirm these associations and determine the direction of effect

Identification of multiple risk loci and regulatory mechanisms influencing susceptibility to multiple myeloma

Genome-wide association studies (GWAS) have transformed our understanding of susceptibility to multiple myeloma (MM), but much of the heritability remains unexplained. We report a new GWAS, a meta-analysis with previous GWAS and a replication series, totalling 9974 MM cases and 247,556 controls of European ancestry. Collectively, these data provide evidence for six new MM risk loci, bringing the total number to 23. Integration of information from gene expression, epigenetic profiling and in situ Hi-C data for the 23 risk loci implicate disruption of developmental transcriptional regulators as a basis of MM susceptibility, compatible with altered B-cell differentiation as a key mechanism. Dysregulation of autophagy/apoptosis and cell cycle signalling feature as recurrently perturbed pathways. Our findings provide further insight

A multimodal cell census and atlas of the mammalian primary motor cortex

ABSTRACT We report the generation of a multimodal cell census and atlas of the mammalian primary motor cortex (MOp or M1) as the initial product of the BRAIN Initiative Cell Census Network (BICCN). This was achieved by coordinated large-scale analyses of single-cell transcriptomes, chromatin accessibility, DNA methylomes, spatially resolved single-cell transcriptomes, morphological and electrophysiological properties, and cellular resolution input-output mapping, integrated through cross-modal computational analysis. Together, our results advance the collective knowledge and understanding of brain cell type organization: First, our study reveals a unified molecular genetic landscape of cortical cell types that congruently integrates their transcriptome, open chromatin and DNA methylation maps. Second, cross-species analysis achieves a unified taxonomy of transcriptomic types and their hierarchical organization that are conserved from mouse to marmoset and human. Third, cross-modal analysis provides compelling evidence for the epigenomic, transcriptomic, and gene regulatory basis of neuronal phenotypes such as their physiological and anatomical properties, demonstrating the biological validity and genomic underpinning of neuron types and subtypes. Fourth, in situ single-cell transcriptomics provides a spatially-resolved cell type atlas of the motor cortex. Fifth, integrated transcriptomic, epigenomic and anatomical analyses reveal the correspondence between neural circuits and transcriptomic cell types. We further present an extensive genetic toolset for targeting and fate mapping glutamatergic projection neuron types toward linking their developmental trajectory to their circuit function. Together, our results establish a unified and mechanistic framework of neuronal cell type organization that integrates multi-layered molecular genetic and spatial information with multi-faceted phenotypic properties

A new species of Fissarcturus Brandt, 1990 (Isopoda, Valvifera, Antarcturidae) from the Southern Ocean, off the South Sandwich Islands

Nickel, Judith M., Brandt, Angelika (2013): A new species of Fissarcturus Brandt, 1990 (Isopoda, Valvifera, Antarcturidae) from the Southern Ocean, off the South Sandwich Islands. Zootaxa 3692 (1): 136-148, DOI: 10.11646/zootaxa.3692.1.