Shape Constrained Regularisation by Statistical Multiresolution for Inverse Problems: Asymptotic Analysis

This paper is concerned with a novel regularisation technique for solving linear ill-posed operator equations in Hilbert spaces from data that is corrupted by white noise. We combine convex penalty functionals with extreme-value statistics of projections of the residuals on a given set of sub-spaces in the image-space of the operator. We prove general consistency and convergence rate results in the framework of Bregman-divergences which allows for a vast range of penalty functionals. Various examples that indicate the applicability of our approach will be discussed. We will illustrate in the context of signal and image processing that the presented method constitutes a locally adaptive reconstruction method

Locally adaptive image denoising by a statistical multiresolution criterion

We demonstrate how one can choose the smoothing parameter in image denoising by a statistical multiresolution criterion, both globally and locally. Using inhomogeneous diffusion and total variation regularization as examples for localized regularization schemes, we present an efficient method for locally adaptive image denoising. As expected, the smoothing parameter serves as an edge detector in this framework. Numerical examples illustrate the usefulness of our approach. We also present an application in confocal microscopy

Image size influences visual search and perception of hemorrhages when reading cranial CT: an eye tracking study

Objectives: To explore reader gaze, performance and preference during interpretation of cranial computed tomography (cCT) in stack mode at two different sizes. Background: Digital display of medical images allows for the manipulation of many imaging factors, like image size, by the radiologists, yet it is often not known what display parameters better suit human perception. Materials and Methods: Twenty-one radiologists provided informed consent to be eye tracked while reading 20 cCT cases. Half of these cases were presented at a size of 14x14 cm (512x512 pixels), half at 28x28 cm (1024x1024 pixels). Visual search, performance and preference for the two image sizes were assessed. Results: When reading small images significantly fewer, but longer fixations were observed, and these covered significantly more slices. Time to first fixation of True Positive findings was faster in small images, but dwell time on true findings was longer. Readers made more False Positive decisions in small images, but no overall difference in either JAFROC or reading time was found. Conclusions: Overall performance is not affected by image size. However, small stack mode cCT images may better support the use of motion perception and acquiring an overview, whereas large stack mode cCT images seem better suited for detailed analyses. Application: Subjective and eye tracking data suggest that image size influences how images are searched and that different search strategies might be beneficial under different circumstances

Modern radiation therapy and potential fertility preservation strategies in patients with cervical cancer undergoing chemoradiation

Young patients with cervical cancer who undergo chemoradiation might be interested in fertility preservation, not only dependent upon the use of a gestational carrier as maybe achieved by the use of ovarian transposition and cryo-conservation of oocytes or ovarian tissue, but may prefer to carry pregnancy to term after cancer treatment. The latter approach is a non- established concept needing both modern radiation therapy approaches as well as modifications -if at all possible- in current recommendations for target volume delineation to spare dose to the unaffected uterus. Future strategies to serve selected patients in this respect should only be conducted in prospective clinical evaluations and are critically discussed in this article

Rectum separation in patients with cervical cancer for treatment planning in primary chemo-radiation

PURPOSE: To proof feasibility of hydrogel application in patients with advanced cervical cancer undergoing chemo-radiation in order to reduce rectal toxicity from external beam radiation as well as brachytherapy. MATERIAL AND METHODS: Under transrectal sonographic guidance five patients with proven cervical cancer underwent hydro gel (20 cc) instillation into the tip of rectovaginal septum adherent to posterior part of the visible cervical tumor. Five days after this procedure all patients underwent T2 weighted transversal and sagittal MRI for brachytherapy planning. MRI protocol included T2 weighted fast spin echo (FSE) imaging in sagittal, coronal and para-axial orientation using an 1.5 Tesla MRI. Separation of anterior rectal wall and cervix was documented. RESULTS: Hydrogel application was uneventful in all patients and no toxicity was reported. Separation ranged from 7 to 26 mm in width (median 10 mm). The length of the separation varied between 18 and 38 mm (median 32 mm). In all patients displacement was seen in the posterior vaginal fornix, and/or at the deepest part of uterine cervix depending on the extension of the cul-de-sac in correlation to the posterior wall of the uterus. In patients with bulky tumor and/or deep (vaginal) extend of peritoneal cavity tumour was seen mainly cranial from the rectovaginal space and therefore above the hydrogeI application. Only in the extra-peritoneal (lower) part of the cervix a good separation could be achieved between the rectum and cervix. CONCLUSION: Hydrgel instillation in patients with cervial cancer undergoing chemoradiation is safe and feasible. Because of the loose tissue of the cul-de-sac and its intra- and extraperitoneal part, hydrogel instillation of 20 cc did not result in a sufficient separation of the cervix from anterior wall

Statistical Multiresolution Estimation for Variational Imaging: With an Application in Poisson-Biophotonics

In this paper we present a spatially-adaptive method for image reconstruction that is based on the concept of statistical multiresolution estimation as introduced in [Frick K, Marnitz P, and Munk A. "Statistical multiresolution Dantzig estimation in imaging: Fundamental concepts and algorithmic framework". Electron. J. Stat., 6:231-268, 2012]. It constitutes a variational regularization technique that uses an supremum-type distance measure as data-fidelity combined with a convex cost functional. The resulting convex optimization problem is approached by a combination of an inexact alternating direction method of multipliers and Dykstra's projection algorithm. We describe a novel method for balancing data-fit and regularity that is fully automatic and allows for a sound statistical interpretation. The performance of our estimation approach is studied for various problems in imaging. Among others, this includes deconvolution problems that arise in Poisson nanoscale fluorescence microscopy

Optimising corporate social responsibility spend a conjoint experiment to determine consumer evaluations of corporate social responsibility strategies

The concept of Corporate Social Responsibility (CSR) is becoming more prominent due to a number of forces, including an increase in ethical consumerism and government or industry regulation. Business owners are coming to the realisation that CSR investment should be viewed as an opportunity to increase the success of companies rather than as damage control or PR campaign; CSR is becoming a critical factor in the competitive success of companies. Increasing social responsibility can indeed result in benefits, financial and otherwise, not just for society but also for companies. This study aimed to determine:• Consumer preferences regarding the various CSR strategies that companies can pursue and• Whether consumers place higher value on CSR strategies which benefit their own society or strategies which benefit society at large.A convenience sample of South Africans were selected for the study and asked to complete a web-based survey. The study was done in the form of a conjoint value analysis.The study found that:• Consumers do have different levels of preference for the different CSR strategies which businesses can follow.• Consumers prefer a CSR strategy that benefits their own society over a CSR strategy that benefits the society at large.Dissertation (MBA)--University of Pretoria, 2012.Gordon Institute of Business Science (GIBS)unrestricte

Statistical Multiresolution Estimatiors in Linear Inverse Problems - Foundations and Algorithmic Aspects

In jüngerer Vergangenheit haben statistische Multiresolutionstechniken viel Aufmerksamkeit erregt. Dies liegt vor allem daran, dass die hieraus resultierenden statistischen Multiresolutionsschätzer (SMR) lokal- und multiskalenadaptiv sind, das heißt, dass sie sich automatisch der Glattheit des wahren Objects lokal und auf verschiedenen Skalen anpassen. In dieser Dissertation wird eine neuartige Methodik eingeführt, um SMR-Schätzer in der Praxis zu berechnen.Hierzu werden SMR-Schätzer rigoros als Lösung eines Optimierungsproblems mit Nebenbedingungen definiert. Neben einer Herleitung dieses Ansatzes wird auch ein Konsistenzresultat erbracht. Die eigentliche Berechnung wird dann über eine Augmented-Lagrangian-Methode durchgeführt, mittels derer das Problem in ein unrestringiertes Minimierungsproblem und ein hochskaliges Projektionsproblem zerlegt wird. Letzteres wird durch den Dykstra-Algorithmius attackiert; eine Methode, welche die Projektion auf den Schnitt von abgeschlossenen und konvexen Mengen berechnet, indem sie sukzessive auf die einzelnen Mengen projiziert. Diese individuellen Projektionen können im hier vorliegenden Kontext explizit angegeben werden, wodurch der Dykstra-Algorithmus zu einer besonders schnellen und somit attraktiven Lösungsmethode wird.Hierdurch können mit unserer Methodik auch vergleichsweise große Datensätze behandelt werden. Insbesondere können zweidimensionale Datensätze bearbeitet werden, während die meisten Publikationen in diesem Themenbereich bislang auf ein eindimensionales Rahmenwerk beschränkt waren. Auf Regressionsprobleme angewendet liefert unsere Methode bessere Ergebnisse als andere aktuelle Methoden im Bereich der SMR-Schätzung. Darüber hinaus ist unser Algorithmus der erste, welcher die Berechnung von SMR-Schätzern in (möglicherweise schlecht-gestellten) inversen Problemen ermöglicht und kann mit einer Vielzahl von Straffunktionalen kombiniert werden

Schmincke's Tumor, Carcinoma of the Base of the Tongue c T1-2, cN2c M0 – A Case Report

Background: Lymphoepithelial tumors are the most common carcinomas of the nasopharynx. The non-differentiated tumor, also called Schmincke’s tumor, is more prevalent in the African and Chinese population. The incidence of the tumor according to age peaks between 20 and 30 years of age, and after 60 years of age. The tumor is rarely located outside of the nasopharynx. Case Report: This report is about a 73-year-old female patient diagnosed with a tumor of the base of the tongue. The histological result shows a low-grade carcinoma of the squamous epithelium, a lymphoepithelial carcinoma. Conclusion: Despite the tumor’s rare manifestation outside the nasopharynx, one must also consider the non-differentiated carcinoma of lymphoepithelial matrix. Especially due to the well-known early tumor spreading, cervical lymph node swelling on both sides can be recognized as a possible early symptom. First-line therapy consists of primary radiation of the tumor’s primary region and its lymphoid draining channels. Concomitant chemotherapy can be applied. In case of cervical tumor spreading, a neck dissection reduces the risk of local recurrence