Less is often more : applied inverse problems using hp-forward models

To solve an applied inverse problem, a numerical forward model for the problem’s physics is required. Commonly, the finite element method is employed with discretizations consisting of elements with variable size h and polynomial degree p. Solutions to hp-forward models are known to converge exponentially by simultaneously decreasing h and increasing p. On the other hand, applied inverse problems are often ill-posed and their minimization rate exhibits uncertainty. Presently, the behavior of applied inverse problems incorporating hp elements of differing p, h, and geometry is not fully understood. Nonetheless, recent research suggests that employing increasingly higher-order hp-forward models (increasing mesh density and p) decreases reconstruction errors compared to inverse regimes using lower-order hp-forward models (coarser meshes and lower p). However, an affirmative or negative answer to following question has not been provided, “Does the use of higher order hp-forward models in applied inverse problems always result in lower error reconstructions than approaches using lower order hp-forward models?” In this article we aim to reduce the current knowledge gap and answer the open question by conducting extensive numerical investigations in the context of two contemporary applied inverse problems: elasticity imaging and hydraulic tomography – nonlinear inverse problems with a PDE describing the underlying physics. Our results support a negative answer to the question – i.e. decreasing h (increasing mesh density), increasing p, or simultaneously decreasing h and increasing p does not guarantee lower error reconstructions in applied inverse problems. Rather, there is complex balance between the accuracy of the hp-forward model, noise, prior knowledge (regularization), Jacobian accuracy, and ill-conditioning of the Jacobian matrix which ultimately contribute to reconstruction errors. As demonstrated herein, it is often more advantageous to use lower-order hp-forward models than higherorder hp-forward models in applied inverse problems. These realizations and other counterintuitive behavior of applied inverse problems using hp-forward models are described in detail herein

An atypical presentation of severe congenital contractures and lack of cerebellar involvement in a patient with a novel LAMA1 mutation

Background: LAMA1 gene is mutated in patients with Poretti-Boltshauser syndrome, which include mainly the characteristic neuroimaging findings of cerebellar dysplasia and cysts. Case Presentation: We present a novel homozygous LAMA1 variant that is predicted to cause atypical phenotype of severe arthrogryposis, feeding difficulties, developmental delay, retinopathy, and no cerebellar involvement. Conclusion: Our findings are suggestive of absence of cerebellar involvement in LAMA1 mutations in some cases and phenotype may include severe arthrogryposis. [JBCGenetics 2018; 1(1.000): 43-46

A left ventricular segmentation based on a parallel watershed transformation towards an accurate heart function evaluation

International audienceMagnetic Resonance Imaging (MRI) has emerged as the golden reference for cardiac examination. This modality allows the assessment of human cardiovascular morphology, functioning, and perfusion. Although a couple of challenging issues, such as the cardiac MR image's features and the large variability of images among several patients, still influences the cardiac cavities' segmentation and needs to be carried out. In this paper, we have profoundly reviewed and fully compared semi-automated segmentation methods performed on cardiac Cine-MR short-axis images for the evaluation of the left ventricular functions. However, the number of parameters handled by the synthesized works is limited if not null. For the sake of ensuring the highest coverage of the LV parameters computing, we have introduced a parallel watershed-based approach to segment the left ventricular allowing hence the computation of six parameters (End-Diastolic Volume, End-Systolic Volume, Ejection Fraction, Cardiac output, Stroke Volume and Left Ventricular Mass). An algorithm is associated with main considered measurements. The experimental results that were obtained through studying twenty patients' MRI data base, demonstrate the accuracy of our approach for estimating real values of the maximal set of parameters thanks to a faithful segmentation of the myocardium

Level set methods for structural inversion and image reconstruction

Chapter 10, sollicitéIn this chapter, an introduction is given into the use of level set techniques for inverse problems and image reconstruction. Several approaches are presented which have been developed and proposed in the literature since the publication of the original (and seminal) paper by F. Santosa in 1996 on this topic. The emphasis of this chapter, however, is not so much on providing an exhaustive overview of all ideas developed so far, but on the goal of outlining the general idea of structural inversion by level sets, which means the reconstruction of complicated images with interfaces from indirectly measured data. As case studies, recent results (in 2D) from microwave breast screening, history matching in reservoir engineering, and crack detection are presented in order to demonstrate the general ideas outlined in this chapter on practically relevant and instructive examples. Various references and suggestions for further research are given as well