Space-Varying Coefficient Models for Brain Imaging

The methodological development and the application in this paper originate from diffusion tensor imaging (DTI), a powerful nuclear magnetic resonance technique enabling diagnosis and monitoring of several diseases as well as reconstruction of neural pathways. We reformulate the current analysis framework of separate voxelwise regressions as a 3d space-varying coefficient model (VCM) for the entire set of DTI images recorded on a 3d grid of voxels. Hence by allowing to borrow strength from spatially adjacent voxels, to smooth noisy observations, and to estimate diffusion tensors at any location within the brain, the three-step cascade of standard data processing is overcome simultaneously. We conceptualize two VCM variants based on B-spline basis functions: a full tensor product approach and a sequential approximation, rendering the VCM numerically and computationally feasible even for the huge dimension of the joint model in a realistic setup. A simulation study shows that both approaches outperform the standard method of voxelwise regressions with subsequent regularization. Due to major efficacy, we apply the sequential method to a clinical DTI data set and demonstrate the inherent ability of increasing the rigid grid resolution by evaluating the incorporated basis functions at intermediate points. In conclusion, the suggested fitting methods clearly improve the current state-of-the-art, but ameloriation of local adaptivity remains desirable

Objectively measuring signal detectability, contrast, blur and noise in medical images using channelized joint observers

ABSTRACT To improve imaging systems and image processing techniques, objective image quality assessment is essential. Model observers adopting a task-based quality assessment strategy by estimating signal detectability measures, have shown to be quite successful to this end. At the same time, costly and time-consuming human observer experiments can be avoided. However, optimizing images in terms of signal detectability alone, still allows a lot of freedom in terms of the imaging parameters. More specifically, fixing the signal detectability defines a manifold in the imaging parameter space on which different “possible” solutions reside. In this article, we present measures that can be used to distinguish these possible solutions from each other, in terms of image quality factors such as signal blur, noise and signal contrast. Our approach is based on an extended channelized joint observer (CJO) that simultaneously estimates the signal amplitude, scale and detectability. As an application, we use this technique to design k-space trajectories for MRI acquisition. Our technique allows to compare the different spiral trajectories in terms of blur, noise and contrast, even when the signal detectability is estimated to be equal

Non-convex optimization for 3D point source localization using a rotating point spread function

We consider the high-resolution imaging problem of 3D point source image recovery from 2D data using a method based on point spread function (PSF) engineering. The method involves a new technique, recently proposed by S.~Prasad, based on the use of a rotating PSF with a single lobe to obtain depth from defocus. The amount of rotation of the PSF encodes the depth position of the point source. Applications include high-resolution single molecule localization microscopy as well as the problem addressed in this paper on localization of space debris using a space-based telescope. The localization problem is discretized on a cubical lattice where the coordinates of nonzero entries represent the 3D locations and the values of these entries the fluxes of the point sources. Finding the locations and fluxes of the point sources is a large-scale sparse 3D inverse problem. A new nonconvex regularization method with a data-fitting term based on Kullback-Leibler (KL) divergence is proposed for 3D localization for the Poisson noise model. In addition, we propose a new scheme of estimation of the source fluxes from the KL data-fitting term. Numerical experiments illustrate the efficiency and stability of the algorithms that are trained on a random subset of image data before being applied to other images. Our 3D localization algorithms can be readily applied to other kinds of depth-encoding PSFs as well.Comment: 28 page

The zCOSMOS Redshift Survey: the role of environment and stellar mass in shaping the rise of the morphology-density relation from z~1

For more than two decades we have known that galaxy morphological segregation is present in the Local Universe. It is important to see how this relation evolves with cosmic time. To investigate how galaxy assembly took place with cosmic time, we explore the evolution of the morphology-density relation up to redshift z~1 using about 10000 galaxies drawn from the zCOSMOS Galaxy Redshift Survey. Taking advantage of accurate HST/ACS morphologies from the COSMOS survey, of the well-characterised zCOSMOS 3D environment, and of a large sample of galaxies with spectroscopic redshift, we want to study here the evolution of the morphology-density relation up to z~1 and its dependence on galaxy luminosity and stellar mass. The multi-wavelength coverage of the field also allows a first study of the galaxy morphological segregation dependence on colour. We further attempt to disentangle between processes that occurred early in the history of the Universe or late in the life of galaxies. The zCOSMOS field benefits of high-resolution imaging in the F814W filter from the Advanced Camera for Survey (ACS). We use standard morphology classifiers, optimised for being robust against band-shifting and surface brightness dimming, and a new, objective, and automated method to convert morphological parameters into early, spiral, and irregular types. We use about 10000 galaxies down to I_AB=22.5 with a spectroscopic sampling rate of 33% to characterise the environment of galaxies up to z~1 from the 100 kpc scales of galaxy groups up to the 100 Mpc scales of the cosmic web. ABRIDGEDComment: 23 pages, 12 figures, accepted for publication in Astronomy and Astrophysic

An alternative solution to the model structure selection problem

An alternative solution to the model structure selection problem is introduced by conducting a forward search through the many possible candidate model terms initially and then performing an exhaustive all subset model selection on the resulting model. An example is included to demonstrate that this approach leads to dynamically valid nonlinear model