Blind Demixing for Low-Latency Communication

In the next generation wireless networks, lowlatency communication is critical to support emerging diversified applications, e.g., Tactile Internet and Virtual Reality. In this paper, a novel blind demixing approach is developed to reduce the channel signaling overhead, thereby supporting low-latency communication. Specifically, we develop a low-rank approach to recover the original information only based on a single observed vector without any channel estimation. Unfortunately, this problem turns out to be a highly intractable non-convex optimization problem due to the multiple non-convex rankone constraints. To address the unique challenges, the quotient manifold geometry of product of complex asymmetric rankone matrices is exploited by equivalently reformulating original complex asymmetric matrices to the Hermitian positive semidefinite matrices. We further generalize the geometric concepts of the complex product manifolds via element-wise extension of the geometric concepts of the individual manifolds. A scalable Riemannian trust-region algorithm is then developed to solve the blind demixing problem efficiently with fast convergence rates and low iteration cost. Numerical results will demonstrate the algorithmic advantages and admirable performance of the proposed algorithm compared with the state-of-art methods.Comment: 14 pages, accepted by IEEE Transaction on Wireless Communicatio

Non-parametric PSF estimation from celestial transit solar images using blind deconvolution

Context: Characterization of instrumental effects in astronomical imaging is important in order to extract accurate physical information from the observations. The measured image in a real optical instrument is usually represented by the convolution of an ideal image with a Point Spread Function (PSF). Additionally, the image acquisition process is also contaminated by other sources of noise (read-out, photon-counting). The problem of estimating both the PSF and a denoised image is called blind deconvolution and is ill-posed. Aims: We propose a blind deconvolution scheme that relies on image regularization. Contrarily to most methods presented in the literature, our method does not assume a parametric model of the PSF and can thus be applied to any telescope. Methods: Our scheme uses a wavelet analysis prior model on the image and weak assumptions on the PSF. We use observations from a celestial transit, where the occulting body can be assumed to be a black disk. These constraints allow us to retain meaningful solutions for the filter and the image, eliminating trivial, translated and interchanged solutions. Under an additive Gaussian noise assumption, they also enforce noise canceling and avoid reconstruction artifacts by promoting the whiteness of the residual between the blurred observations and the cleaned data. Results: Our method is applied to synthetic and experimental data. The PSF is estimated for the SECCHI/EUVI instrument using the 2007 Lunar transit, and for SDO/AIA using the 2012 Venus transit. Results show that the proposed non-parametric blind deconvolution method is able to estimate the core of the PSF with a similar quality to parametric methods proposed in the literature. We also show that, if these parametric estimations are incorporated in the acquisition model, the resulting PSF outperforms both the parametric and non-parametric methods.Comment: 31 pages, 47 figure

Advanced signal processing methods in dynamic contrast enhanced magnetic resonance imaging

Tato dizertační práce představuje metodu zobrazování perfúze magnetickou rezonancí, jež je výkonným nástrojem v diagnostice, především v onkologii. Po ukončení sběru časové sekvence T1-váhovaných obrazů zaznamenávajících distribuci kontrastní látky v těle začíná fáze zpracování dat, která je předmětem této dizertace. Je zde představen teoretický základ fyziologických modelů a modelů akvizice pomocí magnetické rezonance a celý řetězec potřebný k vytvoření obrazů odhadu parametrů perfúze a mikrocirkulace v tkáni. Tato dizertační práce je souborem uveřejněných prací autora přispívajícím k rozvoji metodologie perfúzního zobrazování a zmíněného potřebného teoretického rozboru.This dissertation describes quantitative dynamic contrast enhanced magnetic resonance imaging (DCE-MRI), which is a powerful tool in diagnostics, mainly in oncology. After a time series of T1-weighted images recording contrast-agent distribution in the body has been acquired, data processing phase follows. It is presented step by step in this dissertation. The theoretical background in physiological and MRI-acquisition modeling is described together with the estimation process leading to parametric maps describing perfusion and microcirculation properties of the investigated tissue on a voxel-by-voxel basis. The dissertation is divided into this theoretical analysis and a set of publications representing particular contributions of the author to DCE-MRI.