We examine the rate of convergence of the Lasso estimator of lower dimensional components of the high-dimensional parameter. Under bounds on the l1-norm on the worst possible sub-direction these rates are of order √ |J | log p/n where p is the total number of parameters, J ⊂ {1, . . . , p} represents a subset of the parameters and n is the number of observations. We also derive rates in sup-nor...

INTRODUCTION Dynamic magnetic resonance (MR) inverse imaging (InI) can improve the temporal resolution of blood oxygen level dependent (BOLD) contrasts fMRI to the order of milliseconds [1]. In InI, the spatial resolution and the source localization accuracy both critically rely on the signal-to-noise ratio (SNR) of the measurements [1]. The localization of the functional activity in ill-posed ...

Electrical Impedance Tomography (EIT) reconstructs the conductivity distribution within a medium from electrical stimulation and measurements at the medium surface. Level set based reconstruction method (LSRM) has gained attention during the last decade as an effective solution to address the need of reconstructing structures with limited amount of available data. The classical LSRM is based on...

Next-generation aircraft with a large number of actuators will require advanced control allocation methods to compute the actuator commands needed to follow desired trajectories while respecting system constraints. Previously, algorithms were proposed to minimize the l1 or l2 norms of the tracking error and of the actuator deflections. This paper discusses the alternative choice of the l1 norm,...

We propose a new estimator of the regression coefficients for high-dimensional linear model, which is derived by replacing sample predictor covariance matrix in ordinary least square (OLS) with different estimate obtained nuclear norm plus l 1 penalization. call ALgebraic Covariance Estimator-regression (ALCE-reg). make direct theoretical comparison expected mean error ALCE-reg OLS and RIDGE. s...