Compressed Sensing and Redundant Dictionaries
نویسندگان
چکیده
منابع مشابه
Compressed Sensing with Coherent and Redundant Dictionaries
This article presents novel results concerning the recovery of signals from undersampled data in the common situation where such signals are not sparse in an orthonormal basis or incoherent dictionary, but in a truly redundant dictionary. This work thus bridges a gap in the literature and shows not only that compressed sensing is viable in this context, but also that accurate recovery is possib...
متن کاملA Second-order Method for Compressed Sensing Problems with Coherent and Redundant Dictionaries
In this paper we are interested in the solution of Compressed Sensing (CS) problems where the signals to be recovered are sparse in coherent and redundant dictionaries. CS problems of this type are convex with non-smooth and non-separable regularization term, therefore a specialized solver is required. We propose a primal-dual Newton Conjugate Gradients (pdNCG) method. We prove global convergen...
متن کاملAdaptive Compressed Image Sensing Using Dictionaries
In recent years, the theory of Compressed Sensing has emerged as an alternative for the Shannon sampling theorem, suggesting that compressible signals can be reconstructed from far fewer samples than required by the Shannon sampling theorem. In fact the theory advocates that non-adaptive, ‘random’ functionals are in some sense optimal for this task. However, in practice, Compressed Sensing is v...
متن کاملPerturbations of Measurement Matrices and Dictionaries in Compressed Sensing
The compressed sensing problem for redundant dictionaries aims to use a small number of linear measurements to represent signals that are sparse with respect to a general dictionary. Under an appropriate restricted isometry property for a dictionary, reconstruction methods based on ` minimization are known to provide an effective signal recovery tool in this setting. This note explores conditio...
متن کاملCompressed Sensing Electron tomography using adaptive dictionaries: a simulation study
Electron tomography (ET) is an increasingly important technique for examining the three-dimensional morphologies of nanostructures. ET involves the acquisition of a set of 2D projection images to be reconstructed into a volumetric image by solving an inverse problem. However, due to limitations in the acquisition process this inverse problem is considered illposed (i.e., no unique solution exis...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: IEEE Transactions on Information Theory
سال: 2008
ISSN: 0018-9448
DOI: 10.1109/tit.2008.920190