The solid hulls of the Hardy–Lorentz spaces Hp,q , 0 < p < 1, 0 < q 6∞ and Hp,∞ 0 , 0 < p < 1, as well as of the mixed norm space H p,∞,α 0 , 0 < p 6 1, 0 < α <∞, are determined. Introduction In [JP1] the solid hull of the Hardy space H, 0 < p < 1, is determined. In this article we determine the solid hulls of the Hardy–Lorentz spaces H, 0 < p < 1, 0 < q 6 ∞ and H 0 , 0 < p < 1, as well as of t...

Let (Ω,F,P) be a probability space and L0(F) the algebra of equivalence classes real-valued random variables defined on (Ω,F,P). A left module M over (briefly, an L0(F)-module) is said to regular if x=y for any given two elements x y in such that there exists countable partition {An,n∈N} Ω F I˜An⋅x=I˜An⋅y each n∈N, where IAn characteristic function An I˜An its class. The purpose this paper esta...

Low-dose computed tomography (CT) reconstruction is a challenging problem in medical imaging. To complement the standard filtered back-projection (FBP) reconstruction, sparse regularization reconstruction gains more and more research attention, as it promises to reduce radiation dose, suppress artifacts, and improve noise properties. In this work, we present an iterative reconstruction approach...

In this paper, to monitor the border in real-time with high efficiency and accuracy, we applied the compressed sensing (CS) technology on the border monitoring wireless sensor network (WSN) system and proposed a reconstruction method based on approximately l0 norm and fast gradient descent (AL0FGD) for CS. In the frontend of the system, the measurement matrix was used to sense the border inform...

Greedy algorithms for minimizing L0-norm of sparse decomposition have profound application impact on many signal processing problems. In the sparse coding setup, given the observations y and the redundant dictionary Φ, one would seek the most sparse coefficient (signal) x with a constraint on approximation fidelity. In this work, we propose a greedy algorithm based on the classic orthogonal mat...

Weiwen Wu1,2, Yanbo Zhang2, Qian Wang2, Fenglin Liu1,3,*, Peijun Chen1 and Hengyong Yu2,* 1Key Lab of Optoelectronic Technology and Systems, Ministry of Education, Chongqing University, Chongqing 400044, China 2Department of Electrical and Computer Engineering, University of Massachusetts Lowell, Lowell, MA 01854, USA 3Engineering Research Center of Industrial Computed Tomography Nondestructive...

A new reweighted l1-norm penalized least mean square (LMS) algorithm for sparse channel estimation is proposed and studied in this paper. Since standard LMS algorithm does not take into account the sparsity information about the channel impulse response (CIR), sparsity-aware modifications of the LMS algorithm aim at outperforming the standard LMS by introducing a penalty term to the standard LM...

Subspace recovery from noisy or even corrupted data is critical for various applications in machine learning and data analysis. To detect outliers, Robust PCA (R-PCA) via Outlier Pursuit was proposed and had found many successful applications. However, the current theoretical analysis on Outlier Pursuit only shows that it succeeds when the sparsity of the corruption matrix is of O(n/r), where n...

Frommany fewer acquired measurements than suggested by the Nyquist sampling theory, compressive sensing (CS) theory demonstrates that, a signal can be reconstructed with high probability when it exhibits sparsity in some domain. Most of the conventional CS recovery approaches, however, exploited a set of fixed bases (e.g. DCT, wavelet and gradient domain) for the entirety of a signal, which are...