Fast alternating direction method of multipliers for total-variation-based image restoration

A novel algorithm, i.e. the fast alternating direction method of multipliers （ADMM）, is applied to solve the classical total-variation （ TV ）-based model for image reconstruction. First, the TV-based model is reformulated as a linear equality constrained problem where the objective function is separable. Then, by introducing the augmented Lagrangian function, the two variables are alternatively minimized by the Gauss-Seidel idea. Finally, the dual variable is updated. Because the approach makes full use of the special structure of the problem and decomposes the original problem into several low-dimensional sub-problems, the per iteration computational complexity of the approach is dominated by two fast Fourier transforms. Elementary experimental results indicate that the proposed approach is more stable and efficient compared with some state-of-the-art algorithms.

Multipliers of Hardy Spaces

本文刻划了Hardy空间H^p（1≤p≤∞）到Bloch空间的乘子，推广了前人的结果。

Coefficient Multipliers for Polynomials

Let Q n denote the class of all polynomials p(z) nonvanishing in the unit disk with deg p≤n and p (0)=1, and let W n denote the class of all polynomials s(z) satisfying deg s≤n and for all p∈Q n, s*p∈Q n , where * denotes the Hadamard product. Some properties for W n and Q n are obtained.

Multipliers on Weighted Hardy Spaces over Locally Compact Vilenkin Groups

This paper is devoted to study the atomic decomposition of the weighted Hardy space on Vilenkin groups and a weighted Hp multiplier theorem.

Missile robust gain scheduling autopilot design using full block multipliers

Reduction of conservatism is one of the key and difficult problems in missile robust gain scheduling autopilot design based on multipliers.This article presents a scheme of adopting linear parameter-varying（LPV） control approach with full block multipliers to design a missile robust gain scheduling autopilot in order to eliminate conservatism.A model matching design structure with a high demand on matching precision is constructed based on the missile linear fractional transformation（LFT） model.By applying full block S-procedure and elimination lemma,a convex feasibility problem with an infinite number of constraints is formulated to satisfy robust quadratic performance specifications.Then a grid method is adopted to transform the infinite-dimensional convex feasibility problem into a solvable finite-dimensional convex feasibility problem,based on which a gain scheduling controller with linear fractional dependence on the flight Mach number and altitude is derived.Static and dynamic simulation results show the effectiveness and feasibility of the proposed scheme.

MULTIPLIERS ON HERZ TYPE HARDY SPACES OVER LOCAL FIELDS

In this paper, we establish two multiplier theorems for Herz type Hardy spaces, and as an application, we discuss the boundedness of pseudo-differential operators in these spaces.

CARLESON MEASURES,RIEMANN-STIELTJES OPERATORS AND MULTIPLIERS ON F(p,q,s)SPACES IN THE UNIT BALL OF C^n

This paper is devoted to characterizing the Riemann-Stieltjes operators and pointwise multipliers on F（p, q, s） spaces in the unit ball of C^n which contain many classical function spaces, such as the Bloch space, BMOA and Q8 spaces. The boundedness and compactness of these operators on F（p, q, s） spaces are characterized by means of an embedding theorem, i.e., F（p,q, s） spaces boundedly embedded into the tent-type spaces Tp,s^∞（μ）

MULTIPLIERS AND TENSOR PRODUCTS OF WEIGHTED L^p-SPACES

Let G be a locally compact unimodular group with Haar measure rmdx and ω be the Beurling's weight function on G (Reiter, [10]). In this paper the authors define a space Aωp,q (G) and prove that Aωp,q (G) is a translation invariant Banach space. Fur- thermore the authors discuss inclusion properties and show that if G is a locally compact abelian group then Aωp,q (G) admits an approximate identity bounded in Lω1 (G). It is also proved that the space Lωp (G) Lω1 Lωq (G) is isometrically isomorphic to the space Aωp,q (G) and the space of multipliers from Lωp (G) to Lq-1, (G) is isometrically isomorphic to the dual of the space Aωp,q (G) iff G satisfies a property Ppq. At the end of this work it is showed that if G is a locally compact abelian group then the space of all multipliers from Lω1 (G) to Aωp,q (G) is the space Aωp,q (G).

MULTIPLIERS AND RELATIVE COMPLETION IN WEIGHTED LORENTZ SPACES

Let G be a locally compact Abelian group with Haar measure μ. In the present paper, first the authors discussed some properties of weighted Lorentz space. Then they defined the relative completion A of a subspace A of the weighted Lorentz space, and showed that the space of the multipliers from L_w~1,(G) to A is algebrically isomorphic and homeomorphic to A.

MULTIPLIERS AND TENSOR PRODUCTS OF L(p,q) LORENTZ SPACES

Let G be a locally compact abelian group. The main purpose of this article is to find the space of multipliers from the Lorentz space. L（p1, q1）（G） to L（p＇2, q＇2）（G）. For this reason, the authors define the space A p1,q1^ p2,p2（G）, discuss its properties and prove that the space of multipliers from L（p1, q1）（G） to L（p＇2, q＇2）（G） is isometrically isomorphic to the dual of A p1,q1^p2,q2 （G）.

EXTENDED CESRO OPERATORS AND MULTIPLIERS ON BMOA

In this article, we characterize the boundedness and compactness of extended Cesaro operators on the spaces BMOA by the Carleson measures in the unit ball. Mea while, we study the pointwise multipliers on BMOA.

CHARACTERIZATION OF RESIDUATED LATTICES VIA MULTIPLIERS

In the paper,we introduce some of multipliers on residuated lattices and investigate the relations among them.First,basing on the properties of multipliers,we show that the set of all multiplicative multipliers on a residuated lattice A forms a residuated lattice which is isomorphic to A.Second,we prove that the set of all total multipliers on A is a Boolean subalgebra of the residuated lattice(which is constituted by all multiplicative multipliers on A)and is isomorphic to the Boolean center of A.Moreover,by partial multipliers,we study the maximal residuated lattices of quotients for residuated lattices.Finally,we focus on principal implicative multipliers on residuated lattices and obtain that the set of principal implicative multipliers on A is isomorphic to the set of all multiplicative multipliers on A under the opposite(dual)order.

BILINEAR SPECTRAL MULTIPLIERS ON HEISENBERG GROUPS

As we know,thus far,there has appeared no definition of bilinear spectral multipliers on Heisenberg groups.In this article,we present one reasonable definition of bilinear spectral multipliers on Heisenberg groups and investigate its boundedness.We find some restrained conditions to separately ensure its boundedness from C0(H^(n))×L^(2)(H^(n))to L^(2)(H^(n)),from L2(H^(n))×C0(H^(n))to L^(2)(H^(n)),and from L^(p)×L^(q) to L^(r) with 2<p,q<∞,2≤r≤∞.

Some Applications of E-wavelet Multipliers

Let E= .A measurable function v is called an E- waveletmultiplier if (vψ) is an E-wavelet whenever ψ is an E-wavelet. Some characterizations and applications of E-wavelet multiplier were considered in [1]. In this paper, we give some other applications of E-wavelet multiplier, and prove that the set of all MRA E-wavelets is arcwise connected.

POINTWISE MULTIPLIERS FOR LOCALIZED MORREY-CAMPANATO SPACES ON RD-SPACES

In this article, the authors characterize pointwise multipliers for localized MorreyCampanato spaces, associated with some admissible functions on RD-spaces, which include localized BMO spaces as a special case. The results obtained are applied to Schrdinger operators and some Laguerre operators.

Reconstruction of electrical capacitance tomography images based on fast linearized alternating direction method of multipliers for two-phase flow system

Electrical capacitance tomography(ECT)has been applied to two-phase flow measurement in recent years.Image reconstruction algorithms play an important role in the successful applications of ECT.To solve the ill-posed and nonlinear inverse problem of ECT image reconstruction,a new ECT image reconstruction method based on fast linearized alternating direction method of multipliers(FLADMM)is proposed in this paper.On the basis of theoretical analysis of compressed sensing(CS),the data acquisition of ECT is regarded as a linear measurement process of permittivity distribution signal of pipe section.A new measurement matrix is designed and L1 regularization method is used to convert ECT inverse problem to a convex relaxation problem which contains prior knowledge.A new fast alternating direction method of multipliers which contained linearized idea is employed to minimize the objective function.Simulation data and experimental results indicate that compared with other methods,the quality and speed of reconstructed images are markedly improved.Also,the dynamic experimental results indicate that the proposed algorithm can ful fill the real-time requirement of ECT systems in the application.

Nested Alternating Direction Method of Multipliers to Low-Rank and Sparse-Column Matrices Recovery

The task of dividing corrupted-data into their respective subspaces can be well illustrated,both theoretically and numerically,by recovering low-rank and sparse-column components of a given matrix.Generally,it can be characterized as a matrix and a 2,1-norm involved convex minimization problem.However,solving the resulting problem is full of challenges due to the non-smoothness of the objective function.One of the earliest solvers is an 3-block alternating direction method of multipliers(ADMM)which updates each variable in a Gauss-Seidel manner.In this paper,we present three variants of ADMM for the 3-block separable minimization problem.More preciously,whenever one variable is derived,the resulting problems can be regarded as a convex minimization with 2 blocks,and can be solved immediately using the standard ADMM.If the inner iteration loops only once,the iterative scheme reduces to the ADMM with updates in a Gauss-Seidel manner.If the solution from the inner iteration is assumed to be exact,the convergence can be deduced easily in the literature.The performance comparisons with a couple of recently designed solvers illustrate that the proposed methods are effective and competitive.

Multipliers into Sequence Spaces

This paper describes characteristics of (A p,α,l q) with 0【p≤1,α】0 and p≤q≤∞. As the corollaries, the characteristics of (A p,l q),(H p,l q),(G p,l q) and (B p,l q) with 0【p≤1 and p≤q≤∞ are obtained. (H p,l q) and (H p,H q) with 1【p【∞ and 1≤q≤∞ are also studied.

Distributed Alternating Direction Method of Multipliers for Multi-Objective Optimization

In this paper, a distributed algorithm is proposed to solve a kind of multi-objective optimization problem based on the alternating direction method of multipliers. Compared with the centralized algorithms, this algorithm does not need a central node. Therefore, it has the characteristics of low communication burden and high privacy. In addition, numerical experiments are provided to validate the effectiveness of the proposed algorithm.

Characteristics of Coefficient Multipliers to G^q Spaces

In this paper, we give the characteristics of the coefficient multipliers from H p,G p,B p(0【p【1) and A p(0【p≤1) to G q(1≤q【∞), from G p to G q(1≤p≤q【∞).