Since the matrix formed by nonlocal similar patches in a natural image is of low rank, the nuclear norm minimization (NNM) has been widely used for image restoration. However, NNM tends to over-shrink the rank components and treats the different rank components equally, thus limits its capability and flexibility. This paper proposes a new approach for image restoration based ADMM framework via ...

Let B(H) be the algebra of all bounded linear operators on a complex separable infinite dimensional Hilbert space H. In this paper we minimize the Schatten Cp-norm of suitable affine mappings from B(H) to Cp, using convex and differential analysis (Gâteaux derivative) as well as input from operator theory. The mappings considered generalize Penrose’s inequality which asserts that if A and B den...

The CUR decomposition is a factorization of low-rank matrix obtained by selecting certain column and row submatrices it. We perform thorough investigation what happens to such decompositions in the presence noise. Since are nonuniquely formed, we investigate several variants give perturbation estimates for each terms magnitude noise broad class norms which includes all Schatten $p$-norms. given...

Abstract We study the classical Hermite–Hadamard inequality in matrix setting. This leads to a number of interesting inequalities such as Schatten p -norm estimates $$ \begin{align*}\left(\|A^q\|_p^p + \|B^q\|_p^p\right)^{1/p} \le \|(xA+(1-x)B)^q\|_p+ \|((1-x)A+xB)^q\|_p, \end{align*} for all positive (semidefinite) $n\times n$ matrices $A,B$ and $0<q,x<1$ . A related decomposition, with ...

In this paper, we considered composition operators on weighted Hilbert spaces of analytic functions and  observed that a formula for the  essential norm, gives a Hilbert-Schmidt characterization and characterizes the membership in Schatten-class for these operators. Also, closed range composition operators  are investigated.

The semidefinite matrix rank minimization, which has a broad range of applications in system control, statistics, network localization, econometrics and so on, is computationally NPhard in general due to the noncontinuous and non-convex rank function. A natural way to handle this type of problems is to substitute the rank function into some tractable surrogates, most popular ones of which inclu...

The maximal roundness of a metric space is quantity that arose in the study embeddings and renormings. In setting Banach spaces, it was shown by Enflo takes on much simpler form. this paper we provide simple computations many standard such as $\ell^{p}$, Lebesgue-Bochner spaces $\ell^{p}(\ell^{q})$ Schatten ideals $S_{p}$. We also introduce property dual to roundness, which call coroundness, ma...

We prove Rubio de Francia’s Littlewood-Paley inequality for arbitrary disjoint intervals in the noncommutative setting, i.e. for functions with values in noncommutative L-spaces. As applications, we get sufficient conditions in terms of q-variation for the boundedness of Schur multipliers on Schatten classes.