This paper presents a new video restoration scheme based on the joint sparse and lowrank matrix approximation. By grouping similar patches in the spatiotemporal domain, we formulate the video restoration problem as a joint sparse and low-rank matrix approximation problem. The resulted nuclear norm and `1 norm related minimization problem can also be efficiently solved by many recently developed...

Kippenhahn's Theorem asserts that the numerical range of a matrix is convex hull certain algebraic curve. Here, we show joint finitely many Hermitian matrices similarly semi-algebraic set. We discuss an analogous statement regarding dual cone to hyperbolicity and prove class bases these cones closed under linear operations. The result offers new geometric method analyze quantum states.

This paper is concerned with the minimization of roundoff noise subject to 2-norm dynamic-range scaling constraints in two-dimensional (2-D) state-space digital filters. Two methods are proposed, with the first one using error feedback alone and the second one using joint error feedback and coordinate transformation optimization. In the first method, several techniques for the determination of ...

In this paper, we collect a few fairly well known facts about the numerical range and assemble them into an effective algorithm for computing the numerical range of an n× n matrix. Particular attention is paid to the case in which a line segment is embedded in the boundary of the numerical range, a case in which multiplicity is present. The result is a parametrization of the curve that forms th...

In this note, a generalization of higher rank numerical range isintroduced and some of its properties are investigated

The main purpose of this article is to show that the numerical range a linear pencil λA+B equal C if and only 0 belongs convex hull joint A B. We also prove A+A⁎,B+B⁎⩾0, then B have common isotropic vector. Moreover, we improve classical result which describes Hermitian pencils.

This paper studies the possibilities of the Linear Matrix Inequality (LMI) characterization of the matrix cones formed by nonnegative complex Hermitian quadratic functions over specific domains in the complex space. In its real case analog, such studies were conducted in Sturm and Zhang [11]. In this paper it is shown that stronger results can be obtained for the complex Hermitian case. In part...