We study time-frequency localization operators of the form A12 a , where a is the symbol of the operator and φ1, φ2 are the analysis and synthesis windows, respectively. It is shown in [3] that a sufficient condition for A12 a ∈ Sp(L(R)), the Schatten class of order p, is that a belongs to the modulation space Mp,∞(R2d) and the window functions to the modulation space M1. Here we prove a partia...

We study a new class of structured Schatten norms for tensors that includes two recently proposed norms (“overlapped” and “latent”) for convex-optimization-based tensor decomposition. Based on the properties of the structured Schatten norms, we analyze the performance of “latent” approach for tensor decomposition, which was empirically found to perform better than the “overlapped” approach in s...

The largest volume ratio of a given convex body $K \subset \mathbb R^n$ is defined as $$ \mathrm{lvr}(K):= \mathrm {sup}\_{L R^n} {vr}(K,L), where the sup runs over all bodies $L$. We prove following sharp lower bound: c \sqrt{n} \leq \mathrm{lvr}(K), for every $K$ (where $c > 0$ an absolute constant). This result improves former best known bound, order $\sqrt{{n}/{\log \log(n)}}$. also study e...

In this paper, we prove that each of the following functions is convex on R: f(t) = wN(AtXA1?t ? A1?tXAt), g(t) wN(AtXA1?t), and h(t) wN(AtXAt) where A > 0, X Mn N(.) a unitarily invariant norm onMn. Consequently, answer positively question concerning convexity function t w(AtXAt) proposed by in (2018). We provide some generalizations extensions wN(.) using Kwong functions. More precisely, w...

Low-rank matrix decomposition approaches have achieved significant progress in small and dim object detection satellite videos. However, it is still challenging to achieve robust performance fast processing under complex highly heterogeneous backgrounds since video data can neither adequately fit the foreground structure nor background model existing models. In this letter, we propose a novel m...

We consider Tikhonov and sparsity-promoting regularization in Banach spaces for inverse scattering from penetrable anisotropic media. To this end, we equip an admissible set of material parameters with the L-topology and use Meyers’ gradient estimate for solutions of elliptic equations to analyze the dependence of scattered fields and their Fréchet derivatives on the material parameter. This al...

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 ...