Regularization plays a crucial role in reliably utilizing imaging systems for scientific and medical investigations. It helps to stabilize the process of computationally undoing any degradation caused by physical limitations process. In past decades, total variation regularization played dominant literature. Two forms regularizations, namely first-order second-order (TV-1 TV-2) have been widely...

Low-rank tensor recovery has attracted much attention among various approaches. A rank several definitions, unlike the matrix rank—e.g., CP and Tucker rank. Many low-rank methods are focused on Since is nonconvex discontinuous, many relaxations of have been proposed, e.g., sum nuclear norm, weighted schatten-p norm. In particular, norm two parameters, weight p, special cases these parameters. H...

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 private quantum channel (PQC) maps any state to the maximally mixed for discrete as well bosonic Gaussian systems, and it has fundamental meaning on cryptographic tasks capacity problems. In this paper, we primally introduce a notion of approximate (ε-PQC) fermionic systems (i.e., ε-FPQC), construct its explicit form (Gaussian) channel. First all, suggest general structure ε-FPQC with respe...

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...

Let E and P be nonnegative quadratic forms in a Hilbert space H and assume that E + bP is densely defined and closed for every b ≥ 0. For every b > 0 let Hb be the self-adjoint operator associated with E + bP in the sense of Kato’s representation theorem. By Kato’s monotone convergence theorem, the operators (Hb + 1) −1 converge strongly to an operator L, as b tends to infinity. Let k ∈ N. We g...

In this paper we study general Schatten-p quasi-norm (SPQN) regularized matrix minimization problems. In particular, we first introduce a class of first-order stationary points for them, and show that the first-order stationary points introduced in [11] for an SPQN regularized vector minimization problem are equivalent to those of an SPQN regularized matrix minimization reformulation. We also s...

In this paper, we characterize holomorphic functions / such that the Hankel operators Hj are in the Schatten classes on bounded strongly pseudoconvex domains. It is proved that for p > In , Hj is in the Schatten class Sp if and only if / is in the Besov space Bp ; for p < In , Hj is in the Schatten class Sp if and only if / = constant.

The famous Dantzig estimator(DE) has been applied in quantum state tomography for estimating an unknown low rank density matrix. The density matrices are positively semi-definite Hermitian matrices with unit trace that describe the states of quantum systems. The main contribution of this paper is deriving the low rank oracle inequality of DE and proving its convergence rates in the Schatten p-n...

The Schatten norm for the nuclear operator B*?B? was estimated from both sides. Here B? : L2 ? is Berezin transform regarding Fock spaces in plane. Also, we found case of unweighted Lebesgue spaces.