We prove new results about the robustness of well-known convex noise-blind optimization formulations for reconstruction low-rank matrices from an underdetermined system random linear measurements. Specifically, our address Hermitian rank-one measurements as used in a version phase retrieval problem; that is, each measurement can be represented inner product unknown matrix and outer given realiz...

We consider the following oblivious sketching problem: given ∈ (0, 1/3) and n ≥ d/ 2, design a distribution D over Rk×nd and a function f : R × R → R, so that for any n× d matrix A, Pr S∼D [(1− )‖A‖op ≤ f(S(A), S) ≤ (1 + )‖A‖op] ≥ 2/3, where ‖A‖op = supx:‖x‖2=1 ‖Ax‖2 is the operator norm of A and S(A) denotes S ·A, interpreting A as a vector in R. We show a tight lower bound of k = Ω(d2/ 2) for...

The nuclear norm minimization (NNM) is a special non-convex rank convex relaxation scheme for image denoising and object detection that requires background subtraction. Considering excessive shrinkage of components equal treatment different components, NNM extended to the weighted Schatten-p (WSNM) with weights assigned singular values. In this paper, multi-channel truncated WSNM model based on...

Let A be a C∗-algebra. We prove that every absolutely summing operator from A into l2 factors through a Hilbert space operator that belongs to the 4-Schatten-von Neumann class. We also provide finite dimensional examples that show that one can not replace the 4-Schatten-von Neumann class by p-Schatten-von Neumann class for any p < 4. As an application, we show that there exists a modulus of cap...

Our first aim is to clarify the results obtained by Lidskii devoted decomposition on root vector system of non-selfadjoint operator. We use a technique entire function theory and introduce so-called Schatten–von Neumann class convergence exponent. Considering strictly accretive operators satisfying special conditions formulated in terms norm, we construct sequence contours power type that contr...

The density matrices are positively semi-definite Hermitian matrices of unit trace that describe the state of a quantum system. The goal of the paper is to develop minimax lower bounds on error rates of estimation of low rank density matrices in trace regression models used in quantum state tomography (in particular, in the case of Pauli measurements) with explicit dependence of the bounds on t...

The quantum speed limit is a fundamental upper bound on the speed of quantum evolution.However, the actualmathematical expression of this fundamental limit depends on the choice of ameasure of distinguishability of quantum states.We show that quantum speed limits are qualitatively governed by the Schatten-p-normof the generator of quantumdynamics. Since computing Schatten-p-norms can bemathemat...

Splitting-based CT reconstruction algorithms decompose the reconstruction problem into a iterated sequence of “easier” subproblems. One relatively memory-efficient algorithm decomposes the reconstruction problem into a several subproblems, including a volume denoising problem. While easier to solve in isolation than jointly, these subproblems have highly shiftvarying Hessians that are challengi...

We use the method of interlacing families polynomials to derive a simple proof Bourgain and Tzafriri’s Restricted Invertibility Principle, then sharpen result in two ways. show that stable rank can be replaced by Schatten 4-norm tighter bounds hold when number columns matrix under consideration does not greatly exceed its rows. Our are derived from an analysis smallest zeros Jacobi associated L...