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Let M be a 2 × 2 matrix of Laurent polynomials with real coefficients and symmetry. In this paper, we obtain a necessary and sufficient condition for the existence of four Laurent polynomials (or FIR filters) u 1 , u 2 , v 1 , v 2 with real coefficients and symmetry such that u 1 (z) v 1 (z) u 2 (z) v 2 (z) u 1 (1/z) u 2 (1/z) v 1 (1/z) v 2 (1/z) = M (z) ∀(More)
—This paper demonstrates that if the restricted isom-etry constant δK+1 of the measurement matrix A satisfies δK+1 < 1 √ K + 1 , then a greedy algorithm called Orthogonal Matching Pursuit (OMP) can recover every K–sparse signal x in K iterations from Ax. By contrast, a matrix is also constructed with the restricted isometry constant δK+1 = 1 √ K such that(More)
Let φ be a compactly supported symmetric real-valued refinable function in L 2 (R) with a finitely supported symmetric real-valued mask on Z. Under the assumption that the shifts of φ are stable, in this paper we prove that one can always construct three wavelet functions ψ 1 , ψ 2 and ψ 3 such that (i) All the wavelet functions ψ 1 , ψ 2 and ψ 3 are(More)
For prescribed values of a function and its partial derivatives of orders 1 and 2 at the vertices of a square, we fit an interpolating surface. We investigate two families of solutions provided by two Hermite subdivision schemes, denoted HD 2 and HR 2. Both schemes depend on 2 matrix parameters, a square matrix of order 2 and a square matrix of order 3. We(More)
BACKGROUND Quantitative proteomics technologies have been developed to comprehensively identify and quantify proteins in two or more complex samples. Quantitative proteomics based on differential stable isotope labeling is one of the proteomics quantification technologies. Mass spectrometric data generated for peptide quantification are often noisy, and(More)
Although tensor product real-valued wavelets have been successfully applied to many high-dimensional problems, they can only capture well edge singularities along the coordinate axis directions. As an alternative and improvement of tensor product real-valued wavelets and dual tree complex wavelet transform, recently tensor product complex tight framelets(More)
This paper demonstrates theoretically that if the restricted isometry constant $\delta_K$ of the compressed sensing matrix satisfies $$ \delta_{K+1}<\frac{1}{\sqrt{K}+1}, $$ then a greedy algorithm called Orthogonal Matching Pursuit (OMP) can recover a signal with $K$ nonzero entries in $K$ iterations. In contrast, matrices are also constructed with(More)