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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)

We shall show that if the restricted isometry constant (RIC) δ s+1 (A) of the measurement matrix A satisfies δ s+1 (A) < 1 √ s + 1 , then the greedy algorithm Orthogonal Matching Pursuit(OMP) will succeed. That is, OMP can recover every s-sparse signal x in s iterations from b = Ax. Moreover, we shall show the upper bound of RIC is sharp in the following… (More)

Starting from any two compactly supported d-refinable function vectors in L 2 (R) r with multiplicity r and dilation factor d, we show that it is always possible to construct 2rd wavelet functions with compact support such that they generate a pair of dual d-wavelet frames in L 2 (R) and they achieve the best possible orders of vanishing moments. When all… (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)

- Fan Mo, Qun Mo, Yuanyuan Chen, David R. Goodlett, Leroy Hood, Gilbert S. Omenn +2 others
- BMC Bioinformatics
- 2010

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)

- BIN HAN, QUN MO, ZUOWEI SHEN
- 2010

a family of uni-variate short support Riesz wavelets was constructed from uniform B-splines. A bivariate spline Riesz wavelet basis from the Loop scheme was derived in [B. Motivated by these two papers, we develop in this article a general theory and a construction method to derive small support Riesz wavelets in low dimensions from refinable functions. In… (More)