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This paper demonstrates that if the restricted isometry constant &#x03B4;<i>K</i>+1 of the measurement matrix A satisfies [&#x03B4;<i>K</i>+1 &lt;; 1 &#x221A;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(More)
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) u1, u2, v1, v2 with real coefficients and symmetry such that [ u1(z) v1(z) u2(z) v2(z) ] [ u1(1/z) u2(1/z) v1(1/z) v2(1/z) ] = M(z) ∀ z ∈ C\{0} and(More)
Starting from any two compactly supported d-refinable function vectors in ( L2(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 L2(R) and they achieve the best possible orders of vanishing moments. When all(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)
Let φ be a compactly supported symmetric real-valued refinable function in L2(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, ψ and ψ such that (i) All the wavelet functions ψ, ψ and ψ are compactly supported,(More)
Support recovery of sparse signals from noisy measurements with orthogonal matching pursuit (OMP) has been extensively studied in the literature. In this paper, we show that for any K-sparse signal x, if the sensing matrix A satisfies the restricted isometry property (RIP) of order K+1 with restricted isometry constant (RIC) &#x03B4;<sub>K+1</sub> &lt;;(More)
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 peak detection(More)
Support recovery of sparse signals from noisy measurements with orthogonal matching pursuit (OMP) has been extensively studied. In this paper, we show that for any <inline-formula><tex-math notation="LaTeX">$K$</tex-math> </inline-formula>-sparse signal <inline-formula><tex-math notation="LaTeX">${\boldsymbol{x}}$</tex-math> </inline-formula>, if a sensing(More)