The sparsity of underdetermined linear system via lp minimization for 0 < p < 1

The sparsity problems have attracted a great deal of attention in recent years, which aim to find the sparsest solution of a representation or an equation. In the paper, we mainly study the sparsity of underdetermined linear system via lp minimization for 0 0 such that the following conclusions hold when p < γ(A, b): (1) the problem (pp) generates sparser solution as the value of p decreases; (2) the sparsest optimal solution to the problem (pp) is unique under the sense of absolute value permutation; (3) let X1 and X2 be the sparsest optimal solution to the problems (pp1) and (pp2) , respectively, and let X1 not be the absolute value permutation of X2. Then there exist t1,t2 ε [p1,p2] such that X1 is the sparsest optimal solution to the problem (pt) (∀t ε [p1, t1]) and X2 is the sparsest optimal solution to the problem (pt) (∀t ε (t2, p2])

NP/CMP equivalence: a phenomenon hidden among sparsity models l_{0} minimization and l_{p} minimization for information processing

In this paper, we have proved that in every underdetermined linear system Ax = b, there corresponds a constant p*(A, b) > 0 such that every solution to the l p-norm minimization problem also solves the l0-norm minimization problem whenever 0 <; p <; p*(A, b). This phenomenon is named NP/CMP equivalence

Pulse-duration dependence of high-order harmonic generation with coherent superposition state

We make a systematic study of high-order harmonic generation (HHG) in a He$^+$-like model ion when the initial states are prepared as a coherent superposition of the ground state and an excited state. It is found that, according to the degree of the ionization of the excited state, the laser intensity can be divided into three regimes in which HHG spectra exhibit different characteristics. The pulse-duration dependence of the HHG spectra in these regimes is studied. We also demonstrate evident advantages of using coherent superposition state to obtain high conversion efficiency. The conversion efficiency can be increased further if ultrashort laser pulses are employed