Images decomposition attracts much attention in recent years. Many variational methods were proposed. The most famous variational decomposition model is OSV model because of its concise expression. However, the OSV model suffers from many drawbacks. One is that the discretization of the EularLagrange equation is hard because the 4th order term was introduced. The other drawback is that the effe...

As one of the recently proposed algorithms for sparse system identification, l0 norm constraint Least Mean Square (l0-LMS) algorithm modifies the cost function of the traditional method with a penalty of tap-weight sparsity. The performance of l0-LMS is quite attractive compared with its various precursors. However, there has been no detailed study of its performance. This paper presents compre...

The leastmean p-power (LMP) is one of themost popular adaptive filtering algorithms. With a proper p value, the LMP can outperform the traditional least mean square (p = 2), especially under the impulsive noise environments. In sparse channel estimation, the unknown channel may have a sparse impulsive (or frequency) response. In this paper, our goal is to develop new LMP algorithms that can ada...

Given data d ∈ R , we consider its representation u involving the least number of non-zero elements (denoted by l0(u∗)) using a dictionary A (represented by a matrix) under the constraint ‖Au− d‖ ≤ τ , for τ > 0 and a norm ‖.‖. This (nonconvex) optimization problem leads to the sparsest approximation of d. We assume that data d are uniformly distributed in θBfd (1) where θ>0 and Bfd (1) is the ...

For a bounded system of linear equalities and inequalities we show that the NP-hard l0 norm minimization problem min x ‖x‖0 subject to Ax = a, Bx ≥ b and ‖x‖∞ ≤ 1, is completely equivalent to the concave minimization min x ‖x‖p subject to Ax = a, Bx ≥ b and ‖x‖∞ ≤ 1, for a sufficiently small p. A local solution to the latter problem can be easily obtained by solving a provably finite number of ...

aiXi and γ(a)Y are identically distributed, where γ : R → [0,∞) is called the standard of X. An old problem is to characterize those functions γ that can appear as the standard of an n-dimensional version. In this paper, we prove the conjecture of Lisitsky that every standard must be the norm of a space that embeds in L0. This result is almost optimal, as the norm of any finite dimensional subs...

In this Letter, we present a novel class of diffusion algorithms that can be used to estimate the coefficients of sparse Volterra network (SVN). The development of the algorithms is based on the logarithmic cost and l0-norm constraint. Simulations for Gaussian and impulsive scenarios are conducted to demonstrate the superior performance of the proposed algorithms as compared with the existing a...

Underwater acoustic channels (UWA) are usually sparse, which can be exploited for adaptive equalization to improve the system performance. For shallow UWA channels, based on proportional minimum symbol error rate (PMSER) criterion, framework requires sparsity selection. Since of L0 norm is stronger than that L1, we choose it achieve better convergence. However, because leads NP-hard problems, d...

We construct a quasi-Banach space which cannot be given an equivalent plurisubharmonic quasi-norm, but such that it has a quotient by a onedimensional space which is a Banach space. We then use this example to construct a compact convex set in a quasi-Banach space which cannot be atfinely embedded into the space L0 of all measurable functions.