Linear spectral unmixing is an effective technique to estimate the abundances of materials present in each hyper-spectral image pixel. Recently, sparse-regression-based unmixing approaches have been proposed to tackle this problem. Mostly, l(1) norm minimization is used to approximate the l(0) norm minimization problem in terms of computational complexity. In this letter, we model the hyperspectral unmixing as a constrained sparse l(p) - l(2)( 0 < p < 1) optimization problem and propose to solve it via the iteratively reweighted least squares algorithm. Experimental results on a series of simulated data sets and a real hyperspectral image demonstrate that the proposed method can achieve performance improvement over the state-of-the-art l(1) - l(2) method.
In this paper we characterize weighted shifts (both unilateral and bilateral) on l (p) spaces that are (m, q)-isometries. We explicitly construct the weights of those operators. Properties of those operators, such as norm, similarity and a Berger-Shaw-type result, are also discussed.
Motivated by the study of existence, uniqueness and regularity of solutions to stochastic partial differential equations driven by jump noise, we prove Ito isomorphisms for L-p-valued stochastic integrals with respect to a compensated Poisson random measure. The principal ingredients for the proof are novel Rosenthal type inequalities for independent random variables taking values in a (noncommutative) L-p-space, which may be of independent interest. As a by-product of our proof, we observe some moment estimates for the operator norm of a sum of independent random matrices.
We prove that, for 1 <=3D p < q < infinity, the partially ordered set P(omega)/Fin can be embedded into Borel equivalence relations between R-omega/l(p) and R-omega/l(q). Since there is an antichain of size continuum in P(omega)/Fin, there are continuum many pairwise incomparable Borel equivalence relations between R-omega/l(p) and R-omega/l(q).
We introduce the generalized area operators by using nonnegative measures defined on upper half-spaces a"e (+) (n+1) . The characterization of the boundedness and compactness of the generalized area operator from L (p) (a"e (n) ) to L (q) (a"e (n) ) is investigated in terms of s-Carleson measures with 1 < p,q < + a. In the case of p = q = 1, the weak type estimate is also obtained.
We present a novel proof of the fact that the spectrum of the CesA ro operator acting in a"" (p) , for 1 < p < a, consists of the closed disc centered at q/2 and with radius q/2, where q is the conjugate index of p.
Recently, compressed sensing has been widely applied to various areas such as signal processing, machine learning, and pattern recognition. To find the sparse representation of a vector w.r.t a dictionary, an l(1) minimization problem, which is convex, is usually solved in order to overcome the computational difficulty. However, to guarantee that the l(1) minimizer is close to the sparsest solution, strong incoherence conditions should be imposed. In comparison, nonconvex minimization problems such as those with the l(p) (0 < p < 1) penalties require much weaker incoherence conditions and smaller signal to noise ratio to guarantee a successful recovery. Hence the l(p) (0 < p < 1) regularization serves as a better alternative to the popular l(1) one. In this paper, we review some typical algorithms, Iteratively Reweighted l(1) minimization (IRL1), Iteratively Reweighted Least Squares (IRLS) (and its general form General Iteratively Reweighted Least Squares (GIRLS)), and Iteratively Thresholding Method (ITM), for l(p) minimization and do comprehensive comparison among them, in which IRLS is identified as having the best performance and being the fastest as well. (C) 2013 Elsevier B.V. All rights reserved.
Zhao, Lingling
Yang, He
Cong, Wenxiang
Wang, Ge
Intes, Xavier
Time domain fluorescence molecular tomography (TD-FMT) provides a unique dataset for enhanced quantification and spatial resolution. The time-gate dataset can be divided into two temporal groups around the maximum counts gate, which are early gates and late gates. It is well established that early gates allow for improved spatial resolution and late gates are essential for fluorophore unmixing and concentration quantification. However, the inverse problem of FMT is ill-posed and typically underdetermined, which makes image reconstruction highly susceptible to data noise. More specifically, photon counts are inherently very low at early gates due to high absorption and scattering of tissue, resulting in a low signal-to-noise ratio and unstable reconstructions. In this work, an L(p) regularization-based reconstruction algorithm was developed and tested with our wide-field mesh-based Monte Carlo simulation strategy. We compared the early time-gate reconstructions obtained with the different p (p{1/16,1/8,1/4,1/3,1/2,1,2}) from a synthetic murine model simulating the fluorophore uptake in the kidneys and preclinical data. The results from a 3D mouse atlas and a mouse experiment show that our L(1/4) regularization methods give the best performance for early time gates reconstructions.=20
For a character chi of a finite group G, it is known that the product sh(chi) = Pi(l epsilon L) (chi(1) - l) is a multiple of vertical bar G vertical bar, where L is the image of chi on G - {1}. chi is said to be a sharp character of type L if sh(chi) = vertical bar G vertical bar. This is a generalization of the permutation characters of sharp permutation groups. Without loss of generality, we may assume that (chi, I(G))(G) = 0. In this paper, we classify the finite groups with sharp characters of type {l, l + p} for an odd prime p under the additional hypothesis Z(G) > 1 and (chi, chi)(G) = P.
Let l and p be two distinct primes. Let K be a local field of characteristic 0 and residue characteristic l. In this paper, we prove existence of local epsilon(0)-constants for representations of Galp (K) over bar /K {Kq over Iwasawa algebras of p-adic Lie groups. Existence of these epsilon(0)-constants was conjectured by Kato (for commutative Iwasawa algebras) and Fukaya-Kato (in general).
The norm of the Riesz projection from L(infinity)(T(n)) to L(p)(T(n)) is considered. It is shown that for n = 1, the norm equals 1 if and only if p <= 4 and that the norm behaves asymptotically as p/(pi e) when p -> infinity. The critical exponent p(n) is the supremum of those p for which the norm equals 1. It is proved that 2 + 2/(2(n) - 1) <= p(n) < 4 for n > 1; it is unknown whether the critical exponent for n = infinity exceeds 2. (C) 2011 Elsevier Masson SAS. All rights reserved.
Partial metric spaces are generalization of metric space. The distance from a point to itself need not be zero in partial metric space. By the properties of metric and partial metric space, we have the analogue of the two spaces. Using the analogue, we construct sequences in l(2)(P) with respect to a partial metric. We then investigate the convergence of sequences in l(2) (P). In this work, we obtain that the convergence of sequences in l(2) (N) can be established in l(2) (P) with respect to a partial metric.