*Correspondence: [email protected] School of Science, Lanzhou University of Technology, Lanzhou, Gansu 730050, P.R. China Abstract This paper is devoted to identifying an unknown source for a time-fractional diffusion equation with variable coefficients in a general bounded domain. This is an ill-posed problem. Firstly, we obtain a regularization solution by the Landweber iterative regularizatio...

Based on the block compressed sensing (BCS) framework, a new and non-orthogonal transform named all phase biorthogonal transform (APBT) is introduced to exploit the image sparsity, reduce the encoding complexity and be applicable to the blocked image easily. APBT exploits the signal sparsity better than DCT, and meanwhile it overcomes the defects of multiscale transform such as wavelet transfor...

In this paper, we study a family of gradient descent algorithms to approximate the regression function from reproducing kernel Hilbert spaces. Here early stopping plays a role of regularization, where given a finite sample and some regularity condition on the regression function, a stopping rule is given and some probabilistic upper bounds are obtained for the distance between the function iter...

The extended-domain-eigenfunction method (EDEM) proposed for solving elliptic boundary value problems on annular-like domains requires an inversion process. The procedure thus represents an ill-posed problem, whose numerical solution involves an ill-conditioned system of equations. In this paper, the ill-posed nature of EDEM is studied and numerical solutions based on regularization schemes are...

generalization was given by Atiyah and Hirzebruch [AH], which states that ∧ Agenus of a closed oriented smooth spin manifold is an even integer. Landweber [La] shows that we can use the elliptic genus to get the Ochanine result directly from the divisibility results of Atiyah and Hizebruch [AH]. In 1972, Rokhlin [R2] established a congruence formula of the type φ(B) ≡ Sign(M)−Sign(B·B) 8 mod 2Z...

In this paper, we present a new deconvolution method, able to deal with noninvertible blurring functions. To avoid noise amplification, a prior model of the image to be reconstructed is used within a Bayesian framework. We use a spatially adaptive prior, defined with a complex wavelet transform in order to preserve shift invariance and to better restore variously oriented features. The unknown ...

The goal of this chapter is the construction of the presheaf of elliptic homology theories on the moduli stack of elliptic curves Mell . This sets the stage for many of the later chapters where the objective will be to turn this presheaf into to a sheaf of E∞-ring spectra (using obstruction theory). Even though we use the language of stacks, much of this chapter is closely related to the classi...

Electromagnetic tomography technology is a new process tomography technology. The aim of this study is to develop a new image reconstruction algorithm suitable to electromagnetic tomography and verify its convergence. The advantages and development of electromagnetic tomography technology and image reconstruction algorithms are introduced briefly. Based on conjugate gradient algorithm, modified...

In this paper, we consider nonlinear inverse problems where the solution is assumed to have a sparse expansion with respect to a preassigned basis or frame. We develop a scheme which allows to minimize a Tikhonov functional where the usual quadratic regularization term is replaced by a one–homogeneous (typically weighted `p) penalty on the coefficients (or isometrically transformed coefficients...

In their 2007 paper, Jarvis, Kaufmann, and Kimura defined the full orbifold K-theory of an orbifold X, analogous to the Chen-Ruan orbifold cohomology of X in that it uses the obstruction bundle as a quantum correction to the multiplicative structure. We give an explicit algorithm for the computation of this orbifold invariant in the case when X arises as an abelian symplectic quotient. Our meth...