We present an iterative deconvolution algorithm that minimizes a functional with a non-quadratic waveletdomain regularization term. Our approach is to introduce subband-dependent parameters into the bound optimization framework of Daubechies et al.; it is sufficiently general to cover arbitrary choices of wavelet bases (non-orthonormal or redundant). The resulting procedure alternates between t...

In this paper we investigate convergence of Landweber iteration in Hilbert scales for linear and nonlinear inverse problems. As opposed to the usual application of Hilbert scales in the framework of regularization methods, we focus here on the case s ≤ 0, which (for Tikhonov regularization) corresponds to regularization in a weaker norm. In this case, the Hilbert scale operator L−2s appearing i...

We classify the indecomposable injective E(n)∗E(n)-comodules, where E(n) is the Johnson-Wilson homology theory. They are suspensions of the Jn,r = E(n)∗(MrE(r)) where 0 ≤ r ≤ n, with the endomorphism ring of Jn,r being Ê(r) ∗ Ê(r), where Ê(r) denotes the completion of E(r).

In this manuscript, the Cauchy problem of modified Helmholtz equation is researched. This inverse a serious ill-posed problem. The classical Landweber iterative regularization method designed to find regularized solution error estimations between exact and are all obtained under priori posteriori parameter selection rule. can also be applied solve on spherically symmetric cylindrically regions.

We give a detailed study of the semiconvergence behavior of projected nonstationary simultaneous iterative reconstruction technique (SIRT) algorithms, including the projected Landweber algorithm. We also consider the use of a relaxation parameter strategy, proposed recently for the standard algorithms, for controlling the semiconvergence of the projected algorithms. We demonstrate the semiconve...

I discuss the problem of realizing families of complex orientable homology theories as families of E ∞-ring spectra, including a recent result of Jacob Lurie emphasizing the role of p-divisible groups. A few years ago, I wrote a paper [10] discussing a realization problem for families of Landweber exact spectra. Since Jacob Lurie [27] now has a major positive result in this direction, it seems ...

In this article, we deal with the inverse problem of identifying unknown source time-fractional diffusion equation in a cylinder by A fractional Landweber method. This is ill-posed. Therefore, regularization required. The main result article error between sought solution and its regularized under selection priori parameter choice rule.