Multiscale scanning in inverse problems
نویسندگان
چکیده
منابع مشابه
Inverse Problems with Invariant Multiscale Statistics
We propose a new approach to linear ill-posed inverse problems. Our algorithm alternates between enforcing two constraints: the measurements and the statistical correlation structure in some transformed space. We use a non-linear multiscale scattering transform which discards the phase and thus exposes strong spectral correlations otherwise hidden beneath the phase fluctuations. As a result, bo...
متن کاملNumerical homogenization and model order reduction for multiscale inverse problems
A new numerical method based on numerical homogenization and model order reduction is introduced for the solution of multiscale inverse problems. We consider a class of elliptic problems with highly oscillatory tensors that varies on a microscopic scale. We assume that the micro structure is known and seek to recover a macroscopic scalar parametrization of the microscale tensor (e.g. volume fra...
متن کاملA Bayesian multiscale framework for Poisson inverse problems
This paper describes a maximum a postetioti (MAP) estimation method for linear inverse problems involving Poisson data based on a novel multiscale framework. The framework itself is founded on a carefully designed multiscale prior probability distribution placed on the “splits” in the multiscale partition of the underlying intensity, and it admits a remarkably simple MAP estimation procedure us...
متن کاملA Multiscale Approach to Solving One Dimensional Inverse Problems
2] suggests that multiscale methods are a useful tool for purposes of computational efficiency. In this paper we explore a multiresolution approach We consider inverse problems described by that class to solving one dimensional inverse problems. The apof operators which are made sparse under the action proach we take is motivated by the work of Chou, of the wavelet transform [2]. Thus, the inve...
متن کاملNote: Multiscale scanning probe microscopy.
Combining the nanoscopic and macroscopic worlds is a serious challenge common to numerous scientific fields, from physics to biology. In this paper, we demonstrate nanometric resolution over a millimeter range by means of atomic-force microscopy using metrological stage. Nanometric repeatability and millimeter range open up the possibility of probing components and materials combining multiscal...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: The Annals of Statistics
سال: 2018
ISSN: 0090-5364
DOI: 10.1214/17-aos1669