Sparsity has become a key concept for solving of high-dimensional inverse problems using variational regularization techniques. Recently, using similar sparsity-constraints in the Bayesian framework for inverse problems by encoding them in the prior distribution has attracted attention. Important questions about the relation between regularization theory and Bayesian inference still need to be ...

Electrical Capacitance Tomography is an ill-posed inverse problem that aims at recovering the spatial permittivity distribution of an inhomogeneous medium from capacitance measurements at the boundary. We consider the problem of fast robust estimation of inclusion shape and position in binary mixtures. The boundary of the inclusion is represented implicitly using a radial basis function represe...

Initial condition inverse problems are ill-posed and computationally expensive to solve. We present a computational approach for solving inverse problems in the realm of onedimensional contaminant transport. The approach employs finite differencing as a forward solver and probabilistic methods for inversion. Markov Chain Monte Carlo sampling is used to efficiently recover posterior probabilitie...

We provide exact shape reconstruction formulas in the spirit of the Linear Sampling method for a class of inverse problems in shape determination in the context of timeindependent partial differential equations. To this end, we prove a general theorem how, and under which assumptions, domain characterizations based on the range of the square root of an operator transform into domain characteriz...

If one considers a sampled-data system derived from a continuous-time system with a relative degree of one or two on a finite-time interval, it is not simple to predict the behavior of the output of the inverse of the sampled-data system as the sampling period goes to zero. This is because the number of sample points increases while the zeros of the pulse-transfer function tend to the boundary ...

Given a full rank matrix X with more columns than rows, consider the task of estimating the pseudo inverse X based on the pseudo inverse of a sampled subset of columns (of size at least the number of rows). We show that this is possible if the subset of columns is chosen proportional to the squared volume spanned by the rows of the chosen submatrix (ie, volume sampling). The resulting estimator...

In recent years there has been considerable interest in the inverse scattering problem for anisotropic medium, particularly in the case of acoustic waves and electromagnetic waves. Due to the lack of uniqueness in determining the constitutive parameters, traditional methods for solving the inverse scattering problems based on the use of weak scattering approximations or nonlinear optimization t...

The variety of perception models included in JPEG2000 are the key for its rate-distortion performance. However, the most powerful perceptual model (masking using non-linear divisive normalization) had to be simplified to make it invertible. Recently, a robust and fast algorithm to invert the exact expression of divisive normalization has been derived and successfully used in the achromatic DCT ...

We have developed a robust, accurate inversion techare useful indicators of thermodynamic processes in the snowpack. Changes in snow grain size can help identify nique for estimating the grain size in a snowpack’s surface ice sheet surface features, such as melt areas, snow dunes, layer from imaging spectrometer data. Using a radiative and blue ice regions, and often indicate changes in snowtra...