The regularized least squares methods for the solution of ill-posed inverse problems are summarized, and appropriate references are stated. Additionally, an adap-tive multi-scale algorithm is proposed to solve highly ill-posed inverse problems with fewer degrees of freedom and comparable performance. The algorithm controls the level of detail in the reconstruction by distributing the ¯ne scale ...

the methods applied to regularization of the ill-posed problems can be classified under “direct” and “indirect” methods. practice has shown that the effects of different regularization techniques on an ill-posed problem are not the same, and as such each ill-posed problem requires its own investigation in order to identify its most suitable regularization method. in the geoid computations witho...

Dental tomographic cone-beam X-ray imaging devices record truncated projections and reconstruct a region of interest (ROI) inside the head. Image reconstruction from the resulting local tomography data is an ill-posed inverse problem. A Bayesian multiresolution method is proposed for the local tomography reconstruction. The inverse problem is formulated in a well-posed statistical form where a ...

In this paper we propose a novel learning-based wavelet transform and demonstrate its utility as representation in solving number of linear inverse problems—these are asymmetric problems, where the forward problem is easy to solve, but difficult often ill-posed. The decomposition comprised application an invertible 2D filter-bank comprising symmetric anti-symmetric filters, combination with set...

Regularization of ill-posed linear inverse problems via l1 penalization has been proposed for cases where the solution is known to be (almost) sparse. One way to obtain the minimizer of such an l1 penalized functional is via an iterative soft-thresholding algorithm. We propose an alternative implementation to l1-constraints, using a gradient method, with projection on l1-balls. The correspondin...