Related papers: Sparse regularization in limited angle tomography
Restoration of images degraded by spatially varying blurs is an issue of increasing importance in the context of photography, satellite or microscopy imaging. One of the main difficulty to solve this problem comes from the huge dimensions…
Curvelet frame is of special significance for photoacoustic tomography (PAT) due to its sparsifying and microlocalisation properties. We derive a one-to-one map between wavefront directions in image and data spaces in PAT which suggests…
We study inversion of the spherical Radon transform with centers on a sphere (the data acquisition set). Such inversions are essential in various image reconstruction problems arising in medical, radar and sonar imaging. In the case of…
There has been a growing interest in the use of data-driven regularizers to solve inverse problems associated with computational imaging systems. The convolutional sparse representation model has recently gained attention, driven by the…
We consider a minimization problem whose objective function is the sum of a fidelity term, not necessarily convex, and a regularization term defined by a positive regularization parameter $\lambda$ multiple of the $\ell_0$ norm composed…
In image reconstruction there are techniques that use analytical formulae for the Radon transform to recover an image from a continuum of data. In practice, however, one has only discrete data available. Thus one often resorts to sampling…
Blind image restoration is a non-convex problem which involves restoration of images from an unknown blur kernel. The factors affecting the performance of this restoration are how much prior information about an image and a blur kernel are…
Computed tomography (CT) has become an essential part of modern science and medicine. A CT scanner consists of an X-ray source that is spun around an object of interest. On the opposite end of the X-ray source, a detector captures X-rays…
Here we present new joint reconstruction and regularization techniques inspired by ideas in microlocal analysis and lambda tomography, for the simultaneous reconstruction of the attenuation coefficient and electron density from X-ray…
In this paper, we consider minimizing the L1/L2 term on the gradient for a limited-angle scanning problem in computed tomography (CT) reconstruction. We design a specific splitting framework for an unconstrained optimization model so that…
Electron tomographic reconstruction is a method for obtaining a three-dimensional image of a specimen with a series of two dimensional microscope images taken from different viewing angles. Filtered backprojection, one of the most popular…
This paper proposes a systematic mathematical analysis of both the direct and inverse acoustic scattering problem given the source in Radon measure space. For the direct problem, we investigate the well-posedness including the existence,…
The discrete curvelet transform decomposes an image into a set of fundamental components that are distinguished by direction and size as well as a low-frequency representation. The curvelet representation is approximately sparse; thus, it…
Compressed sensing allows for the recovery of sparse signals from few measurements, whose number is proportional to the sparsity of the unknown signal, up to logarithmic factors. The classical theory typically considers either random linear…
In tomographic reconstruction, the goal is to reconstruct an unknown object from a collection of line integrals. Given a complete sampling of such line integrals for various angles and directions, explicit inverse formulas exist to…
The reconstruction of images from their corresponding noisy Radon transform is a typical example of an ill-posed linear inverse problem as arising in the application of computerized tomography (CT). As the (naive) solution does not depend…
This work addresses the recovery and demixing problem of signals that are sparse in some general dictionary. Involved applications include source separation, image inpainting, super-resolution, and restoration of signals corrupted by…
We propose a variational regularization approach based on a multiscale representation called cylindrical shearlets aimed at dynamic imaging problems, especially dynamic tomography. The intuitive idea of our approach is to integrate a…
Sparsity promoting regularization is an important technique for signal reconstruction and several other ill-posed problems. Theoretical investigation typically bases on the assumption that the unknown solution has a sparse representation…
We study the problem of sparse reconstruction from noisy undersampled measurements when the following two things are available. (1) We are given partial, and partly erroneous, knowledge of the signal's support, denoted by $T$. (2) We are…