Related papers: Sparse interferometric Stokes imaging under polari…
A common task in inverse problems and imaging is finding a solution that is sparse, in the sense that most of its components vanish. In the framework of compressed sensing, general results guaranteeing exact recovery have been proven. In…
It is now well understood that (1) it is possible to reconstruct sparse signals exactly from what appear to be highly incomplete sets of linear measurements and (2) that this can be done by constrained L1 minimization. In this paper, we…
The use of polarimetric techniques is nowadays widespread among solar and stellar astronomers. However, notwithstanding the recommandations that have often been made about the publication of polarimetric results in the astronomical…
The classical sparse parameter identification methods are usually based on the iterative basis selection such as greedy algorithms, or the numerical optimization of regularized cost functions such as LASSO and Bayesian posterior probability…
In the context of optical interferometry, only undersampled power spectrum and bispectrum data are accessible. It poses an ill-posed inverse problem for image recovery. Recently, a tri-linear model was proposed for monochromatic imaging,…
We present a new model for the propagation of polarized light in a random birefringent medium. This model is based on a decomposition of the higher order statistics of the reduced Stokes parameters along the irreducible representations of…
The success of compressed sensing relies essentially on the ability to efficiently find an approximately sparse solution to an under-determined linear system. In this paper, we developed an efficient algorithm for the sparsity promoting…
Non-convex constraints have recently proven a valuable tool in many optimisation problems. In particular sparsity constraints have had a significant impact on sampling theory, where they are used in Compressed Sensing and allow structured…
The sparse-driven radar imaging can obtain the high-resolution images about target scene with the down-sampled data. However, the huge computational complexity of the classical sparse recovery method for the particular situation seriously…
In this paper, we develop a randomized algorithm and theory for learning a sparse model from large-scale and high-dimensional data, which is usually formulated as an empirical risk minimization problem with a sparsity-inducing regularizer.…
Accurate measurement of polarization in spectral lines is important for the reliable inference of magnetic fields on the Sun. For ground based observations, polarimetric precision is severely limited by the presence of Earth's atmosphere.…
A new non-linear optimization approach is proposed for the sparse reconstruction of log-conductivities in current density impedance imaging. This framework comprises of minimizing an objective functional involving a least squares fit of the…
Multispectral polarisation imaging has a broad range of applications, from biological cell imaging to agricultural remote surveying. For such applications, especially involving lightweight unmanned aerial vehicles like drones, it is…
The polarization state of light is a key parameter in many imaging systems. For example, it can image mechanical stress and other physical properties that are not seen with conventional imaging, and can also play a central role in quantum…
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…
Block-sparse regularization is already well-known in active thermal imaging and is used for multiple measurement based inverse problems. The main bottleneck of this method is the choice of regularization parameters which differs for each…
We characterize the problem of artificial polarization for the Submillimeter High Angular Resolution Polarimeter (SHARP) through the use of simulated data and observations made at the Caltech Submillimeter Observatory (CSO). These…
We propose a convex and fast signal reconstruction method for block sparsity under arbitrary linear transform with unknown block structure. The proposed method is a generalization of the similar existing method and can reconstruct signals…
We develop techniques to convexify a set that is invariant under permutation and/or change of sign of variables and discuss applications of these results. First, we convexify the intersection of the unit ball of a permutation and…
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…