# Sparse inpainting and isotropy

@article{Feeney2014SparseIA, title={Sparse inpainting and isotropy}, author={Stephen M. Feeney and Domenico Marinucci and Jason D. McEwen and Hiranya V. Peiris and Benjamin D. Wandelt and Valentina Cammarota}, journal={Journal of Cosmology and Astroparticle Physics}, year={2014}, volume={2014}, pages={050 - 050} }

Sparse inpainting techniques are gaining in popularity as a tool for cosmological data analysis, in particular for handling data which present masked regions and missing observations. We investigate here the relationship between sparse inpainting techniques using the spherical harmonic basis as a dictionary and the isotropy properties of cosmological maps, as for instance those arising from cosmic microwave background (CMB) experiments. In particular, we investigate the possibility that…

## 7 Citations

### Sparse Image Reconstruction on the Sphere: Analysis and Synthesis

- MathematicsIEEE Transactions on Image Processing
- 2017

We develop techniques to solve ill-posed inverse problems on the sphere by sparse regularization, exploiting sparsity in both axisymmetric and directional scale-discretized wavelet space. Denoising,…

### Group sparse optimization for inpainting of random fields on the sphere

- Mathematics, Computer Science
- 2022

An approximation error bound of the inpainted random ﬁeld deﬁned by a scaled KKT point of the constrained optimization problem in the square-integrable space on the sphere with probability measure is provided.

### Needlet thresholding methods in component separation

- Computer ScienceJournal of Cosmology and Astroparticle Physics
- 2020

This work develops algorithms based on different needlet-thresholding schemes and uses them as extensions of existing, well-known component separation techniques, namely ILC and template-fitting to find that thresholding can be useful as a denoising tool for internal templates in experiments with few frequency channels, in conditions of low signal-to-noise.

### Isotropic sparse regularization for spherical harmonic representations of random fields on the sphere

- Mathematics
- 2020

### Sparse image reconstruction on the sphere: a general approach with uncertainty quantification

- MathematicsArXiv
- 2021

This article considers the Bayesian interpretation of the unconstrained problem which, combined with recent developments in probability density theory, permits rapid, statistically principled uncertainty quantification (UQ) in the spherical setting and linearity is exploited to significantly increase the computational efficiency of such UQ techniques.

### Sparse Isotropic Regularization for Spherical Harmonic Representations of Random Fields on the Sphere

- Mathematics
- 2018

This paper discusses sparse isotropic regularization for a random field on the unit sphere $\mathbb{S}^2$ in $\mathbb{R}^{3}$, where the field is expanded in terms of a spherical harmonic basis. A…

## References

SHOWING 1-10 OF 39 REFERENCES

### Low-ℓ CMB analysis and inpainting

- Physics
- 2012

Reconstructing the cosmic microwave background (CMB) in the Galactic plane is extremely difficult due to the dominant foreground emissions such as dust, free-free or synchrotron. For cosmological…

### Morphological Component Analysis and Inpainting on the Sphere: Application in Physics and Astrophysics

- Physics
- 2007

Morphological Component Analysis (MCA) is a new method which takes advantage of the sparse representation of structured data in large overcomplete dictionaries to separate features in the data based…

### Sparsity and the Bayesian perspective

- Computer Science
- 2013

This paper is by no means against the Bayesian approach, but warns against a Bayesian-only interpretation in data analysis, which can be misleading in some cases.

### Sparse Image Reconstruction on the Sphere: Implications of a New Sampling Theorem

- Computer Science, MathematicsIEEE Transactions on Image Processing
- 2013

Through numerical simulations, the enhanced fidelity of sparse image reconstruction due to the more efficient sampling of the sphere provided by the new sampling theorem is verified.

### Sparse signal reconstruction on the sphere: implications of a new sampling theorem

- Computer ScienceArXiv
- 2012

A framework for total variation (TV) inpainting, which relies on a sampling theorem to define a discrete TV norm on the sphere, and verifies the enhanced fidelity of sparse signal reconstruction due to the more efficient sampling of the sphere provided by the new sampling theorem.

### Avoiding bias in reconstructing the largest observable scales from partial-sky data

- Mathematics
- 2011

Obscuration due to Galactic emission complicates the extraction of information from cosmological surveys, and requires some combination of the (typically imperfect) modeling and subtraction of…

### Fast Wiener filtering of CMB maps

- Computer Science
- 2012

A messenger field is introduced to mediate between the different preferred bases in which signal and noise properties can be specified most conveniently, and rephrase the signal reconstruction problem in terms of this auxiliary variable.

### Low-Dimensional Models for Dimensionality Reduction and Signal Recovery: A Geometric Perspective

- Computer ScienceProceedings of the IEEE
- 2010

This work compares and contrast from a geometric perspective a number of low-dimensional signal models that support stable information-preserving dimensionality reduction, and points out a common misconception related to probabilistic compressible signal models.

### Proximal Splitting Methods in Signal Processing

- Computer ScienceFixed-Point Algorithms for Inverse Problems in Science and Engineering
- 2011

The basic properties of proximity operators which are relevant to signal processing and optimization methods based on these operators are reviewed and proximal splitting methods are shown to capture and extend several well-known algorithms in a unifying framework.

### Efficient Wiener filtering without preconditioning

- Computer Science
- 2012

The algorithm can be modified to synthesize fluctuation maps, which, combined with the Wiener filter solution, result in unbiased constrained signal realizations, consistent with the observations.