# Coherence Bounds for Sensing Matrices in Spherical Harmonics Expansion

@article{Bangun2018CoherenceBF, title={Coherence Bounds for Sensing Matrices in Spherical Harmonics Expansion}, author={Arya Bangun and Arash Behboodi and Rudolf Mathar}, journal={2018 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)}, year={2018}, pages={4634-4638} }

The mutual coherence provides a basis for deriving recovery guarantees in compressed sensing. In this paper, the mutual coherence of spherical harmonics sensing matrices is examined for a class of sensing patterns common in practice and is used as a figure of merit for designing sensing matrices. We will show that for each sampling pattern, the coherence is lower bounded by the inner product of two Legendre polynomials with different degrees. In some practical situation, it is desirable to have…

## 12 Citations

Tight bounds on the mutual coherence of sensing matrices for Wigner D-functions on regular grids

- Computer ScienceSampling Theory, Signal Processing, and Data Analysis
- 2021

This paper analyzes the mutual coherence for sensing matrices that correspond to a class of regular patterns to angular momentum analysis in quantum mechanics and provides simple lower bounds for it and provides algorithms that can achieve the lower bound for spherical harmonics.

Sensing Matrix Design and Sparse Recovery on the Sphere and the Rotation Group

- Computer ScienceIEEE Transactions on Signal Processing
- 2020

The goal is to design deterministic sampling patterns on the sphere and the rotation group and, thereby, construct sensing matrices for sparse recovery of band-limited functions and provides a new expression for the mutual coherence, which encourages the use of regular elevation samples.

On Grid Compressive Sensing for Spherical Field Measurements in Acoustics

- Mathematics
- 2022

We derive a theoretically guaranteed compressive sensing method for acoustic ﬁeld reconstructions using spherical ﬁeld measurements on a predeﬁned grid. This method can be used to reconstruct sparse…

Signal Recovery from Phaseless Measurements of Spherical Harmonics Expansion

- Mathematics2019 27th European Signal Processing Conference (EUSIPCO)
- 2019

This work will numerically show that recovery can be achieved by carefully choosing the appropriate sampling patterns for spherical harmonics coefficients from phaseless measurements and evaluate the empirical performance of several well-known algorithms.

Adaptive Sampling for Compressed Spherical Near-Field Measurements

- Computer Science2020 Antenna Measurement Techniques Association Symposium (AMTA)
- 2020

To improve the probability of the acquired samples resulting in linearly independent equations while allowing for a fast acquisition, a compressed sampling scheme based on the minimum mutual coherence of the sampling matrix for an equidistant distribution on elevation is chosen.

A Modified Minimum-Coherence Sampling for Fast Spherical Near-Field Measurements

- Environmental Science2019 13th European Conference on Antennas and Propagation (EuCAP)
- 2019

A modified compressed sampling based on minimal mutual coherence for spherical near-field measurements is proposed. After defining the sampling points for minimal coherence, more sampling points…

A Compressed Sampling for Spherical Near-Field Measurements

- Computer Science2018 AMTA 2018 Proceedings
- 2018

A novel sampling strategy is proposed and is combined with compressed-sensing techniques, such as basis pursuit solvers, to retrieve the sparse SMC, which are then used to obtain the AUT's far-field radiation.

On the Influence of the Transformation Matrix in Compressed Spherical Near-Field Measurements

- Physics2020 14th European Conference on Antennas and Propagation (EuCAP)
- 2020

The radiation characteristics of an object are represented by the coefficients vector of a Wigner-D expansion. For most physical antennas and with appropriate choice of the expansion’s center, the…

Practical Considerations in Compressed Spherical Near-Field Measurements

- Engineering2019 Antenna Measurement Techniques Association Symposium (AMTA)
- 2019

Results from a sparse data acquisition performed with a physical system are reported, demonstrating the viability of this method to accelerate SNF measurements and pave the way for further research.

Fast Spherical Near-Field Measurements on Arbitrary Surfaces by Application of Pointwise Probe Correction to Compressed Sampling Schemes

- Physics2019 Antenna Measurement Techniques Association Symposium (AMTA)
- 2019

The major disadvantage of Spherical Near-Field (SNF) measurements is their long acquisition time. To calculate the Antenna Under Test’s (AUT) far-field radiation characteristics, a sphere containing…

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