Compressed sensing applied to spherical near-field to far-field transformation

Cornelius, Rasmus; Heberling, Dirk; Koep, Niklas; Behboodi, Arash; Mathar, Rudolf

doi:10.1109/eucap.2016.7481140

Cited by 33 publications

(27 citation statements)

References 8 publications

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“…If the vector of coefficients g, or f , are sparse or compressible, there are many algorithms for finding the coefficients from a number of samples m that is smaller than the dimension N . In this paper, we use quadratically constrained basis pursuit, i.e., 1 -minimization problem to solve the problem (11). The focus, however, is more on different sampling patterns and their effectiveness for signal recovery.…”

Section: Linear Inverse Problems and The 1 -Minimizationmentioning

confidence: 99%

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

Bangun

Behboodi

Mathar

2020

IEEE Trans. Signal Process.

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In this paper, 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. It is first shown that random sensing matrices, which consists of random samples of Wigner D-functions, satisfy the Restricted Isometry Property (RIP) with proper preconditioning and can be used for sparse recovery on the rotation group. The mutual coherence, however, is used to assess the performance of deterministic and regular sensing matrices. We show that many of widely used regular sampling patterns yield sensing matrices with the worst possible mutual coherence, and therefore are undesirable for sparse recovery. Using tools from angular momentum analysis in quantum mechanics, we provide a new expression for the mutual coherence, which encourages the use of regular elevation samples. We construct low coherence deterministic matrices by fixing the regular samples on the elevation and minimizing the mutual coherence over the azimuth-polarization choice. It is shown that once the elevation sampling is fixed, the mutual coherence has a lower bound that depends only on the elevation samples. This lower bound, however, can be achieved for spherical harmonics, which leads to new sensing matrices with better coherence than other representative regular sampling patterns. This is reflected as well in our numerical experiments where our proposed sampling patterns perfectly match the phase transition of random sampling patterns.that are obtained from sampling functions in finite-dimensional function spaces. The sensing matrix entries in these applications are samples of orthonormal basis functions of the ambient space. Fourier matrices [5], matrices from trigonometric polynomials [6], orthogonal polynomials [7,8] and spherical harmonics [9,10] are some examples of these matrices. Fortunately, when the orthonormal functions are uniformly bounded, also called Bounded Orthonormal Systems (BOSs), a similar recovery guarantee can be obtained. If the samples are taken randomly from a certain probability measure, BOS matrices are proven to satisfy the RIP property [4, Chapter 12]. If the orthonormal functions are uniformly bounded by K, the required number of measurements scales with K 2 .This randomness in the measurement process, however, is inadmissible in many applications, for instance when the measurement process involves movements of mechanical devices. Random measurements require arbitrary movements that are possibly harmful to the measurement device. In these applications, the measurement process should be designed by considering the physical characteristics of the measurement device. An example, which is the main motivation of the current work, is the antenna measurement application. The samples in antenna measurements are taken using a robotic arm or which samples of a smooth trajectory are preferred over random samples. Therefore, regular sampling patterns like equiangular patterns are widely used for the measurement proces...

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Section: Linear Inverse Problems and The 1 -Minimizationmentioning

confidence: 99%

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

Bangun

Behboodi

Mathar

2020

IEEE Trans. Signal Process.

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“…The standard method described in [1] requires a (high) number of measurement points M H = 2(2N +1)(N +1) to analytically retrieve the spherical coefficients. However, antenna radiation patterns can be accurately described from a limited number of spherical harmonics, as shown in [2]- [5]. This sparse vector x can then be identified from a reduced number of measurements M .…”

Section: Sparse Spherical Harmonic Expansion a Spherical Harmonimentioning

confidence: 99%

“…The standard technique [1] requires an important amount of field samples, which is approximately proportional to (kr 0 ) 2 , k being the wavenumber and r 0 the radius of the minimum sphere enclosing the radiating structure. Recently, the sparse expansion of the field radiated by antennas into spherical harmonic basis has been shown to greatly reduce the number of field samples, leading to important decreases in acquisition time, as shown in [2]- [5]. This fast measurement procedure, combined to the associated post-processing method, needs a proper tuning to ensure a reliable field interpolation.…”

Section: Introductionmentioning

confidence: 99%

On the Application of Sparse Spherical Harmonic Expansion for Fast Antenna Far-Field Measurements

Mézières

Fuchs

Coq

et al. 2020

Antennas Wirel. Propag. Lett.

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The characterization of 3D antenna radiation patterns is time consuming. The field acquisition duration can be dramatically reduced by leveraging the sparsity of the radiated field spectrum into spherical harmonic basis. Only a small number of measurements points are then necessary to identify the few significant spherical coefficients describing accurately the antenna pattern. In practice, this compressed sensing based procedure requires carefully chosen settings to work efficiently. The fitting to the data and the field sampling strategy are two crucial points in order to ensure a successful fast antenna measurement procedure. Techniques with experimental validations are proposed to ensure a reliable field interpolation. Estimation of savings in acquisition time are also provided to show the interest of the proposed method.

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“…In [6] the insertion of a-priori information on the AUT combined to the suitable use of advanced numerical modeling tools enables to achieve an important undersampling and therefore speed up the measurement time. In [7]- [9], the sparse representation of the electromagnetic field on general purpose basis functions, spherical harmonics, leads to a significant reduction of the required sampling points and a reduction of measurement time. The paper is organized as follows.…”

Section: Introductionmentioning

confidence: 99%

Reduced Order Models for Fast Antenna Characterization

Fuchs

Polimeridis

2019

IEEE Trans. Antennas Propagat.

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A reduced order model (ROM) for antenna characterization problems is proposed. It exploits the outer dimensions of the antenna under test (AUT) and the geometry of the measurement surface scan and leads to a significant reduction of the required number of field sampling points and therefore time to measure antenna radiation patterns. The inputs of the ROM are the equivalent currents enclosing the AUT and the outputs are their corresponding radiated fields on the measurement surface. By performing the singular value decomposition (SVD) of the radiating operator, we derive the minimal order model of the system and thereby numerically construct the basis of the fields radiated by the AUT. The evaluation of the so-reduced model is expedited by using a discrete empirical interpolation method (DEIM) that returns the sampling positions of the radiated field. The approach is tailored to the antenna characterization problem and specifically the antenna shape and the measurement surface scan. The proposed methodology is general, it can be easily adapted to any type of radiating structures and shape of the field measurement scans. Two experimental results of complex radiating structures measured in near and far field demonstrate the interest and potentialities of the approach.

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Compressed sensing applied to spherical near-field to far-field transformation

Cited by 33 publications

References 8 publications

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

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

On the Application of Sparse Spherical Harmonic Expansion for Fast Antenna Far-Field Measurements

Reduced Order Models for Fast Antenna Characterization

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