Sparse Multidimensional Exponential Analysis with an Application to Radar Imaging

Decomposition is integral to most image processing algorithms and often required in texture analysis. We present a new approach using a recent 2-dimensional exponential analysis technique. Exponential analysis offers the advantage of sparsity in the model and continuity in the parameters. This results in a much more compact representation of textures when compared to traditional Fourier or wavelet transform techniques. Our experiments include synthetic as well as real texture images from standard benchmark datasets. The results outperform FFT in representing texture patterns with significantly fewer terms while retaining RMSE values after reconstruction. The underlying periodic complex exponential model works best for texture patterns that are homogeneous. We demonstrate the usefulness of the method in two common vision processing application examples, namely texture classification and defect detection.

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“…We now summarize the 2-d idea explained in [6]. How to combine this with the 1-d technique of [17] is further detailed in [18].…”

Section: Exponential Image Analysismentioning

confidence: 99%

Decomposing Textures using Exponential Analysis

Hou

Cuyt

Lee

et al. 2021

ICASSP 2021 - 2021 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

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“…Also, there are further Prony-like techniques available in higher dimensions, cf. [13]. There is no explicit analysis of runtime and sample complexity available, however, which is why we cannot include this approach in Table 1.…”

Section: Theorem 2 (Dimension-incremental Strategy) Let the Sparsitymentioning

confidence: 99%

A sample efficient sparse FFT for arbitrary frequency candidate sets in high dimensions

2021

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In this paper, a sublinear time algorithm is presented for the reconstruction of functions that can be represented by just few out of a potentially large candidate set of Fourier basis functions in high spatial dimensions, a so-called high-dimensional sparse fast Fourier transform. In contrast to many other such algorithms, our method works for arbitrary candidate sets and does not make additional structural assumptions on the candidate set. Our transform significantly improves upon the other approaches available for such a general framework in terms of the scaling of the sample complexity. Our algorithm is based on sampling the function along multiple rank-1 lattices with random generators. Combined with a dimension-incremental approach, our method yields a sparse Fourier transform whose computational complexity only grows mildly in the dimension and can hence be efficiently computed even in high dimensions. Our theoretical analysis establishes that any Fourier s-sparse function can be accurately reconstructed with high probability. This guarantee is complemented by several numerical tests demonstrating the high efficiency and versatile applicability for the exactly sparse case and also for the compressible case.

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“…If (7) is not satisfied, we have a subsampled exponential analysis problem that we can solve with a technique similar to [6,7]. This dealiasing method works with coprime scale parameters r 1 and r 2 and can also be used in the multivariate case [5]. The equations for the near-field base terms W mp in (4) are nonlinear, so in order to recover from aliasing using this approach, we first linearize our model with a first-order Taylorseries partial sum.…”

Section: Subsampled Exponential Analysismentioning

confidence: 99%

Antenna Position Estimation Through Subsampled Exponential Analysis of Signals in the Near Field

2021

RSL

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In a previous article we explored the use of a subsampled exponential analysis algorithm to find the antenna-element positions in a large irregular planar array after the installation phase. The application requires an unmanned aerial vehicle to be flown over the antenna array while transmitting several odd harmonic signals. The received signal samples at a chosen reference antenna element are then compared to those at every other element in the array in order to find its position. Previously, the far-field approximation was used to calculate the time delay between received signals. In this article the method is reconsidered for the more realistic case of when the source is in the near field of the array. A number of problems that arise are addressed, and results from a controlled simulation are presented to illustrate that the computational method works.

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Sparse Multidimensional Exponential Analysis with an Application to Radar Imaging

Cited by 13 publications

References 33 publications

Decomposing Textures using Exponential Analysis

Decomposing Textures using Exponential Analysis

A sample efficient sparse FFT for arbitrary frequency candidate sets in high dimensions

Antenna Position Estimation Through Subsampled Exponential Analysis of Signals in the Near Field

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