Millimeter-wave compressive holography

Cull, Christy Fernandez; Wikner, David A.; Mait, Joseph N.; Mattheiss, Michael; Brady, David J.

doi:10.1364/ao.49.000e67

Cited by 109 publications

(50 citation statements)

References 28 publications

(42 reference statements)

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“…In this Letter, we derive the theoretical bounds on the performance of compressive imaging systems based on Fresnel wave propagation, and we show that it is related to the imaging sensor's physical attributes, illumination wavelength, and working distance. © 2011 Optical Society of America OCIS codes: 090.1995, 070.0070, 100.3190, 110.1758 Recent works [1][2][3][4][5][6][7] have applied compressive sensing (CS) [8,9] operators based on free-space wave propagation and sparsity promoting image reconstruction from a hologram [10,11]. Using wave propagation as a sensing operator is appealing because it is closely related to the Fourier transform, which is often used as a sensing operator in CS [8].…”

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confidence: 99%

Conditions for practicing compressive Fresnel holography

Rivenson

Stern

2011

Opt. Lett.

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Recent works have applied diffraction-based wave propagation for compressive imaging applications. In this Letter, we derive the theoretical bounds on the performance of compressive imaging systems based on Fresnel wave propagation, and we show that it is related to the imaging sensor's physical attributes, illumination wavelength, and working distance. © 2011 Optical Society of America OCIS codes: 090.1995, 070.0070, 100.3190, 110.1758 Recent works [1][2][3][4][5][6][7] have applied compressive sensing (CS) [8,9] operators based on free-space wave propagation and sparsity promoting image reconstruction from a hologram [10,11]. Using wave propagation as a sensing operator is appealing because it is closely related to the Fourier transform, which is often used as a sensing operator in CS [8]. In this Letter, we study the performance and limitations of CS systems based on wave propagation described by the Fresnel transform. The results are applicable for any type of holography, regardless of the recording setup. For simplicity, let us consider 1D free-space propagation in the Fresnel approximation, which relates the complex values of a propagating wave measured in a plane perpendicular to the direction of propagation and separated by a distance z [12]:where u in ðxÞ is the input object, uðξÞ is the propagated field, λ is the wavelength, and z is the propagation distance of the light wave. The relation between the Fresnel transform and the Fourier transform is evident in Eq. (1). It is also clear that this relation depends on the distance z, suggesting that the applicability of the Fresnel transform as a sensing operator should also depend on z.For the sake of clarity, let us give a brief review of CS. We assume that an image, u, is composed of n pixels, but only s ≪ n coefficients are meaningful under some arbitrary sparsifying operator, Ψ, such as a wavelet transform. We measure the signal using a sensing operator Φ (the Fresnel transform in our case). This process is usually written in vector-matrix form: u out ¼ Φu, where u out has only m < n measurements, hence making the signal reconstruction an ill-posed problem. CS theory asserts that the signal can be accurately reconstructed when taking m uniformly at random selected measurements, obeying [9] m ≥ Cμs log n;where μ, which is referred to as the coherence parameter, measures the dissimilarity between the sensing operator, Φ, and the sparsifying basis Ψ, and C is a positive numerical constant, which depends on the desired reconstruction accuracy [9]. The coherence parameter gets values of 1 ≤ μ ≤ n. Under the conditions of Eq. (2), an almost perfect signal reconstruction is guaranteed by performing an ℓ 1 -norm minimization procedure [8,9]. From Eq. (2) we notice that the smaller μ is, the fewer samples are needed in order to reconstruct the underlying sparse image. The coherence parameter can also be interpreted as the amount of the spreading of the sparse input signal in the measurement domain, i.e., it is desired that each acquired sample will contain as ...

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confidence: 99%

Conditions for practicing compressive Fresnel holography

Rivenson

Stern

2011

Opt. Lett.

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“…A slice-by-slice reconstruction of a 3D object from the holographic data is considered in [20] and [21]. In [22] a maximum likelihood approach is developed for estimation of the object density from 2D scattered fully developed speckle …eld measurements.…”

Section: Image Formationmentioning

confidence: 99%

High-accuracy wave field reconstruction: decoupled inverse imaging with sparse modeling of phase and amplitude

Katkovnik

Astola²

2011

J. Opt. Soc. Am. A

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We apply a nonlocal adaptive spectral transform for sparse modeling of phase and amplitude of a coherent wave …eld. The reconstruction of this wave …eld from complex-valued Gaussian noisy observations is considered. The problem is formulated as a multi-objective constrained optimization. The developed iterative algorithm decouples the inversion of the forward propagation operator and the …ltering of phase and amplitude of the wave …eld. It is demonstrated by simulations that the performance of the algorithm, both visually and numerically, is the current state-of-the-art.

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“…In general, all natural scenes can be compressed on some basis. Scenes can be perfectly reconstructed with significantly fewer measurement modes than the space bandwidth product (SBP) [1][2][3]. These measurement modes are composed of radiated field patterns of the metamaterial aperture antenna (MAA) at different frequencies.…”

Section: Introductionmentioning

confidence: 99%

Measurement Matrix Analysis and Radiation Improvement of a Metamaterial Aperture Antenna for Coherent Computational Imaging

Kou

Tian

et al. 2017

Applied Sciences

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Abstract:A metamaterial aperture antenna (MAA) that generates frequency-diverse radiation field patterns has been introduced in the context of microwave wave imaging to perform compressive image reconstruction. This paper presents a new metamateriapl aperture design, which includes two kinds of metamaterial elements with random distribution. One is a high-Q resonant element whose resonant frequency is agile, and the other one is a low-Q element that has a high radiation efficiency across frequency band. Numerical simulations and measurements show that the radiation efficiency of up to 60% can be achieved for the MAA and the far-field patterns owns good orthogonality, when using the complementary electric-field-coupled (CELC) element and the complementary Jerusalem cross (CJC) element with a random distribution ratio of 4 to 1, which could be effectively used to reconstruct the target scattering scene.

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Millimeter-wave compressive holography

Cited by 109 publications

References 28 publications

Conditions for practicing compressive Fresnel holography

Conditions for practicing compressive Fresnel holography

High-accuracy wave field reconstruction: decoupled inverse imaging with sparse modeling of phase and amplitude

Measurement Matrix Analysis and Radiation Improvement of a Metamaterial Aperture Antenna for Coherent Computational Imaging

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