A minimax dictionary expansion for sparse continuous reconstruction

Passarin, Thiago Alberto Rigo; Pipa, Daniel Rodrigues; Zibetti, Marcelo V. W.

doi:10.23919/eusipco.2017.8081587

Cited by 2 publications

(6 citation statements)

References 11 publications

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“…In [31], a minimize-maximum (Minimax) formulation is presented for the definition of the expanded set {B (n) }. The resulting approximation minimizes the maximum residual within the representation of each n-th local ROI.…”

Section: Off-grid Events and Dictionary Expansionmentioning

confidence: 99%

“…This extension is facilitated by the fact that the formulation is non-parametric, i.e., the deviation from originally modelled positions is not mapped onto any independent variable and does not play any role on the definition on the bases. On the other hand, in the Taylor, Polar [23] and Minimax [31] expansions, the off-grid deviation is a parameter from which the elements of the expanded dictionary are derived. Consequently, except for the Taylor expansion, their extensions to 2 or higher dimensions are not promptly defined.…”

Section: Rank-k Approximation Of Local Manifoldsmentioning

confidence: 99%

See 1 more Smart Citation

Sparse Ultrasound Imaging via Manifold Low-Rank Approximation and Non-Convex Greedy Pursuit

Passarin¹,

Pipa²,

Zibetti³

2018

Preprint

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Model-based image reconstruction has brought improvements in terms of contrast and spatial resolution to imaging applications such as magnetic resonance imaging and emission computed tomography. However, their use for pulse-echo techniques like ultrasound imaging is limited by the fact that model-based algorithms assume a finite grid of possible locations of scatterers in a medium -- which does not reflect the continuous nature of real world objects and creates a problem known as off-grid deviation. To cope with this problem, we present a method of dictionary expansion and constrained reconstruction that approximates the continuous manifold of all possible scatterer locations within a region of interest. The expanded dictionary is created using a highly coherent sampling of the region of interest, followed by a rank reduction procedure based on a truncated singular value decomposition. We develop a greedy algorithm, based on the Orthogonal Matching Pursuit (OMP), that uses a correlation-based non-convex constraint set that allows for the division of the region of interest into cells of any size. To evaluate the performance of the method, we present results of 2-dimensional ultrasound image reconstructions with simulated data in a nondestructive testing application. Our method succeeds in the reconstructions of sparse images from noisy measurements, providing higher accuracy than previous approaches based on regular discrete models.

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Section: Off-grid Events and Dictionary Expansionmentioning

confidence: 99%

Section: Rank-k Approximation Of Local Manifoldsmentioning

confidence: 99%

Sparse Ultrasound Imaging via Manifold Low-Rank Approximation and Non-Convex Greedy Pursuit

Passarin¹,

Pipa²,

Zibetti³

2018

Preprint

View full text Add to dashboard Cite

show abstract

“…In [31], a minimize–maximum (Minimax) formulation is presented for the definition of the expanded set {B(boldn)}. The resulting approximation minimizes the maximum residual within the representation of each n -th local ROI.…”

Section: Off-grid Events and Dictionary Expansionmentioning

confidence: 99%

“…This extension is facilitated by the fact that the formulation is non-parametric, i.e., the deviation from originally modelled positions is not mapped onto any independent variable and does not play any role on the definition on the bases. On the other hand, in the Taylor, Polar [23] and Minimax [31] expansions, the off-grid deviation is a parameter from which the elements of the expanded dictionary are derived. Consequently, except for the Taylor expansion, their extensions to two or higher dimensions are not promptly defined.…”

Section: Rank-k Approximation Of Local Manifoldsmentioning

confidence: 99%

“…For higher orders of K , such a cone is defined for all K−1 relations between each k -th (k≥2) component and the first one. The resulting linear constraint set is defined as [29,31] trueprefixmin1≤i≤Rfk,i(n)f1,i(n)≤xk(n)x1(n)≤trueprefixmax1≤i≤Rfk,i(n)f1,i(n), 5.8cmf1,i(n)≥0, 1.5cm∀k∈{2,⋯,K},n∈{1,2,⋯,N}, where …”

Section: Reconstruction Algorithmmentioning

confidence: 99%

See 1 more Smart Citation

Sparse Ultrasound Imaging via Manifold Low-Rank Approximation and Non-Convex Greedy Pursuit

Passarin

Zibetti

Pipa

2018

Sensors

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Model-based image reconstruction has improved contrast and spatial resolution in imaging applications such as magnetic resonance imaging and emission computed tomography. However, these methods have not succeeded in pulse-echo applications like ultrasound imaging due to the typical assumption of a finite grid of possible scatterer locations in a medium–an assumption that does not reflect the continuous nature of real world objects and creates a problem known as off-grid deviation. To cope with this problem, we present a method of dictionary expansion and constrained reconstruction that approximates the continuous manifold of all possible scatterer locations within a region of interest. The expanded dictionary is created using a highly coherent sampling of the region of interest, followed by a rank reduction procedure. We develop a greedy algorithm, based on the Orthogonal Matching Pursuit, that uses a correlation-based non-convex constraint set that allows for the division of the region of interest into cells of any size. To evaluate the performance of the method, we present results of two-dimensional ultrasound imaging with simulated data in a nondestructive testing application. Our method succeeds in the reconstructions of sparse images from noisy measurements, providing higher accuracy than previous approaches based on regular discrete models.

show abstract

A minimax dictionary expansion for sparse continuous reconstruction

Cited by 2 publications

References 11 publications

Sparse Ultrasound Imaging via Manifold Low-Rank Approximation and Non-Convex Greedy Pursuit

Sparse Ultrasound Imaging via Manifold Low-Rank Approximation and Non-Convex Greedy Pursuit

Sparse Ultrasound Imaging via Manifold Low-Rank Approximation and Non-Convex Greedy Pursuit

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