Sparse Deconvolution of B-Scan Images

Olofsson, Tomas; Wennerström, Erik

doi:10.1109/tuffc.2007.434

Cited by 13 publications

(13 citation statements)

References 11 publications

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“…Let denote the current Monte Carlo state of the unknown vectorized image ( ) (39) with, by definition, . Updating consists of drawing according to the Bernoulli-truncated Gaussian distribution in (23) with (40) The proposed strategy to simulate efficiently according to (23) is based on the following property.…”

Section: Appendix B Fast Recursive Computations For Simulating Accordmentioning

confidence: 99%

Hierarchical Bayesian Sparse Image Reconstruction With Application to MRFM

Dobigeon

Hero

Tourneret

2009

IEEE Trans. on Image Process.

101

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Abstract-This paper presents a hierarchical Bayesian model to reconstruct sparse images when the observations are obtained from linear transformations and corrupted by an additive white Gaussian noise. Our hierarchical Bayes model is well suited to such naturally sparse image applications as it seamlessly accounts for properties such as sparsity and positivity of the image via appropriate Bayes priors. We propose a prior that is based on a weighted mixture of a positive exponential distribution and a mass at zero. The prior has hyperparameters that are tuned automatically by marginalization over the hierarchical Bayesian model. To overcome the complexity of the posterior distribution, a Gibbs sampling strategy is proposed. The Gibbs samples can be used to estimate the image to be recovered, e.g., by maximizing the estimated posterior distribution. In our fully Bayesian approach, the posteriors of all the parameters are available. Thus, our algorithm provides more information than other previously proposed sparse reconstruction methods that only give a point estimate. The performance of the proposed hierarchical Bayesian sparse reconstruction method is illustrated on synthetic data and real data collected from a tobacco virus sample using a prototype MRFM instrument.Index Terms-Bayesian inference, deconvolution, Markov chain Monte Carlo (MCMC) methods, magnetic resonance force microscopy (MRFM) imaging, sparse representation.

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Section: Appendix B Fast Recursive Computations For Simulating Accordmentioning

confidence: 99%

Hierarchical Bayesian Sparse Image Reconstruction With Application to MRFM

Dobigeon

Hero

Tourneret

2009

IEEE Trans. on Image Process.

101

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“…The response for all observation points is obtained by superimposing the responses for all points in the ROI. For the discrete case, this summation can be written as a matrixvector multiplication as follows: 19,30,34 …”

Section: A Discrete Linear Model Of the Imaging Systemmentioning

confidence: 99%

Statistically motivated design of input signals for modern ultrasonic array systems

Lingvall

Olofsson

2008

The Journal of the Acoustical Society of America

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Modern array systems allow for excitation of separate elements using arbitrary wave forms. This is utilized in pulse compression and coded excitation techniques to improve the imaging performance. Such techniques are however somewhat inflexible since they use predefined excitation schemes. This paper presents a more flexible method for optimizing the input signals to an ultrasonic array in such a way that the scattering strengths at arbitrarily chosen control points in the insonified object can be estimated with as small an error as possible, measured with a mean squared error criteria. The statistically motivated method is based on a linear model of the array imaging system and the method takes into account both prior information regarding the scattering strengths and measurement errors. The input signals are found by using genetic optimization and are constrained to have finite duration and bounds on the maximum amplitudes. Different constellations of control points, and different signal-to-noise ratios, yield different excitation schemes. The design approach finds multiple selective focal laws when choosing relatively well separated control points and when the control points are closely spaced, the resulting excitations result in more diffuse fields. Because of the flexibility in choosing the control points, the design method will be useful when developing transmission schemes aiming at fast imaging of large image areas using few transmissions.

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“…Naturally, real-world inspected objects easily break this assumption and many scatteres may be located off-grid. Many previous studies with model-based algorithms for ultrasound imaging, including but not limited to [4][5][6][7][8][9][10][11], have reported that resolution and contrast are substantially improved in comparison to delay-and-sum (DAS) algorithms when data comes from simulations with scatterers…”

Section: Introductionmentioning

confidence: 99%

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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Sparse Deconvolution of B-Scan Images

Cited by 13 publications

References 11 publications

Hierarchical Bayesian Sparse Image Reconstruction With Application to MRFM

Hierarchical Bayesian Sparse Image Reconstruction With Application to MRFM

Statistically motivated design of input signals for modern ultrasonic array systems

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

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