Conjugate-gradient algorithm with edge-preserving regularization for image reconstruction from Ipswich data for mystery objects

Lobel, P.; Pichot, Ch.; Blanc‐Féraud, Laure; Barlaud, Michel

doi:10.1109/74.584492

Cited by 19 publications

(14 citation statements)

References 6 publications

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“…• Every time the difference between the permittivity unknown and the VP value becomes much larger than the differences between and the other VP values , the corresponding term vanishes in (12). This is a direct result of property 4).…”

Section: Value Picking Regularizationmentioning

confidence: 95%

“…Thanks to the particular form of the choice function, these choices are made in an intuitively attractive way. To investigate this, the VP function (5) is rewritten using property 10): (12) which can be seen as a weighted sum of the penalty functions , where the weights are calculated with the weight functions defined in (52) (13) The following observations can be made:…”

Section: Value Picking Regularizationmentioning

confidence: 99%

“…This search direction, however, is not directly computed from the cost function (4), but from a modified cost function (15) with (16) The difference between (16) and (12) [or between (15) and (4)] is that in (16) the weights are computed in and then kept fixed when changes. Because of properties 10) and 11), bounds from above and touches with in .…”

Section: A the Gauss-newton Descent Direction For The Permittivitymentioning

confidence: 99%

“…It satisfies a set of unifying criteria, proposed by Charbonnier et al [10], which determine wether a regularization function is edge preserving. Such edge preserving regularization methods have been used in microwave imaging [11], [12]. Also methods based on level set techniques are used in inverse scattering [13], [14].…”

mentioning

confidence: 99%

“…Both methods have been used with success, but some possible disadvantages may be noted. The definition of the potential functions in edge preserving regularization generally implies the choice of some free parameter which tunes the aforementioned transitional region, such as in the TV scheme of [8], in [7], in [10] and and in [12]. It appears to us that the use of level set methods in situations with more than two different permittivities is somewhat complicated.…”

mentioning

confidence: 99%

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A New Value Picking Regularization Strategy—Application to the 3-D Electromagnetic Inverse Scattering Problem

Zaeytijd

Franchois

Geffrin

2009

IEEE Trans. Antennas Propagat.

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Abstract-The nonlinear electromagnetic inverse scattering problem of reconstructing a possibly quasi-piecewise constant inhomogeneous complex permittivity profile is solved by iterative minimization of a pixel-based data fit cost function. Because of the ill-posedness it is necessary to introduce some form of regularization. Many authors apply a smoothing constraint on the reconstructed permittivity profile, but such regularization smooths away sharp edges. In this paper, a simple yet effective regularization strategy, the value picking (VP) regularization, is proposed. This new technique is capable of reconstructing piecewise constant permittivity profiles without degrading the edges. It is based on the knowledge that only a few different permittivity values occur in such profiles, the values of which need not be known in advance. VP regularization does not impose this a priori information in a strict sense, such that it can be applied also to profiles that are only approximately piecewise constant. The VP regularization is introduced in the solution of the inverse problem by adding a choice function to the data fit cost function for every permittivity unknown in the discretized problem. When minimized, the choice function forces the corresponding permittivity unknown to be close to one member of a set of auxiliary variables, the VP values, which are continuously updated throughout the iterations. To minimize the regularized cost function, a half quadratic Gauss-Newton optimization technique is presented. Finally, a stepwise relaxed VP regularization scheme is proposed, in which the number of VP values is gradually increased. This scheme is tested with synthetic and measured scattering data, obtained from inhomogeneous 3-D targets, and is shown to achieve high reconstruction quality.

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Section: Value Picking Regularizationmentioning

confidence: 95%

Section: Value Picking Regularizationmentioning

confidence: 99%