
Contents
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7.1 Statistical Stability With Measurement Noise 7.1 Statistical Stability With Measurement Noise
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7.1.1 Measurement Noise Model 7.1.1 Measurement Noise Model
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7.1.2 Propagation of Measurement Noise in the Backpropagation Step 7.1.2 Propagation of Measurement Noise in the Backpropagation Step
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7.1.3 Stability Analysis 7.1.3 Stability Analysis
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7.1.3.1 Case I: Density contrast 7.1.3.1 Case I: Density contrast
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7.1.3.2 Case II: Elastic contrast 7.1.3.2 Case II: Elastic contrast
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7.2 Statistical Stability With Medium Noise 7.2 Statistical Stability With Medium Noise
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7.2.1 Medium Noise Model 7.2.1 Medium Noise Model
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7.2.2 Statistics of the Speckle Field in the Case of a Density Contrast Only 7.2.2 Statistics of the Speckle Field in the Case of a Density Contrast Only
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7.2.3 Statistics of the Speckle Field in the Case of an Elastic Contrast 7.2.3 Statistics of the Speckle Field in the Case of an Elastic Contrast
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7.2.4 Random Elastic Medium 7.2.4 Random Elastic Medium
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Concluding Remarks Concluding Remarks
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Seven Stability of Topological Derivative Based Imaging Functionals
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Published:April 2015
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Abstract
This chapter performs a detailed stability analysis of the topological derivative based imaging functionals with respect to medium and measurement noises. It begins with a discussion of the stability analysis with respect to measurement noise. In particular, it considers how the result with respect to the resolution of the imaging functional in the ideal situation will be modified when the measurement is not accurate but is corrupted by noise. The simplest model for the measurement noise is used in this case. The chapter then analyzes the stability with respect to medium noise of the proposed imaging functionals. For simplicity, a medium that fluctuates in the density parameter only is used. Finally, the case when the random fluctuations occur in the elastic coefficients is described.
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