by Nikolai V. Shokhirev

Basics of Indirect Measurements

• Introduction
• Measurements scheme
• Linear systems
• System parameters and Measured parameters
• Integral Form
• "Easy" solution
• Ill posed problems
• Model kernel
• Some conclusions
• Incomplete measurements

Singular Value Decomposition

• Introduction
• Notations
• Singular Value Decomposition
• Completeness of singular basis sets
• Formal solution
• Pseudo-inverse operator
• References

Analysis of accuracy and resolution

• Introduction
• Definitions
• 3D-space Example
• Mapping of Spaces
• Interpretation of Mapping
• Use of singular functions
• Experimental noise
• Reconstruction criterion
• Units of Information
• Accuracy and Resolution
• Reliable Reconstruction Region
• Accuracy and Interval of Measurements
• References

Implementations

• Discretization
• Regularization
• Handling of infinities 
• Weighted measurements
• Variable transformation
• Units of Information
• Accuracy
• Resolution
• Reliable Reconstruction Region

©Nikolai Shokhirev, 2001-2009

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