Joint minimum entropy method for simultaneous processing and fusion of multi-physics data and images

A physical non-transitory computer readable medium having stored thereon computer executable instructions that when executed by a processor cause a computing system to perform a method for the simultaneous imaging of different physical properties of an examined medium from the simultaneous joint inversion of multiple datasets of physical field/signal measurements, the method comprising:

• a. measuring at least one component of at least two physical fields and/or signals with at least two sensors and recording the observed data by a corresponding recording device;
• b. determining a nonnegative joint entropy functional which measures the degree of disorder of at least two model parameters and/or their attributes;
• d. determining smoothing or focusing stabilizing functionals for producing smooth inverse images or images with sharp boundaries;
• e. constructing a parametric functional defined as a linear combination of misfit functionals for at least two datasets, smoothing or focusing stabilizing functional, and the joint entropy functional;
• f. determining multi-modal model parameters, which correspond to the minimum of the parametric functional, by solving a minimization problem for the parametric functional using linear and/or nonlinear optimization methods.

A system for the simultaneous imaging of different physical properties of an examined medium from the simultaneous joint inversion of multiple datasets of physical field/signal measurements comprising:

• one or more sensors;
• and
• a computing system, the computing system comprising:
• a processor;
• and
• one or more physical non-transitory computer readable medium having computer executable instructions stored thereon that when executed by the processor, cause the computing system to perform the following:
• measure at least one component of at least two physical fields and/or signals with the one or more sensors and recording the observed data by a corresponding recording device;
• determine a nonnegative joint entropy functional which measures the degree of disorder of at least two model parameters and/or their attributes of at least two model parameters and/or their attributes;
• determine smoothing or focusing stabilizing functionals for producing smooth inverse images or images with sharp boundaries;
• construct a parametric functional defined as a linear combination of misfit functionals for at least two datasets, smoothing or focusing stabilizing functional, and the joint entropy functional;
• and
• determine multi-modal model parameters, which correspond to the minimum of the parametric functional, by solving a minimization problem for the parametric functional using linear and/or nonlinear optimization methods.

A method for simultaneous imaging of different physical properties of an examined medium from multi-physics datasets, the method comprising:

• receiving a plurality of measured parameters from a plurality of corresponding sensors, the plurality of sensors measuring at least two different measured parameter types;
• determining a nonnegative joint entropy functional of at least two model parameters corresponding to the plurality of measured parameters;
• determining stabilizing functionals for the at least two model parameters;
• determining misfit functionals between the at least two different measured parameters and corresponding predicted geophysical data;
• constructing a parametric functional, the parametric functional being a linear combination of the misfit functionals, the stabilizing functionals, and the joint entropy functional;
• and
• determining multi-modal model parameters corresponding to a minimum of the parametric functional by solving a minimization problem for the parametric functional.