On the method of logarithmic cumulants for parametric probability density function estimation

Area of Science:

• Statistical image and signal processing
• Probability density function estimation

Background:

• Parameter estimation is crucial in statistical image and signal processing.
• Classical methods include Maximum Likelihood (ML) and Method of Moments (MoM).
• The Method of Logarithmic Cumulants (MoLC) is a recently proposed alternative estimation approach.

Purpose of the Study:

• To explore the properties and limitations of the MoLC parameter estimation method.
• To derive conditions for the strong consistency of MoLC estimates.
• To assess the applicability and performance of MoLC compared to ML and MoM.

Main Methods:

• Derivation of the general sufficient condition for strong consistency of MoLC estimates.
• Analytical derivation of MoLC applicability conditions for specific distribution families.
• Empirical assessment using synthetic and real data experiments, including supervised image classification on medical ultrasound and remote-sensing SAR imagery.

Main Results:

• Established the strong consistency of MoLC for selected distribution families.
• Determined analytical conditions for MoLC applicability.
• Experimental results indicate MoLC is a feasible and fast alternative to MoM, particularly when ML is unfeasible.
• MoLC demonstrated effectiveness in supervised image classification tasks.

Conclusions:

• MoLC is a viable and computationally efficient parameter estimation technique.
• Its applicability is demonstrated for specific distributions common in SAR imaging.
• MoLC serves as a valuable alternative to MoM and ML, especially in computationally constrained scenarios or when ML is intractable.