Applications of algorithmic differentiation to phase retrieval algorithms

Area of Science:

• Computational Mathematics
• Numerical Analysis
• Signal Processing

Background:

• Algorithmic differentiation is crucial for gradient computation in scientific computing.
• Phase retrieval problems often involve complex error metrics requiring accurate gradient information.
• Existing methods for gradient calculation can be computationally intensive or prone to errors.

Purpose of the Study:

• To generalize reverse-mode algorithmic differentiation for multidimensional arrays of complex numbers.
• To apply these generalized techniques to phase retrieval error metrics.
• To demonstrate a more efficient and straightforward method for gradient calculation.

Main Methods:

• Generalization of reverse-mode algorithmic differentiation to complex number operations on multidimensional arrays.
• Application of the generalized differentiation to phase retrieval error functions.
• Comparison with traditional methods like finite differences and symbolic differentiation.

Main Results:

• Successfully extended reverse-mode algorithmic differentiation to handle complex multidimensional arrays.
• Demonstrated the framework's applicability to phase retrieval error metrics.
• Showcased the avoidance of finite differences and symbolic differentiation for gradient computation.

Conclusions:

• Reverse-mode algorithmic differentiation offers a robust framework for calculating gradients of complex error metrics in phase retrieval.
• This generalized approach simplifies gradient computation, enhancing efficiency and accuracy.
• The method provides a valuable tool for researchers in computational science and signal processing.