Two-dimensional nonseparable discrete linear canonical transform based on CM-CC-CM-CC decomposition.

Area of Science:

• Digital signal processing
• Image processing
• Optical transform theory

Background:

• The 2D nonseparable linear canonical transform (2D NsLCT) is a generalization of 2D FT and 2D fractional FT.
• Existing decompositions of 2D NsLCT often involve 2D affine transformations, which can introduce interpolation errors and increase complexity.

Purpose of the Study:

• To propose a novel decomposition method for the 2D NsLCT that avoids affine transformations.
• To enhance the accuracy and efficiency of digital implementations of the 2D NsLCT.

Main Methods:

• Introduced a new CM-CC-CM-CC decomposition for the 2D NsLCT.
• Decomposed the 2D NsLCT into two 2D chirp multiplications (2D CMs) and two 2D chirp convolutions (2D CCs).
• Avoided the use of 2D affine transformations in the decomposition process.

Main Results:

• The proposed CM-CC-CM-CC decomposition demonstrates higher accuracy.
• Achieved lower computational complexity compared to previous decomposition methods.
• Exhibited smaller errors in the additivity property of the transform.
• Ensured perfect reversibility for lossless signal/image reconstruction.

Conclusions:

• The CM-CC-CM-CC decomposition offers a superior alternative for digital implementation of the 2D NsLCT.
• The method provides enhanced accuracy, efficiency, and perfect reversibility.
• This advancement is beneficial for applications in optics and signal/image processing.