Fast space-varying convolution using matrix source coding with applications to camera stray light reduction.

Area of Science:

• Image processing
• Computational imaging
• Applied mathematics

Background:

• Space-varying convolution is crucial for image restoration and reconstruction but computationally intensive.
• Direct implementation of dense space-varying convolution operators is often impractical.
• Existing methods like Fast Fourier Transform are unsuitable for space-varying operators.

Purpose of the Study:

• To develop an efficient method for implementing space-varying convolution.
• To reduce the computational complexity and memory requirements of dense convolution operators.
• To demonstrate the method's effectiveness in practical applications like stray light reduction.

Main Methods:

• Developed a novel approach called matrix source coding.
• Applied lossy source coding to dense space-varying convolution matrices.
• Factored the dense convolution operator into a product of sparse transforms.

Main Results:

• Achieved significant reduction in computation for matrix-vector products.
• Demonstrated dramatic reduction in computational cost for stray light reduction.
• Maintained high accuracy in image restoration tasks.

Conclusions:

• Matrix source coding offers an efficient solution for implementing space-varying convolution.
• The method significantly reduces computational load and memory usage.
• This approach is effective for demanding imaging applications such as stray light reduction.