Comparison of two SVD-based color image compression schemes

Area of Science:

• Digital Image Processing
• Data Compression
• Linear Algebra

Background:

• Color image compression is crucial for efficient data representation, balancing file size and visual quality.
• Quaternion-based Singular Value Decomposition (SVD) methods are increasingly common for color image compression.
• Existing methods face challenges in computational efficiency and resource allocation.

Purpose of the Study:

• To propose and evaluate a novel color image compression scheme based on real SVD.
• To compare the performance of the proposed real compression scheme against quaternion-based compression methods.
• To analyze compression efficiency, operational speed, and image quality (PSNR) of both schemes.

Main Methods:

• A new real rectangular matrix C is formed from the RGB components of the color image.
• Real SVD is applied to matrix C, and dominant singular values/vectors are selected for compression.
• The proposed real compression scheme is compared with a quaternion SVD method using a real structure-preserving algorithm.

Main Results:

• The real compression scheme achieves higher compression ratios (CR) and significantly less operation time compared to the quaternion scheme for the same number of singular values.
• The real scheme exhibits a slightly lower Peak Signal-to-Noise Ratio (PSNR) when using the same number of singular values.
• When achieving the same CR, the real compression scheme demonstrates superior performance in both operation time and PSNR.

Conclusions:

• The proposed real SVD-based compression scheme offers a computationally efficient and effective alternative for color image compression.
• This method provides a favorable trade-off between compression ratio, speed, and image fidelity.
• The real compression scheme presents significant advantages over quaternion-based methods, particularly in terms of operational efficiency and speed.