Iterative PCA Basis Set Truncation for Image Compression
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Solution Overview
Problem
Current image compression techniques face challenges in achieving high compression ratios while maintaining fidelity to the original image, particularly in lossy compression methods which often result in significant loss of information.
Innovation Solution
The method employs a multi-pass Principal Component Analysis (PCA) with puncturing and truncation of orthogonal basis sets to compress images, using a projector and truncator to form a truncated basis set for image projection, thereby achieving extreme compression with substantial retention of high-frequency details.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Quantity of substance
If lossy compression techniques are used to achieve high compression ratios, then the compressed file size is reduced, but the fidelity to the original image deteriorates with significant loss of information
Solution Approach 1:
The image is divided into multiple blocks or regions, and PCA is applied iteratively to each block. This segmentation allows different basis sets to be generated for different regions, enabling selective retention of important features while compressing less critical areas, thus achieving high compression ratios while maintaining overall image fidelity.
Solution Approach 2:
The patent transforms the image data from spatial domain to frequency domain through iterative PCA, creating a multi-dimensional representation. By operating in this transformed dimension space and selectively truncating basis vectors, the method achieves compression while preserving essential image information that would be lost in traditional single-pass approaches.
2Quantity of substance
If traditional PCA compression is used to reduce image size, then the compression ratio is improved, but the retention of high-frequency details deteriorates
Solution Approach 1:
The patent performs preliminary iterative PCA analysis to generate a complete set of orthogonal basis vectors before truncation. This preliminary action allows the system to identify and prioritize basis vectors that capture high-frequency details, ensuring these are retained even when the basis set is truncated for compression, thus preserving image sharpness and detail.
Solution Approach 2:
The method dynamically adjusts the number of retained basis vectors based on local image characteristics and frequency content. By changing the truncation parameter adaptively across different image regions and iteration stages, the system preserves high-frequency details where needed while achieving aggressive compression in smoother regions.
Data Source
AI summary
An apparatus for compressing an image including: a principal component analyzer, a puncture, a truncator, and a projector. The principal component analyzer iteratively performs a Principal Component Analysis (PCA) on a selected portion of the image, wherein each resulting orthogonal basis set has “N” basis vectors. The puncturer punctures selected dimensional components of the orthogonal basis set resulting from each PCA of the selected portion of the image, without removing any of the associated “N” basis vectors thereof. The truncator removes selected basis vectors of a final one of the resulting orthogonal basis sets of the principal component analyzer, thereby forming a truncated basis set for compression of the selected portion of the image. The projector projects the image onto the truncated basis set thereby obtaining coefficients of the selected portion of the image, relative to the truncated basis set.