Projective Data Compression for Recoverable Component Magnitudes
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Solution Overview
Problem
Existing data compression techniques using 1-bit compressive sensing struggle to preserve the sizes of components of a numeric string during compression, making it difficult to decompress back to the original string accurately.
Innovation Solution
Performing projective transformation of the numeric string into a string with more components, ensuring the sum of squares of components meets a predetermined value, and generating a bit string indicating positive and negative signs of the operation result with an observation matrix, allowing for accurate decompression.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Quantity of substance
If 1-bit compressive sensing is used to compress a numeric string to a bit string, then data compression ratio is improved, but the ability to specify component sizes during decompression deteriorates
Solution Approach 1:
The patent applies preliminary action by performing projective transformation on the numeric string before compression. This transformation preprocesses the data to embed component size information into the transformed representation, ensuring that this information is preserved through the subsequent 1-bit compressive sensing process. The transformation is designed so that the magnitude information is encoded in a way that can be recovered during decompression.
Solution Approach 2:
The patent changes parameters by transforming the numeric string into a different mathematical representation through projective transformation. This parameter change converts the original numeric values into a transformed space where the component size information is preserved in the structure of the transformed data, allowing it to survive the aggressive 1-bit quantization process.
2Measurement precision
If projective transformation is performed to increase the number of components, then decompression accuracy is improved, but computational complexity increases
Solution Approach 1:
The patent applies parameter changes by using projective transformation to convert the numeric string into a transformed representation with more components. This transformation changes the parameter space in a structured mathematical way that preserves information while enabling accurate decompression. The transformation uses predetermined matrices and mathematical operations that maintain the relationship between original and transformed values.
Data Source
AI summary
An information processing method for a computer for data compression, the method includes: performing projective transformation of a first numeric string corresponding to an input signal into a second numeric string which contains more components than the first numeric string and having a sum of squares of components as a predetermined value by using a plurality of projective parameters; and generating a bit string in which bits indicating positive and negative signs of the respective components of an operation result obtained by a vector product operation of the second numeric string obtained by the projective transformation and an observation matrix are arranged.