DCT to DWT Coefficient Transformation via Fundamental Matrices
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Solution Overview
Problem
There is a need for a method to transform between discrete cosine transform (DCT) coefficients and discrete wavelet transform (DWT) coefficients to transcode images compressed using different standards, specifically from DWT-compressed images in JPEG2000 to DCT-compressed images in conventional JPEG, and vice versa, as no existing method can perform this conversion effectively.
Innovation Solution
An apparatus and method that calculate fundamental matrices to transform 2-dimensional 1-level DWT coefficients into 2-dimensional 8×8 DCT coefficients and vice versa, using forward and reverse DWT and DCT transform matrices with specific diagonal and zero-component configurations, allowing for the conversion of image data between the two transform domains without requiring the original image data.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If conventional image compression standards (JPEG/MPEG) use DCT transform, then compatibility with existing systems is maintained, but the compression rate and image quality are inferior compared to wavelet-based standards
Solution Approach 1:
The patent introduces a transformation mechanism that acts as an intermediary between DCT and DWT domains. The apparatus converts DCT coefficients to DWT coefficients (or vice versa) through matrix operations, enabling interoperability between JPEG and JPEG2000 formats without requiring original image data. This intermediary transformation resolves the contradiction by allowing systems to maintain DCT-based compatibility while achieving DWT-level compression efficiency.
2Productivity
If JPEG2000 uses DWT transform, then compression rate and image quality are improved, but compatibility with conventional DCT-based systems is lost
Solution Approach 1:
The patent applies inversion by enabling bidirectional transformation between DCT and DWT domains. Instead of only converting from DCT to DWT, the apparatus can also convert from DWT to DCT coefficients. This allows JPEG2000 systems to maintain their superior compression performance while providing a conversion path back to conventional DCT formats when needed, thus maintaining compatibility with legacy systems.
3Productivity
If direct conversion between DCT and DWT coefficients is implemented, then transcoding efficiency is improved, but computational complexity increases due to matrix operations
Solution Approach 1:
The patent implements preliminary action by pre-calculating and storing transformation matrices for converting between DCT and DWT domains. These fundamental matrices are computed in advance and can be reused for multiple transcoding operations. This approach reduces the computational burden during actual transcoding by replacing complex real-time matrix calculations with simpler matrix multiplications using pre-computed values.
Data Source
AI summary
Provided is an apparatus and method for transforming between a DCT coefficient and a DWT coefficient. The transforming apparatus includes a first fundamental matrix calculating unit, a second fundamental matrix calculating unit, and a DWT coefficient calculating unit. The first fundamental matrix calculating unit calculates a first fundamental matrix by multiplying an N×N forward DWT transform matrix and an N×N matrix that has diagonal components corresponding to a transpose matrix of an 8×8 DCT transform matrix and the remaining components corresponding to an 8×8 matrix with all elements being zero. The second fundamental matrix calculating unit calculates a second fundamental matrix by multiplying an M×M matrix, which has diagonal components corresponding to an 8×8 DCT transform matrix and the remaining components corresponding to an 8×8 matrix with all elements being zero, and a transpose matrix of an M×M forward DWT transform matrix. The DWT coefficient calculating unit calculates a 2-dimensional 1-level DWT coefficient by multiplying the first fundamental matrix, a 2-dimensional 8×8 DCT transform coefficient, and the second fundamental matrix.