DCT Domain Down-Sampling Using Transform Matrices
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Solution Overview
Problem
Existing methods for down-sampling images represented in the Discrete Cosine Transform (DCT) domain require conversion to the spatial domain, resulting in high computational complexity and increased processing time due to the need for inverse DCT and subsequent re-conversion, making them inefficient for wireless image transfer and display on diverse devices.
Innovation Solution
The method involves applying two linear transform double-sided matrices directly in the DCT domain to down-sample images, using a row transform matrix and a column transform matrix to directly reduce the dimensions of DCT images, thereby bypassing the need for spatial domain conversion and reducing computational complexity.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of operation
If conversion to spatial domain is performed for down-sampling DCT images, then standard down-sampling methods can be applied, but computational complexity increases significantly
Solution Approach 1:
The patent introduces transform matrices as intermediary components that enable direct down-sampling in the DCT domain. These matrices serve as mediators between the DCT domain and the down-sampling operation, eliminating the need for spatial domain conversion while maintaining down-sampling effectiveness.
Solution Approach 2:
The patent replaces the mechanical process of converting to spatial domain, performing down-sampling, and converting back with a direct matrix-based operation in the DCT domain. This substitution eliminates multiple transformation steps while achieving the same down-sampling result with reduced computational complexity.
2Ease of operation
If inverse DCT and DCT operations are applied for down-sampling, then spatial domain down-sampling is enabled, but processing time increases
Solution Approach 1:
The patent pre-computes and stores transform matrices that encapsulate the down-sampling operation. By having these matrices ready in advance, the system can directly apply them to DCT images without performing time-consuming inverse DCT and DCT conversions during actual down-sampling operations.
Solution Approach 2:
The patent creates a simplified representation of the down-sampling operation through transform matrices that copy the essential down-sampling functionality directly into the DCT domain. This copying approach preserves down-sampling effectiveness while eliminating the need for multiple domain conversions.
3Quantity of substance
If standard down-sampling methods are used for DCT images, then image size is reduced, but bandwidth requirements for wireless transfer increase
Solution Approach 1:
The patent changes the parameter space in which down-sampling is performed, moving from spatial domain to DCT domain operations. This parameter change allows the system to directly manipulate frequency coefficients, achieving effective size reduction without the energy loss associated with repeated domain transformations and without compromising image quality for wireless transmission.
Data Source
AI summary
A method and device that uses transform matrices to down-sample a DCT image directly in the DCT domain. The transform matrices have been selected to minimize an optimization problem which is a function of the visual quality of down-sampled images obtained using the matrices and the computational complexity associated with using the transform matrices. The transform matrices comprise a row transform matrix and a column transform matrix. A down-sampled image is produced by determining an intermediary matrix as the product of the DCT image and one of either the row transform matrix or the column transform matrix and then determining the down-sampled image as the product of the intermediary matrix and the transform matrix not already used to determine the intermediary matrix.