Image Coding Using Rate-Distortion Optimal Orthogonal Matching Pursuit
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Solution Overview
Problem
Transform-based image and video compression using over-complete dictionaries faces challenges due to the NP-hard problem of finding sparse representations, which increases computational complexity and resource usage.
Innovation Solution
The method employs Rate-Distortion (R-D) optimal Orthogonal Matching Pursuit (OMP) selection, determining a sparsity constraint and iteratively finding approximations with dictionary element indices and coefficients, terminating when the constraint is met, and selecting the optimal solution based on minimum R-D cost.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Loss of information
If basis selection methods using over-complete dictionaries are used for signal approximation, then compression efficiency is improved, but computational complexity increases due to the NP-hard problem
Solution Approach 1:
The patent changes the parameter of sparsity constraint to control the number of iterations in the OMP algorithm. By setting a fixed sparsity constraint value, the algorithm terminates after a predetermined number of iterations, transforming the NP-hard basis selection problem into a tractable iterative process with controlled computational complexity while maintaining good compression efficiency.
Solution Approach 2:
Instead of seeking the complete optimal solution to the NP-hard basis selection problem, the patent applies partial action by using the OMP algorithm to find a sufficiently good approximate solution within a fixed number of iterations defined by the sparsity constraint. This partial solution approach achieves acceptable compression performance without the prohibitive computational cost of exhaustive search.
2Measurement precision
If iterative approximation methods are used to find sparse representations, then approximation quality is improved, but encoding time increases
Solution Approach 1:
The patent employs periodic action through the iterative nature of the OMP algorithm, which systematically refines the approximation in discrete steps. Each iteration adds one basis element and updates coefficients, providing periodic improvements in approximation quality while allowing the process to be terminated after a fixed number of periods (iterations) to control encoding time.
Solution Approach 2:
The patent applies preliminary action by pre-determining the sparsity constraint value before encoding begins. This preliminary setting of the iteration limit prepares the encoding process in advance, allowing the iterative approximation to proceed with a known time budget, thus balancing approximation quality improvement against encoding time consumption.
3Manufacturing precision
If more iterations are performed in the OMP algorithm, then the approximation accuracy is improved, but system resource usage increases
Solution Approach 1:
The patent uses parameter changes by adjusting the sparsity constraint to control the number of iterations. This parameter serves as a knob to tune the balance between approximation accuracy and system resource usage, allowing the encoding process to achieve sufficient accuracy without exhausting computational resources.
Solution Approach 2:
The patent implements feedback through the iterative OMP process, where each iteration provides feedback on the improvement in approximation quality. The algorithm continues iterating while resources are available and stops when the predetermined iteration limit is reached, using the feedback from intermediate results to determine when to terminate the process to conserve system resources.
Data Source
AI summary
System and method embodiments for image coding are disclosed. In an embodiment, a method in a data processing system for image encoding includes determining a sparsity constraint according to a dimension of an input image signal. The method also includes iteratively determining a plurality of approximations to the input image signal. Each iteration provides an approximation of the input image signal. Each approximation includes a set of dictionary element indices and coefficients. The dictionary is an over-complete dictionary. Iterations of the determining step are terminated when a number of iterations is equal to the sparsity constraint. The method also includes selecting one of the plurality of approximations according to a minimum rate-distortion cost. The method also includes determining an encoded image signal according to non-zero coefficients and corresponding indices for each non-zero coefficient in the selected approximation.