Multidirectional Context Trees for Adaptive Signal Denoising
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Solution Overview
Problem
Optimizing context size and geometry in context-based signal and data processing is computationally expensive and conceptually challenging, leading to a need for more efficient and accurate methods for determining optimal or near-optimal context sets.
Innovation Solution
Constructing a multidirectional context tree by selecting a maximum context size, generating leaf nodes, and pruning level by level, using a problem-domain-related weighting function to determine optimal or near-optimal context sets for context-based analysis and processing.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If fixed-size context is employed in context-based analysis, then processing simplicity is maintained, but processing efficiency and accuracy are suboptimal
Solution Approach 1:
The patent applies dynamics by transitioning from fixed-size contexts to variable-size contexts that adapt to local data characteristics. The context size and geometry are allowed to vary dynamically based on the position within the symbol sequence and local statistical properties, enabling optimal processing efficiency without requiring complex manual optimization at each position.
Solution Approach 2:
The patent changes parameters by optimizing context size and geometry based on local data statistics and position-dependent characteristics. Instead of using a fixed context size, the system determines optimal context parameters dynamically for each position in the sequence, improving processing efficiency while managing complexity through systematic optimization methods.
2Measurement precision
If context size and geometry are optimized for each position, then processing accuracy is improved, but computational cost increases significantly
Solution Approach 1:
The patent applies preliminary action by precomputing and storing optimal context sets for different positions in the symbol sequence. These precomputed context sets are generated based on local statistics and position-dependent characteristics, allowing the system to achieve high processing accuracy without performing expensive optimization computations during actual processing operations.
Solution Approach 2:
The patent uses partial action by determining context sets for only the most relevant positions and contexts rather than exhaustively optimizing all possible contexts. The system focuses computational resources on determining optimal contexts where they provide the most benefit, reducing overall computational energy consumption while maintaining high accuracy where it matters most.
3Reliability
If variable context size is used to improve processing accuracy, then denoising performance is enhanced, but system complexity increases
Solution Approach 1:
The patent applies segmentation by dividing the context determination process into hierarchical levels using a context tree structure. The tree segments contexts by size and geometry, organizing them in a systematic hierarchy that simplifies management and selection. This segmented approach enables variable context sizes to be used effectively while reducing system complexity through structured organization.
Solution Approach 2:
The patent uses an intermediary context tree structure that mediates between the raw data and the denoising process. The context tree serves as an intermediate data structure that pre-organizes optimal contexts, allowing the denoising algorithm to access appropriate context sizes efficiently without directly managing the complexity of variable context determination.
Data Source
AI summary
In various embodiments of the present invention, optimal or near-optimal multidirectional context sets for a particular data-and/or-signal analysis or processing task are determined by selecting a maximum context size, generating a set of leaf nodes corresponding to those maximally sized contexts that occur in the data or signal to be processed or analyzed, and then building up and concurrently pruning, level by level, a multidirectional optimal context tree constructing one of potentially many optimal or near-optimal context trees in which leaf nodes represent the context of a near-optimal or optimal context set that may contain contexts of different sizes and geometries. Pruning is carried out using a problem-domain-related weighting function applicable to nodes and subtrees within the context tree. In one described embodiment, a bi-directional context tree suitable for a signal denoising application is constructed using, as the weighting function, an estimated loss function.