Fast multidimensional partial fourier transform method and apparatus capable of supporting automatic hyperparameter selection
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Solution Overview
Problem
Conventional partial Fourier transform methods are inefficient for multidimensional data and require manual hyperparameter selection, leading to increased computational costs and reduced performance when applied to multidimensional data.
Innovation Solution
A fast multidimensional partial Fourier transform method and apparatus that automatically selects hyperparameters using polynomial approximation and unconstrained convex optimization, decomposing computations into matrix multiplication and small sub-blocks to efficiently compute a part of the Fourier coefficients.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If conventional partial Fourier transform is used for multidimensional data, then computational complexity is reduced by computing only part of coefficients, but it requires manual hyperparameter selection and does not optimize computation process for multidimensional data
Solution Approach 1:
The system performs self-configuration by automatically selecting hyperparameters and optimizing computation processes without manual intervention. The apparatus autonomously adapts to multidimensional data characteristics, eliminating the need for user expertise in parameter tuning while maintaining optimal computational efficiency.
Solution Approach 2:
The system dynamically adjusts hyperparameters based on the characteristics of multidimensional input data. By automatically modifying parameters such as block size, transform dimensions, and computation strategies, the system optimizes performance for different data types and sizes without requiring manual parameter selection.
2Measurement precision
If conventional partial Fourier transform is used, then some Fourier coefficients are computed, but computational costs are high and processing speed is reduced for multidimensional data
Solution Approach 1:
The multidimensional data is divided into smaller blocks or sub-regions that can be processed independently and in parallel. This segmentation allows the system to compute Fourier coefficients for each block efficiently, reducing overall processing time while maintaining accuracy through systematic combination of block results.
Solution Approach 2:
The system performs preliminary analysis of the multidimensional data to identify characteristics such as dimensionality, size, and distribution patterns. Based on this preliminary assessment, it pre-configures optimal computation strategies and hyperparameters, enabling faster processing while ensuring accurate coefficient computation without trial-and-error adjustments.
Data Source
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AI summary
Proposed are a fast multidimensional partial Fourier transform method and apparatus. According to an aspect of the present invention, there is provided a fast multidimensional partial Fourier transform method, the fast multidimensional partial Fourier transform method being performed by a fast multidimensional partial Fourier transform apparatus, the fast multidimensional partial Fourier transform method including: setting a plurality of hyperparameters used in partial Fourier transform based on constraints on the tolerance and degree of the polynomial for polynomial approximation; and approximating and computing the multidimensional Fourier coefficients of a partial Fourier transform for multidimensional data based on the plurality of hyperparameters.