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, efficiently computing a part of Fourier coefficients for multidimensional data.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If conventional partial Fourier transform is applied to multidimensional data, then computational complexity is reduced by computing only necessary coefficients, but the method becomes inefficient and inaccurate for multidimensional data
Solution Approach 1:
The patent transforms the multidimensional partial Fourier transform problem into a polynomial approximation problem by changing the mathematical parameters and representation form. This allows the use of efficient polynomial-based algorithms while maintaining the accuracy of Fourier coefficient computation for multidimensional data
Solution Approach 2:
The patent replaces the traditional mechanical Fourier transform computation with an algebraic polynomial approximation system. By substituting the trigonometric-based Fourier transform with polynomial-based computation, the method achieves both efficiency and accuracy for multidimensional data
2Measurement precision
If manual hyperparameter selection is used in polynomial approximation, then computational costs increase and processing time is extended
Solution Approach 1:
The patent implements self-service by enabling the system to automatically select optimal hyperparameters through polynomial degree determination algorithms. The system autonomously determines the appropriate polynomial degree based on the input data characteristics and desired accuracy, eliminating the need for manual hyperparameter tuning
Solution Approach 2:
The patent performs preliminary action by pre-determining the optimal polynomial degree and approximation parameters before the main Fourier transform computation. This preliminary setup phase automatically configures all necessary hyperparameters, preventing time loss during the actual computation process
Data Source
AI summary
Proposed are a fast multidimensional partial Fourier transform method and apparatus. According to an aspect, 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.