Multi-dimensional Wavelet Transform Partitioning for MRI
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Solution Overview
Problem
Existing methods for calculating multi-dimensional wavelet transforms in parallel computing environments require communication between computation units, leading to time latency that is unacceptable for applications like MRI image reconstruction, where quick processing is critical.
Innovation Solution
The method involves partitioning input signal data into multi-dimensional arrays that overlap by a number of pixels equal to the overlap value corresponding to non-zero filter coefficients, allowing each computation unit to perform the wavelet transform independently without communication, and aggregating results in memory.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If data is divided into one-dimensional arrays and processed on separate computation units, then parallel computing speed is improved, but communication latency between computation units increases
Solution Approach 1:
The patent segments the multi-dimensional wavelet transform into independent one-dimensional transform stages, where each stage processes data independently without requiring communication between computation units. The input data is partitioned into multiple one-dimensional arrays, and each computation unit processes its assigned array independently through the transform stages.
Solution Approach 2:
The patent transforms the traditional two-dimensional data organization into a multi-dimensional partitioning scheme where data is divided along multiple dimensions (e.g., row dimension, column dimension, and block dimension). This dimensional transformation allows computation units to process data independently by assigning different dimensional slices to different units, eliminating the need for inter-unit communication during the transform process.
2Loss of time
If communication between computation units is minimized, then processing time is reduced, but calculation accuracy may be compromised
Solution Approach 1:
The patent performs preliminary data preparation by organizing input data into specifically structured one-dimensional arrays before processing. The data is pre-partitioned and pre-formatted so that each computation unit receives complete, self-contained data sets that require no additional communication or coordination during the actual transform calculation, thus preserving accuracy while minimizing processing time.
Solution Approach 2:
The patent creates multiple independent copies of the transform computation logic across different computation units, where each unit executes the same transform algorithm on its assigned data partition. This copying approach ensures that each computation unit produces accurate results independently, and the final output is obtained by combining these independent results without requiring communication during the critical computation phases.
3Reliability
If traditional wavelet transform methods are used, then calculation between arrays is required, but this introduces unacceptable time latency for MRI reconstruction
Solution Approach 1:
The patent changes the fundamental parameters of the wavelet transform implementation by switching from a traditional multi-dimensional sequential approach to a series of independent one-dimensional transforms. By changing the transform dimensionality parameter and the data partitioning parameter, the system achieves faster processing suitable for MRI reconstruction while maintaining the mathematical correctness and image quality through proper synthesis of the independent transform results.
Data Source
AI summary
A computer-implemented method for calculating a multi-dimensional wavelet transform in an image processing system comprising a plurality of computation units includes receiving multi-dimensional image data. An overlap value corresponding to a number of non-zero filter coefficients associated with the multi-dimensional wavelet transform is identified. Then the multi-dimensional image data is divided into a plurality of multi-dimensional arrays, wherein the multi-dimensional arrays overlap in each dimension by a number of pixels equal to the overlap value. A multi-dimensional wavelet transform is calculated for each multi-dimensional array, in parallel, across the plurality of computation units.