MRI FIR Filtering Using Incremental Integral Value Updates
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Solution Overview
Problem
It has been challenging to put a finite impulse response (FIR) digital filter with a large number of taps into practical use due to computational complexity and efficiency issues.
Innovation Solution
A signal processing apparatus that computes integral values by adding and subtracting non-overlapping values from input sequences, using a representative coefficient to reduce computational complexity and achieve efficient FIR filtering, particularly in magnetic resonance imaging applications.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If an FIR digital filter with a large number of taps is used, then filtering accuracy is improved, but computational complexity increases
Solution Approach 1:
The patent divides the filter coefficient sequence into multiple segments or groups, and processes them separately using integral value computation. This segmentation reduces the computational burden on individual processing units while maintaining the overall filtering accuracy of the large-tap FIR filter.
Solution Approach 2:
The patent transforms the conventional direct computation approach into an integral value-based computation method. By changing the computational parameters from direct coefficient multiplication to integral value accumulation and difference calculation, the system achieves reduced computational complexity while preserving filtering performance.
2Measurement precision
If an FIR digital filter with a large number of taps is used, then filtering accuracy is improved, but processing time increases
Solution Approach 1:
The patent pre-computes and stores integral values based on the input signal sequences before the actual filtering operation. This preliminary action allows the filter to use pre-prepared integral values and their differences, significantly reducing the processing time during actual filter operation while maintaining accuracy.
Solution Approach 2:
The patent implements a continuous computation scheme where integral values are updated incrementally as new input data arrives, rather than re-computing from scratch. This continuous action maintains filtering accuracy while reducing redundant calculations and processing time.
3Measurement precision
If integral value computation with high precision is performed, then output accuracy is improved, but memory requirements increase
Solution Approach 1:
The patent applies different precision levels to different parts of the computation process. High precision is maintained for critical integral value calculations and final output, while lower precision can be used for intermediate steps where accuracy requirements are less stringent. This local differentiation optimizes memory usage while preserving overall output accuracy.
Data Source
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AI summary
A signal processing apparatus (1) according to the present embodiment computes a first integral value corresponding to an element in a coefficient sequence of a first input sequence and a second integral value corresponding to the element in a coefficient sequence of a second input sequence next to the first input sequence, and includes an integral value computing unit (151). The integral value computing unit adds a value not overlapping the first input sequence in the second input sequence to the first integral value and subtracts a value not overlapping the second input sequence in the first input sequence from the first integral value for the element, thereby computing the second integral value.