MRI Signal Processing for Large-Tap FIR Filter Computation

The patent divides the filter coefficient sequence into multiple segments and processes each segment separately. By segmenting the large-scale filter into smaller manageable parts, the computational complexity is reduced while maintaining the overall filtering precision of the large-tap FIR filter.

The patent performs preliminary computation of integral values and stores them for reuse. By pre-computing and storing integral values that will be needed for subsequent filtering operations, the actual filtering process requires fewer computations, thus reducing computational complexity while preserving filtering accuracy.

The patent pre-computes and stores integral values before the actual filtering operation. This preliminary action ensures that large cumulative sums are calculated once and stored, avoiding repeated computation that would exacerbate significant digit cancellation and maintain calculation reliability.

The patent introduces integral values as intermediary quantities that mediate between the input signal and the final filtered output. These intermediary integral values are computed with sufficient precision and stored, serving as a buffer that prevents significant digit cancellation from propagating through the filtering process.

By segmenting the filter coefficients and processing different segments with different levels of computational effort, the patent achieves a balance between processing speed and filtering precision. Important segments can be processed with higher precision while less critical segments use simplified computation.

The patent changes computational parameters dynamically, using full precision for critical computations and reduced precision for less critical ones. The integral value computation uses appropriate precision levels based on the specific filtering requirements, optimizing the trade-off between processing speed and filtering precision.