2D Discrete Fourier Transform Edge Artifact Removal
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Solution Overview
Problem
Existing techniques for removing edge artifacts in 2D discrete Fourier transforms are computationally intensive and inefficient, particularly for real-time applications, as they require large memory usage and multiple invocations of 1D DFT routines, and do not effectively address edge artifacts in a conveniently implementable manner on Field Programmable Gate Arrays (FPGAs).
Innovation Solution
A method and system that perform a 2D discrete Fourier transform by extracting boundary data, performing 1D FFTs on rows and columns, and using a simplified processing technique to derive a smooth component, which is then subtracted from the 2D FFT to remove edge artifacts, reducing the need for column-by-column 1D FFTs and minimizing external memory access.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If conventional 2D FFT implementations using row-column decomposition are used, then computational throughput is improved, but edge artifacts are generated in the frequency domain
Solution Approach 1:
The image is divided into multiple blocks, and the FFT is computed for each block separately. This segmentation approach allows the algorithm to process local regions independently, reducing the propagation of edge artifacts across the entire frequency domain while maintaining computational efficiency through parallel processing of blocks.
2Object-generated harmful factors
If image blocking is applied to reduce edge artifacts, then artifact removal is improved, but computational complexity increases
Solution Approach 1:
Instead of computing FFT for every possible block configuration, the algorithm selectively processes only necessary blocks and uses overlap-add methodology to combine results. This partial action approach reduces computational complexity by avoiding redundant calculations while still effectively removing edge artifacts through strategic block selection and combination.
3Object-generated harmful factors
If overlapping block processing with overlap-add methodology is used, then edge artifact removal is improved, but memory usage increases
Solution Approach 1:
The algorithm pre-computes and stores convolution kernels and intermediate results in memory before the main FFT processing begins. By performing preliminary actions such as pre-calculating block transformation matrices and preparing overlap-add weightings, the system reduces the need for extensive temporary memory during the actual processing phase, thereby managing memory usage more efficiently.
Data Source
AI summary
A method for performing 2-dimensional discrete Fourier transform of a subject image data to be performed in one or more digital processors includes performing 1-dimensional fast Fourier transform on each row of the subject image data and 1-dimensional fast Fourier transform on each column of the subject image, and performing a simplified fast Fourier transform processing on the extracted boundary image without performing column-by-column 1-dimensional fast Fourier transform by: performing 1-dimensional fast Fourier transform only on a first column vector in the extracted boundary image data, using scaled column vectors to derive fast Fourier transform of remaining columns of the extracted boundary image data, and performing 1-dimensional fast Fourier transform on each row of the extracted boundary image data. Then, fast Fourier transform of a periodic component of the subject image data with edge-artifacts removed and fast Fourier transform of a smooth component of the subject image data are derived from results of steps (b) and (c).