Image Processing System Polar Form Fourier Transform
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Solution Overview
Problem
Current image processing systems face inefficiencies in performing two-dimensional Fourier transforms and data compression of complex image data, particularly in holographic display applications, where phase information is critical and existing methods lead to quality losses and increased processing time due to memory bottlenecks.
Innovation Solution
An image processing system that performs a 1D Fourier transform on each linear array of a complex data set, converts values to polar form, reduces the bit number format, stores and processes these values efficiently, and then converts back to Cartesian form for further processing, thereby reducing memory requirements and maintaining image quality by prioritizing phase information.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Manufacturing precision
If the full precision complex data is stored in memory during row-column transformation, then image quality is maintained, but memory requirements and processing time increase significantly
Solution Approach 1:
The patent applies local quality by treating magnitude and phase components differently during compression. The magnitude component is compressed with higher precision (maintaining more bits) while the phase component uses lower precision, reflecting the local importance of each component to image quality. This resolves the contradiction by allocating memory resources non-uniformly based on local quality requirements.
Solution Approach 2:
The patent changes the representation parameters of complex data by separating magnitude and phase, then applying different bit-depth reductions to each. This parameter change allows selective compression that maintains critical quality attributes while reducing overall memory requirements, directly addressing the contradiction between quality and memory usage.
2Quantity of substance
If bit reduction is applied to complex image data, then memory requirements decrease, but image quality and phase information accuracy deteriorate
Solution Approach 1:
The patent implements local quality by applying differential compression to magnitude and phase components. The phase component, which is critical for holographic quality, retains more precision while magnitude undergoes greater compression. This resolves the contradiction by preserving quality in the most critical local components while reducing overall data size.
Solution Approach 2:
The patent changes the precision parameters selectively for different components of the complex data. By maintaining higher bit-depth for phase information and reducing it for magnitude, the system achieves memory reduction without sacrificing the quality-critical phase accuracy, thus resolving the contradiction.
3Productivity
If conventional Fourier transform methods are used, then image processing is performed, but processing speed is limited by memory bottlenecks
Solution Approach 1:
The patent changes the data representation parameters by converting complex data to polar form (magnitude and phase) before processing. This parameter change enables more efficient memory usage during the Fourier transform, as the separated components can be processed with different precision levels, reducing memory bandwidth requirements and improving processing speed.
Solution Approach 2:
The patent applies local quality principles by processing magnitude and phase components with different precision levels during the Fourier transform. This allows the system to allocate memory bandwidth efficiently, prioritizing the transport of critical phase information while using less bandwidth for magnitude data, thus improving overall processing speed.
Data Source
AI summary
Methods of performing a complex Fourier transform of a complex data set corresponding to an image are disclosed. The methods comprise receiving a complex data set and performing a first 1D complex Fourier transform in the complex data set in Cartesian form; converting the complex data set into polar form and compressing the complex data set in polar form; performing a row-column transformation of the complex data set; decompressing the complex data set and converting the complex data set back into Cartesian form; and performing a second 1D Fourier transform in the complex data set in Cartesian form, wherein the second 1D complex Fourier transform is orthogonal to the first 1D complex Fourier transform. Corresponding systems are also disclosed, as are application to the iterative computation of computer-generated holograms.