Spherical Shearlet Compression for 3D Scalar Data
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Solution Overview
Problem
Current methods lack an effective technique for three-dimensional information compression and reconstruction based on spherical shearlet representation, which is essential for accurately capturing and processing data with spherical features in three-dimensional spaces, such as medical imaging and natural surface analysis.
Innovation Solution
A spherical shearlet-based compression and reconstruction method that decomposes three-dimensional space into concentric spherical layers, using a discrete spherical shearlet system to extract and store scalar data information, allowing for efficient decomposition and reconstruction of data with spherical features.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If conventional methods (Fourier analysis, spline analysis, wavelet analysis) based on Cartesian coordinates are used, then the processing is simple and straightforward, but the accuracy in capturing spherical distribution features and linear singularities is insufficient
Solution Approach 1:
The patent transforms the coordinate system from Cartesian to spherical coordinates, and introduces spherical shearlet functions that are adapted to spherical geometry. The spherical shearlet transform uses spherical harmonics and spherical dilations to capture features on spherical surfaces, making the processing system inherently suited for spherical distribution data rather than forcing spherical data into a Cartesian framework.
Solution Approach 2:
The patent changes the fundamental parameters of the analysis system by introducing spherical coordinates (r, θ, φ) and spherical shearlet parameters including scale parameters (a, b), rotation parameters (R), and frequency parameters (n, l, m). This parameter transformation enables the system to naturally represent spherical features and linear singularities that cannot be efficiently captured by conventional Cartesian-based methods.
2Loss of information
If a spherical shearlet representation is adopted to accurately capture key information from spherical data, then the representation accuracy and efficiency are improved, but there is currently no technical method for three-dimensional information compression and reconstruction based on spherical shearlet
Solution Approach 1:
The patent segments the three-dimensional space into multiple spherical shells or layers, each characterized by specific radial distance ranges. The spherical shearlet transform is applied independently to each shell, allowing for localized processing and compression. This segmentation strategy enables efficient compression by treating different radial regions separately while maintaining the ability to reconstruct the complete three-dimensional field.
Solution Approach 2:
The patent introduces spherical shearlet coefficients as an intermediary representation between the original spherical data and the compressed storage format. These coefficients serve as a compact intermediate form that captures the essential features of the data, enabling lossy or lossless compression while preserving the ability to reconstruct the original information through inverse transform.
3Productivity
If three-dimensional scalar data with spherical features is processed using conventional methods, then the processing framework is well-established, but the efficiency and accuracy for data with curvelinear singular distributions are insufficient
Solution Approach 1:
The patent employs spherical shearlet functions that are specifically designed to capture curvelinear features on spherical surfaces. These functions incorporate spherical harmonics and are adapted to the curvature of spherical geometry, enabling efficient representation of ridges, trenches, and other curvelinear singularities that conventional flat-based wavelets cannot represent efficiently.
Solution Approach 2:
The patent introduces multi-scale and multi-orientation spherical shearlet bases that can dynamically adapt to the local features of the data. By using variable scale parameters and rotation parameters, the system can dynamically adjust its resolution and orientation to match the local geometry of spherical features, improving both processing efficiency and accuracy for complex curvelinear distributions.
Data Source
AI summary
A spherical shearlet-based compression and reconstruction method for three-dimensional scalar information is disclosed. The method is used for processing data distributed in accordance to certain probability distribution in a three-dimensional space, and is especially suitable for processing random or deterministic scalar data having a spherical distribution feature under polar coordinates and being anisotropic on a sphere, including spatial data with physical significance and clinical observation data in biomedicine. In the present disclosure, on the basis of reasonably dividing the three-dimensional space into multiple concentric spherical layers, the three-dimensional data distribution is decomposed into multiple layers of spherical data. In each layer related spherical information is decomposed, and key information is extracted, compressed and stored by using the mathematical property of a spherical shearlet system, and the original three-dimensional data information can be reconstructed or approximately restored from extracted key data.