Compressed Signal Encoding With Sparse Projection Reconstruction
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Solution Overview
Problem
Current Compressed Sensing methods lack an algorithmic approach for reconstructing signals with fewer computations, and existing algorithms are not efficient for general results or succinct dictionary transformations.
Innovation Solution
A method involving a signal processor that encodes signals into linear projections and uses a decoding algorithm with matrix construction steps (macro separation, micro separation, and estimation) to reconstruct signals approximately, utilizing Sparse Approximation Theory and randomized constructions to achieve efficient and accurate signal reconstruction.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If Compressed Sensing is used to reduce the number of measurements, then the number of computations is reduced, but there is no algorithmic approach available for reconstruction
Solution Approach 1:
The patent replaces traditional mechanical/mathematical approximation methods with a randomized algorithmic system. The randomized construction of measurement matrices and decoding algorithms substitutes conventional deterministic approaches, enabling efficient signal reconstruction from compressed measurements while maintaining theoretical guarantees through probabilistic analysis.
2Device complexity
If fewer linear measurements are used for signal reconstruction, then computational complexity is reduced, but measurement precision may be compromised
Solution Approach 1:
The patent transforms the measurement process by changing parameters of the measurement matrix through randomized construction. By using random matrices with specific probabilistic properties rather than deterministic structures, the system achieves accurate signal reconstruction from fewer measurements while controlling computational complexity through randomized algorithms.
Solution Approach 2:
The decoding algorithm incorporates iterative refinement and feedback mechanisms that use the compressed measurements to progressively reconstruct the signal. The algorithm adjusts its estimates based on feedback from the measurement residuals, improving reconstruction accuracy even with limited measurements while maintaining computational efficiency.
Data Source
AI summary
Described is a system and method for receiving a signal for transmission and encoding the signal into a plurality of linear projections representing the signal. The encoding includes defining a transform matrix. The transform matrix being defined by processing the signal using a macroseparation matrix, processing the signal using a microseparation matrix and processing the signal using an estimation vector.