Walsh-Transform Signal Compression for Low-Sparsity Decompression
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Solution Overview
Problem
Conventional compressive sensing techniques struggle with accurate decompression when the original input digital signal has low sparsity, leading to increased decompression errors and power consumption in wireless sensor nodes.
Innovation Solution
The use of a Walsh function-based observation matrix for data compression and decompression, which extracts specific frequency components, allowing for accurate decompression even with low sparsity signals by converting the input digital signal and utilizing inverse Walsh or discrete Fourier transforms.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of manufacture
If conventional compressive sensing with random observation matrix is used, then compression operations are simple (addition and subtraction only), but decompression accuracy deteriorates when the original input digital signal has low sparsity
Solution Approach 1:
The patent changes the observation matrix from a random matrix to a Walsh-Hadamard matrix, which has structured properties that enable both simple compression operations and accurate decompression for low-sparsity signals. The Walsh-Hadamard matrix elements are still ±1, maintaining the simple addition/subtraction operation, but the structured pattern improves decompression accuracy.
Solution Approach 2:
The patent combines the simplicity of random matrix operations with the structured properties of Walsh-Hadamard matrices to create a composite approach that achieves both compression simplicity and decompression accuracy for low-sparsity signals.
2Quantity of substance
If data compression techniques like ZIP and LZH are used, then data compression ratio is improved, but power consumption increases due to many arithmetic operations
Solution Approach 1:
The patent replaces complex compression algorithms (ZIP, LZH) with a linear algebra-based compressive sensing approach using Walsh-Hadamard transform. This substitution reduces the computational complexity from many iterative arithmetic operations to simple matrix multiplication with ±1 elements, significantly reducing power consumption while maintaining compression effectiveness.
Solution Approach 2:
The patent changes the compression approach from traditional lossy compression algorithms to compressive sensing with Walsh-Hadamard matrix, which achieves comparable compression ratios with dramatically reduced arithmetic operations and power consumption.
3Loss of energy
If the number of compressed data M is reduced (M < N), then wireless transmission power is reduced, but decompression accuracy deteriorates when sparsity is low
Solution Approach 1:
The patent changes the observation matrix structure to Walsh-Hadamard, which maintains decompression accuracy for low-sparsity signals even when M is significantly less than N. The structured properties of the Walsh-Hadamard matrix enable accurate signal recovery from highly compressed data.
Data Source
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AI summary
An object is to provide a transmitting device, a receiving device, and a transmitting and receiving system, which enable accurate decompression even if sparsity of an original input digital signal is low. Accordingly, a compressing unit 11 is included, which generates and outputs a compressed digital signal d that has been compressed, by converting an input digital signal x by use of a Walsh function and extracting a specific frequency component. The compressing unit 11 has an extracted observation matrix multiplying unit 12 that multiplies the input digital signal x by an observation matrix corresponding to a Walsh function of the specific frequency component, and generates and outputs, as the compressed digital signal d, the digital signal converted by the extracted observation matrix multiplying unit 12.