Sparse Signal Sampling With Denoising for Sub-Nyquist Reconstruction
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Solution Overview
Problem
Existing signal processing technologies face challenges in accurately sampling and reconstructing non-bandlimited signals without violating Nyquist constraints, particularly in noisy environments, as they often require higher sampling rates and struggle with noise reduction.
Innovation Solution
The use of sparse sampling techniques at the rate of innovation of the signal, combined with a denoising process like the Cadzow algorithm, allows for sub-Nyquist sampling and reconstruction of signals with a Finite Rate of Innovation (FRI), which reduces noise and improves signal-to-noise ratio, enabling perfect or improved interpolation.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If traditional sampling methods are used to reconstruct non-bandlimited signals, then signal reconstruction accuracy is maintained, but sampling rate must exceed Nyquist rate and noise reduction is difficult
Solution Approach 1:
The patent changes the fundamental parameter from sampling rate to sparsity level. By exploiting the sparsity of signal innovations in the time domain, the method enables reconstruction at sub-Nyquist rates. The sampling rate is adapted to the sparsity level k, requiring only O(k log n) samples instead of the Nyquist rate proportional to bandwidth B.
Solution Approach 2:
The patent introduces dynamic adaptation between sampling rate and signal characteristics. The sampling scheme adjusts to the sparsity level of the signal, making the system flexible rather than fixed. This dynamic approach allows optimal sampling rates to be selected based on the actual signal structure.
2Measurement precision
If higher sampling rates are used to reconstruct non-bandlimited signals, then signal reconstruction accuracy is improved, but noise components are amplified and processing complexity increases
Solution Approach 1:
The patent changes the approach from increasing sampling rate to exploiting signal sparsity. By formulating reconstruction as a sparse optimization problem, the method achieves accurate reconstruction without amplifying noise. The sparsity constraint acts as a regularizer that suppresses noise components while recovering the true signal.
Solution Approach 2:
The patent converts the sparsity property of the signal into a beneficial constraint for noise rejection. By assuming the signal innovations are sparse, the method transforms this structural property into a powerful tool for separating signal from noise, achieving denoising as a byproduct of sparse reconstruction.
3Productivity
If sparse sampling at sub-Nyquist rates is applied, then sampling efficiency is improved, but noise reduction becomes more challenging
Solution Approach 1:
The patent changes the reconstruction approach from traditional filtering to sparse optimization. By solving a convex optimization problem that enforces sparsity, the method achieves both efficient sub-Nyquist sampling and effective noise reduction simultaneously. The sparsity constraint provides regularization that suppresses noise even with fewer samples.
Solution Approach 2:
The patent creates a multi-functional reconstruction framework that simultaneously achieves sampling and denoising. The sparse reconstruction algorithm serves dual purposes: recovering the signal from sub-Nyquist samples and suppressing noise components, eliminating the need for separate processing stages.
4Object-affected harmful factors
If denoising processes are applied to sampled signals, then signal-to-noise ratio is improved, but processing complexity and computational load increase
Solution Approach 1:
The patent merges sampling and denoising into a single unified sparse reconstruction process. Instead of separate sampling followed by separate denoising steps, the method performs both operations simultaneously through convex optimization, reducing overall processing complexity while achieving both goals.
Solution Approach 2:
The sparse reconstruction algorithm serves as a universal tool that simultaneously handles signal recovery and noise suppression. This multi-functional approach eliminates the need for multiple specialized processing stages, reducing computational overhead while maintaining effectiveness.
Data Source
AI summary
A method of signal processing, comprising: obtaining a digital signal (yn) based on another signal (xt) and noise; and estimating information relating to the another signal (xt) by using a denoising process to produce a denoised signal (y′n) and by processing the denoised signal (y′n), wherein the denoised signal (y′n) produced by the denoising process has a substantially Finite Rate of Innovation.