Learned Signal Sampling and Decoding for Limited Measurements
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Solution Overview
Problem
Existing signal sampling methods face challenges in adaptively constructing sampling operators for efficient reconstruction and classification, often relying on 'hand-crafted' decoders and not fully utilizing training signals, particularly in applications where the number of samples is limited.
Innovation Solution
A method that jointly trains sampling operators and decoders using learnable priors, allowing for adaptive sampling and decoding optimized for specific applications, enabling efficient reconstruction and classification with a reduced number of samples.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Device complexity
If hand-crafted decoders are used in signal sampling, then device complexity is reduced, but measurement precision and reconstruction accuracy deteriorate
Solution Approach 1:
The decoder is trained in advance on a training set of signals to learn optimal decoding parameters before actual signal reconstruction. This preliminary training phase allows the decoder to adapt to specific signal characteristics, improving reconstruction accuracy without increasing operational complexity during the sampling phase.
Solution Approach 2:
The system uses the training signals themselves to automatically learn and optimize the decoder parameters, eliminating the need for manual hand-crafting. The training process enables the decoder to self-adjust its parameters based on the statistical properties of the target signal class, improving precision while maintaining ease of deployment.
2Productivity
If the number of samples is reduced, then productivity and efficiency improve, but loss of information increases
Solution Approach 1:
The system changes the parameters of the sampling operator based on the training set characteristics. By learning optimal sampling parameters from training data, the system can efficiently select which coefficients to retain, maximizing information preservation with fewer samples. The sampling operator parameters are adapted to the specific signal class being processed.
Solution Approach 2:
The training process provides feedback about the statistical properties of the signal class, which is then used to optimize both the sampling operator and decoder. This feedback loop allows the system to learn the minimal sufficient set of samples needed for accurate reconstruction, balancing information retention with sampling efficiency.
3Measurement precision
If sampling operators are adapted to training signals, then measurement precision improves, but device complexity increases
Solution Approach 1:
The sampling operator parameters are determined in advance during the training phase on a training set. This preliminary adaptation allows the system to learn optimal sampling strategies specific to the target signal class before deployment. The learned parameters are then fixed, avoiding the need for complex real-time adaptation during actual sampling operations.
Solution Approach 2:
The system transitions from static, generic sampling operators to dynamic, learned sampling operators that adapt to the specific characteristics of the signal class. The sampling operator becomes tailored to the training signals through the learning process, improving precision while maintaining a manageable level of complexity through parameter learning rather than structural complexity.
4Measurement precision
If training signals are fully utilized, then measurement precision improves, but loss of time in training increases
Solution Approach 1:
The system uses a training set that is sufficient but not necessarily exhaustive for achieving the desired accuracy. By carefully selecting the size and composition of the training set, the system achieves good reconstruction performance without requiring excessive training time. The training process stops when sufficient accuracy is reached, balancing training investment with performance gains.
Data Source
AI summary
A method of sampling and decoding of a signal of interest x comprising, at a training stage: acquiring a set of training signals {xi}i=1M, providing a sampling operator PΩ and a decoder gθ<sub2>g</sub2>(.), training operator PΩ on signals {xi}i=1M to obtain a learned sampling operator P{circumflex over (Ω)}; and, at a sampling stage: applying P{circumflex over (Ω)} in a transform domain Ψ to signal x, resulting in observation signal y; applying the decoder gθ<sub2>g</sub2>(.) to y, to produce an estimate {circumflex over (x)} of signal x to decode and/or, decide about, the signal. Decoder gθ<sub2>g</sub2>(.) is trained jointly with PΩ on signals {xi}i=1M, to obtain a learned decoder g{circumflex over (θ)}<sub2>g</sub2>, by jointly determining, during a cost minimization step, sampling parameters Ω and decoding parameters θg according to a cost function, and wherein the step of applying the decoder gθg(.) uses decoding parameters θg, such that estimate {circumflex over (x)} is produced by the learned decoder g{circumflex over (θ)}<sub2>g</sub2>.