Jointly Trained Sampling Operator and Decoder for Signal Reconstruction
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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 selection of the transform basis is constrained.
Innovation Solution
A method that jointly trains sampling operators and decoders using learnable priors, allowing for the optimization of sampling parameters and decoding parameters together based on a cost function tailored to the specific application, enabling efficient reconstruction and classification.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Manufacturing precision
If hand-crafted decoders are used with fixed sampling operators, then device complexity is reduced, but reconstruction accuracy and adaptability deteriorate
Solution Approach 1:
The patent merges the sampling operator and decoder into a unified trainable system. The sampling operator P_Ω and decoder g_θ are jointly optimized through backpropagation, allowing them to adapt to each other's characteristics. This combination enables the system to achieve high reconstruction accuracy while maintaining manageable complexity through end-to-end learning.
Solution Approach 2:
The patent transforms fixed, hand-crafted decoder parameters into learnable parameters θ. The decoder evolves from a static structure to a dynamic one where parameters are automatically adjusted during training to optimize reconstruction performance for specific sampling patterns and signal characteristics.
2Manufacturing precision
If training signals are fully utilized for decoder adaptation, then reconstruction accuracy improves, but the number of required samples increases
Solution Approach 1:
By combining sampling operator learning and decoder learning into a single joint training process, the system efficiently utilizes training signals. The shared gradient updates allow both components to adapt simultaneously, achieving high accuracy with fewer samples compared to separate training approaches.
Solution Approach 2:
The joint training framework enables continuous optimization of both sampling and decoding throughout the training process. Rather than sequentially adapting components, the system continuously refines both simultaneously, maximizing the information extracted from each training sample.
3Productivity
If separate training of sampling operators and decoders is performed, then training efficiency is improved, but overall system performance deteriorates
Solution Approach 1:
The patent implements joint training where sampling operators P_Ω and decoders g_θ are optimized together through a unified loss function and gradient descent process. This allows the system to capture interactions between sampling and decoding that separate training would miss, achieving superior performance despite increased computational overhead.
Solution Approach 2:
The joint training framework establishes feedback loops where reconstruction errors directly inform updates to both sampling operators and decoders. The gradient of the loss function with respect to both P and θ is computed and used to simultaneously adjust both components, ensuring they co-adapt to each other's characteristics.
Data Source
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AI summary
The present invention concerns a method of sampling and decoding of a signal of interest x (60) comprising, at a training stage, the steps of - acquiring a set of training signals xii=1M (20), - providing a sampling operator PΩ (120) and a decoder gθg(.) (140), - training said sampling operator PΩ (120) on said set of training signals xii=1M (20) to obtain a learned sampling operator PΩ̂ (40), as well as, at a sampling stage, the steps of - applying during a sampling step the learned sampling operator PΩ̂ (40) in a transform domain Ψ (110) to the signal of interest x, resulting in observation signal y (80), - applying during a decoding step the decoder gθg(.) (140) to the observation signal y (80), to produce an estimate x̂ (100) of the signal of interest x (60) in order to decode the signal and/or to make a decision about the signal. The method distinguishes by the fact that it further comprises the step of - training said decoder gθg(.) (140) jointly with said sampling operator PΩ (120) on said set of training signals xii=1M (20), to obtain a learned decoder gθ̂g (50), by - jointly determining, during a cost minimisation step (180) of the training stage, a set of sampling parameters Q and a set of decoding parameters θg according to a cost function, and by the fact that the step of applying the decoder gθg(.) (140) uses said set of decoding parameters θg, such that the estimate x̂ (100) of the signal of interest x (60) is produced by the learned decoder gθ̂g (50).