\begin{algorithm}[H]
\caption{ TADRED Forward \& Backward Pass (FBP) in Step $ t $}\label{FBP:alg}
\textbf{Requires:}
\\ Input and Target Data $ X_{\bar{D}}, Y $, Mask $ \textbf{m}_{t} $
\\ Scoring and Task Networks $ \mathcal{S}_{t}, \mathcal{T}_{t} $, Loss  $ L $
\\ Sample-independent Feature Score $ \bar{\textbf{s}}_{t} $
\\ Mix Parameter $ \alpha \in [0,1] $, Feature Fill $ X_{\bar{D}}^{\text{fill}} $

\begin{algorithmic}[1]
\State{$ \tilde{s} = \sigma(\mathcal{S}_{t}(X_{\bar{D}})) $} 
\State{$ \textbf{s} = \alpha \odot \tilde{s} + (1-\alpha) \odot \bar{\textbf{s}}_{t} $ \hfill \# Equation~\ref{score_both:eq}}
\State{$ X_{D_{t}} = \textbf{m}_{t} \odot X_{\bar{D}} + (\mathbf{1}_{\bar{C}} - \textbf{m}_{t}) \odot X_{\bar{D}}^{\text{fill}} $}
\State{$ \widehat{Y} = \mathcal{T}_{t}(\textbf{s} \odot X_{D_{t}})$ }
\State{Compute $ L(\widehat{Y},Y) $ and backpropagate}
\end{algorithmic}
\end{algorithm}

\begin{algorithm}
[H]
\caption{ TADRED Forward \& Backward Pass (FBP) in Step $ t $}\textbf{Requires:}
\\ Input and Target Data $ X_{\bar{D}}, Y $, Mask $ \textbf{m}_{t} $
\\ Scoring and Task Networks $ \mathcal{S}_{t}, \mathcal{T}_{t} $, Loss $ L $
\\ Sample-independent Feature Score $ \bar{\textbf{s}}_{t} $
\\ Mix Parameter $ \alpha \in [0,1] $, Feature Fill $ X_{\bar{D}}^{\text{fill}} $
\begin{algorithmic}
[1]
\State{$ \tilde{s} = \sigma(\mathcal{S}_{t}(X_{\bar{D}})) $}
\State{$ \textbf{s} = \alpha \odot \tilde{s} + (1-\alpha) \odot \bar{\textbf{s}}_{t} $ \hfill \# Equation~\ref{score_both:eq}}
\State{$ X_{D_{t}} = \textbf{m}_{t} \odot X_{\bar{D}} + (\mathbf{1}_{\bar{C}} - \textbf{m}_{t}) \odot X_{\bar{D}}^{\text{fill}} $}
\State{$ \widehat{Y} = \mathcal{T}_{t}(\textbf{s} \odot X_{D_{t}})$ }
\State{Compute $ L(\widehat{Y},Y) $ and backpropagate}
\end{algorithmic}
\end{algorithm}
{
    "title": "experimental design for multi-channel imaging via task-driven feature   selection",
    "id": "2210.06891",
    "abstract": "this paper presents a data-driven, task-specific paradigm for experimental design, to shorten acquisition time, reduce costs, and accelerate the deployment of imaging devices. current approaches in experimental design focus on model-parameter estimation and require specification of a particular model, whereas in imaging, other tasks may drive the design. furthermore, such approaches often lead to intractable optimization problems in real-world imaging applications. here we present a new paradigm for experimental design that simultaneously optimizes the design (set of image channels) and trains a machine-learning model to execute a user-specified image-analysis task. the approach obtains data densely-sampled over the measurement space (many image channels) for a small number of acquisitions, then identifies a subset of channels of prespecified size that best supports the task. we propose a method: tadred for task-driven experimental design in imaging, to identify the most informative channel-subset whilst simultaneously training a network to execute the task given the subset. experiments demonstrate the potential of tadred in diverse imaging applications: several clinically-relevant tasks in magnetic resonance imaging; and remote sensing and physiological applications of hyperspectral imaging. results show substantial improvement over classical experimental design, two recent application-specific methods within the new paradigm, and state-of-the-art approaches in supervised feature selection. we anticipate further applications of our approach. code is available: https://github.com/sbb-gh/experimental-design-multichannel",
    "categories": "cs.lg cs.ai q-bio.nc",
    "doi": "",
    "created": "2022-10-13",
    "updated": "2024-02-23",
    "authors": [
        "stefano b. blumberg",
        "paddy j. slator",
        "daniel c. alexander"
    ],
    "affiliation": [],
    "url": "https://arxiv.org/abs/2210.06891"
}
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