\begin{algorithmic}[1]
\State{$ t \gets 1; \ \textbf{m}_{1} \gets \mathbf{1}_{\bar{C}}; \ \alpha \gets 1 $ \hfill \# Step t = 1}\label{start_t1:ln}
\For{$ e \gets 1,...,E $ }
    \State{FBP() \hfill \# Algorithm~\ref{FBP:alg}}
\EndFor
\State{$ \bar{\textbf{s}}_{1} \gets \text{mean of} \ \tilde{s} \ \text{across data} $ }\label{first_sample_independent_score:ln}\label{end_t1:ln}
\For{$ t \gets 2,...,T $} \hfill \# Steps $ t \geq 2 $
    \State{\hfill \# Phase 1}
    \State{$ \bar{\textbf{s}}_t \gets \bar{\textbf{s}}_{t-1}; \ \alpha \gets \frac{1}{2}; \ \textbf{m}_{t} \gets \textbf{m}_{t-1} $ }
    \For{$ e \gets 1,...,E_{1} $}
        \State{FBP()}
    \EndFor
    \State{$ \bar{\textbf{s}} \gets \text{mean of} \ \tilde{s} \ \text{on data} $ \hfill \# Phase 2}
        \State{$ \bar{\textbf{s}}_{t} \gets \frac{1}{2}(\bar{\textbf{s}}_{t} + \bar{\textbf{s}}) $ }\label{update_sample_independent_score:ln}
    \For{$ e \gets E_{1}+1,...,E_{2} $}
        \State{$ \alpha \gets \max \{\alpha - \frac{1}{2(E_{2}-E_{1})},0 \} $} \label{modify_alpha:ln}
        \State{FBP()}
    \EndFor
    \State{\# Indices that sort an array; \hfill Phase 3}
    \State{$ R = \text{argsort} \{ \bar{\textbf{s}}_{t}[i] : \textbf{m}_{t}[i] = 1 \} $}\label{argsort_features:ln}
    \State{$ D_{t} \gets \{R[0],...,R[C_{t-1}-C_{t}] \} $}\label{select_set:ln}
    \For{$ e \gets E_{2} + 1,...,E_{3} $}
        \State{$ \textbf{m}_{t} \gets \max \{\textbf{m}_{t} - \frac{\mathbb{I}[i]_{i \in D_{t}} }{E_{3} - E_{2}}, \textbf{0}_{\bar{C}} \} $}\label{modify_mask:ln}
        \State{FBP()}
    \EndFor
    \For{$ e \gets E_{3}+1,...,E $} \hfill \# Phase 4
        \State{FBP()}
    \EndFor
    \State{Cache $ \mathcal{T}_{t} $, $ \textbf{m}_{t},\bar{\textbf{s}}_{t} $ for equation~\ref{Outer_Loop:eq}}
\EndFor
\end{algorithmic}

\begin{algorithmic}
[1]
\State{$ t \gets 1; \ \textbf{m}_{1} \gets \mathbf{1}_{\bar{C}}; \ \alpha \gets 1 $ \hfill \# Step t = 1}\For{$ e \gets 1,...,E $ }
\State{FBP() \hfill \# Algorithm~\ref{FBP:alg}}
\EndFor
\State{$ \bar{\textbf{s}}_{1} \gets \text{mean of} \ \tilde{s} \ \text{across data} $ }\For{$ t \gets 2,...,T $} \hfill \# Steps $ t \geq 2 $
\State{\hfill \# Phase 1}
\State{$ \bar{\textbf{s}}_t \gets \bar{\textbf{s}}_{t-1}; \ \alpha \gets \frac{1}{2}; \ \textbf{m}_{t} \gets \textbf{m}_{t-1} $ }
\For{$ e \gets 1,...,E_{1} $}
\State{FBP()}
\EndFor
\State{$ \bar{\textbf{s}} \gets \text{mean of} \ \tilde{s} \ \text{on data} $ \hfill \# Phase 2}
\State{$ \bar{\textbf{s}}_{t} \gets \frac{1}{2}(\bar{\textbf{s}}_{t} + \bar{\textbf{s}}) $ } \For{$ e \gets E_{1}+1,...,E_{2} $}
\State{$ \alpha \gets \max \{\alpha - \frac{1}{2(E_{2}-E_{1})},0 \} $} \State{FBP()}
\EndFor
\State{\# Indices that sort an array; \hfill Phase 3}
\State{$ R = \text{argsort} \{ \bar{\textbf{s}}_{t}[i] : \textbf{m}_{t}[i] = 1 \} $} \State{$ D_{t} \gets \{R[0],...,R[C_{t-1}-C_{t}] \} $} \For{$ e \gets E_{2} + 1,...,E_{3} $}
\State{$ \textbf{m}_{t} \gets \max \{\textbf{m}_{t} - \frac{\mathbb{I}[i]_{i \in D_{t}} }{E_{3} - E_{2}}, \textbf{0}_{\bar{C}} \} $} \State{FBP()}
\EndFor
\For{$ e \gets E_{3}+1,...,E $} \hfill \# Phase 4
\State{FBP()}
\EndFor
\State{Cache $ \mathcal{T}_{t} $, $ \textbf{m}_{t},\bar{\textbf{s}}_{t} $ for equation~\ref{Outer_Loop:eq}}
\EndFor
\end{algorithmic}
{
    "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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