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    Summary
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    This study introduces a novel bounded dynamic sparsifying transform network (BSTNet) for compressive imaging (CI). BSTNet improves deep unfolded CI (DUCI) performance by adaptively generating transforms without restrictive constraints.

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    Area of Science:

    • Signal Processing
    • Machine Learning
    • Image Reconstruction

    Background:

    • Compressive imaging (CI) recovers images from undersampled data.
    • Deep unfolded CI (DUCI) algorithms integrate deep neural networks (DNNs) with iterative methods for enhanced performance.
    • Existing DUCI methods often require constraints that can limit performance.

    Purpose of the Study:

    • To develop a provably bounded dynamic sparsifying transform network (BSTNet) for DUCI.
    • To enable adaptive sparsifying transforms without compromising network stability.
    • To evaluate BSTNet's effectiveness in spectral snapshot CI (SCI) and compressed sensing magnetic resonance imaging (CSMRI).

    Main Methods:

    • Designed a dynamic sparsifying transform generator using a trainable DNN to extract multi-feature information.
    • Developed a BSTNet that is provably bounded without constraints on the sparsifying transform.
    • Integrated BSTNet as a prior network within a DUCI framework.

    Main Results:

    • BSTNet was demonstrated to be a bounded network.
    • DUCI algorithms incorporating BSTNet achieved competitive image recovery quality on SCI and CSMRIs.
    • Theoretical proofs confirmed the network's boundedness and the convergence of the proposed iterative algorithms.

    Conclusions:

    • The proposed BSTNet offers a stable and effective approach for DUCI.
    • Adaptive sparsifying transforms generated by DNNs enhance CI performance.
    • The framework provides theoretical guarantees for network boundedness and algorithm convergence.