Dual-Domain Scale Recurrent Module (DSRM)

• DSRM is a dual-domain module that integrates spatial and frequency signals to fuse deconvolution outputs for progressive restoration.
• It employs an encoder-decoder backbone with a sequential dual-domain module (DDM) to capture both local details and global structure.
• Its recurrent, coarse-to-fine design propagates contextual information across scales, improving image quality in challenging restoration tasks.

Searching arXiv for the papers on arXiv and the term “Dual-Domain Scale Recurrent Module (DSRM)” to ground the article in current arXiv records. The term Dual-Domain Scale Recurrent Module (DSRM) denotes an architectural motif in deep neural reconstruction and restoration systems that combines dual-domain processing with scale-recurrent refinement. In the material associated with this term, DSRM most explicitly refers to the module introduced in the Frequency-Driven Inverse Kernel Prediction network for single-image defocus deblurring, where it fuses deconvolution results from spatial and frequency-informed processing and progressively improves restoration from coarse to fine (Zhang et al., 18 Aug 2025). Closely related recurrent dual-domain designs also appear in MRI and CT reconstruction, where alternating updates in image and transform or projection domains are coupled with recurrence, data consistency, and multi-scale feature extraction (Zhou et al., 2020, Zhang et al., 2020). The acronym DSRM is also used in an unrelated sense for Distribution Shift Risk Minimization in textual adversarial training, indicating that the abbreviation is overloaded across subfields rather than naming a single canonical module (Gao et al., 2023).

1. Definition and scope

In the deblurring formulation that explicitly names the component, DSRM is a Dual-Domain Scale Recurrent Module that predicts coefficient maps for fusing deconvolution feature maps and supports progressive restoration across three scales in a coarse-to-fine architecture (Zhang et al., 18 Aug 2025). Its role is not to estimate blur kernels directly, but to aggregate dual-domain deconvolution results, coordinate information flow between scales, and refine outputs stage by stage.

The defining elements are therefore threefold. First, dual-domain indicates joint use of spatial-domain and frequency-domain representations. Second, scale recurrent indicates repeated refinement across multiple resolutions with hidden-state propagation. Third, module indicates that this logic is embedded as a reusable network component rather than treated as a complete end-to-end system.

A broader reading of the literature in the supplied sources suggests that DSRM belongs to a family of architectures that alternate or combine processing in complementary domains while refining estimates recurrently. In MRI, DuDoRNet alternates between image and k-space restorations over recurrent blocks, with Fourier-domain transformations and interleaved data consistency (Zhou et al., 2020). In compressed sensing CT, LEARN++ performs parallel and interactive updates in image and projection domains over multiple iterations (Zhang et al., 2020). This suggests that “DSRM” can be understood both as a specific named module in deblurring and as a more general architectural pattern centered on cross-domain recurrent correction.

2. Canonical instantiation in defocus deblurring

Within the Frequency-Driven Inverse Kernel Prediction network, the overall architecture is a scale recurrent architecture with three stages, where each stage processes the image at a different scale, from coarse to fine (Zhang et al., 18 Aug 2025). At scale $s$, the Frequency-Driven Inverse Kernel Prediction module produces deconvolution outputs $F_s$, and DSRM produces coefficient maps $C_s$. The stage output is

$\hat{y}_s = \text{Conv}(F_s \odot C_s)$

where $\odot$ denotes feature-wise multiplication and the $1 \times 1$ convolution adapts channels (Zhang et al., 18 Aug 2025).

This formulation places DSRM downstream of inverse-kernel-based deconvolution. The module acts as a learned fusion and refinement operator, modulating the deconvolution features rather than replacing the deconvolution stage. Its recurrent aspect arises from the passage of a hidden state across scales through an APU unit, allowing information accumulated at coarser scales to guide finer-scale restoration (Zhang et al., 18 Aug 2025).

The design motivation is tied to the limitations of spatial-only kernel estimation in severely blurry regions. The supplied description states that frequency-domain information offers global structure modeling via the amplitude spectrum and fine local details via the phase spectrum, and DSRM is introduced to fuse spatial and frequency information while enabling progressive refinement (Zhang et al., 18 Aug 2025). A plausible implication is that DSRM is intended to stabilize restoration when local high-frequency cues are weak but global spectral structure remains informative.

3. Internal organization and dual-domain mechanism

The DSRM in the deblurring setting is built on an encoder-decoder backbone with a bottleneck Dual-Domain Module (DDM) and a recurrent APU unit (Zhang et al., 18 Aug 2025). The encoder extracts multi-scale features using ResBlocks, the bottleneck embeds the DDM, and the decoder fuses encoder and bottleneck features before the APU produces coefficient maps and the updated hidden state.

The DDM itself adopts a sequential two-stage strategy rather than a parallel branch design. It first applies a spatial self-attention block, described as strip-based self-attention, and then a frequency-domain block composed of FFT, Conv–ReLU–Conv in the frequency domain, and inverse FFT, with a ResBlock running in parallel to preserve local features (Zhang et al., 18 Aug 2025). The supplied interpretation is that the sequential order, spatial followed by frequency, allows the spatial block to “clean up” features before global modeling in the frequency domain, reducing feature conflicts and facilitating more stable global modeling.

This dual-domain sequence can be summarized structurally as follows:

Component	Operation	Stated function
Spatial self-attention block	Spatial-domain attention	Captures local/high-frequency details
Frequency-domain block	FFT $\rightarrow$ Conv–ReLU–Conv $\rightarrow$ iFFT	Extracts global structural features
ResBlock	Parallel residual branch	Preserves local features

The same source contrasts this sequential DDM with alternative designs. In ablation, the sequential DDM surpasses spatial-only, frequency-only, and dual-branch baselines, achieving 26.42 dB, compared with 26.24 dB for spatial-only, 26.17 dB for frequency-only, and 26.25 dB for dual-branch (Zhang et al., 18 Aug 2025). This is a concrete empirical argument for ordered spatial-to-frequency interaction rather than simple parallel aggregation.

4. Recurrent and multi-scale refinement

The “scale recurrent” aspect of DSRM is central rather than incidental. In the FDIKP network, the architecture operates over three stages, each at a different resolution, and a hidden state is recurrently passed using the APU unit (Zhang et al., 18 Aug 2025). The stated effect is that outputs at higher scales benefit from guidance and “memory” accumulated at coarser scales, which is particularly beneficial in regions with severe blur.

The recurrent logic is thus not a conventional temporal recurrence over video frames. Instead, it is recurrence over restoration stages at different scales. This is important because “recurrent” in DSRM refers to iterative refinement of a single image across a scale pyramid. The module therefore combines two distinct hierarchies: a domain hierarchy, spatial and frequency, and a scale hierarchy, coarse to fine.

Related work in MRI and CT exhibits analogous recurrent behavior, though under different names. DuDoRNet alternates image-domain and k-space-domain restoration inside each recurrent block, with shared weights across blocks and interleaved data consistency layers (Zhou et al., 2020). Its recurrent block contains an image-domain DRD-Net, a k-space-domain DRD-Net, and data consistency after each domain update, with the output of one domain transformed by Fourier or inverse Fourier operators to inform the next domain’s processing (Zhou et al., 2020). The description explicitly states that, although not named DSRM in the paper, this recurrent block is architecturally equivalent to a DSRM because it performs multi-scale, cross-domain recurrent updates and derives its scale properties from the multi-receptive-field SDRDB structure inside DRDNet (Zhou et al., 2020).

LEARN++ in compressed sensing CT offers a parallel but not explicitly multi-scale dual-domain recurrence. Each iteration contains an image-domain CNN and a projection-domain CNN, with the improved image projected into the sinogram domain, inpainted, overwritten at measured entries, and then backprojected to refine the image (Zhang et al., 2020). The supplied interpretation again notes that, although the paper does not explicitly refer to a DSRM, its iteration block is “essentially a dual-domain scale recurrent module” in the sense of repeated, tightly coupled refinement over image and projection spaces (Zhang et al., 2020). This suggests that the DSRM idea is broader than the specific deblurring module and includes recurrent cross-domain correction mechanisms in inverse problems.

5. Relation to dual-domain reconstruction in MRI and CT

The MRI and CT examples sharpen the operational meaning of “dual-domain.” In DuDoRNet, the two domains are image space and k-space. The network addresses the claim that aliasing artifacts generated in the image domain are structural and non-local, making sole image-domain restoration insufficient, and that the use of a fully sampled T1 protocol as complementary information had been underexplored (Zhou et al., 2020). The dual-domain recurrent network therefore jointly restores both the image and k-space and embeds a deep T1 prior at every recurrent block.

Its per-block optimization includes image-domain and k-space-domain losses with data consistency terms, and the total loss is summed over all recurrent blocks, with $N_{rec}$ typically set to 5 (Zhou et al., 2020). The reported ablation states that removing either dual-domain processing or recurrence degrades performance, while using both yields a synergistic gain: average SSIM of 0.897 for the baseline, 0.931 for recurrent only, 0.914 for dual-domain only, and 0.949 for both (Zhou et al., 2020). This is strong evidence that dual-domain coupling and recurrence address complementary error modes.

In LEARN++, the two domains are image and projection (sinogram). The update equation is given as

$$\mathbf{x}^{t+1} = \mathbf{x}^t - \lambda^t A_f^T \big(A_f \mathbf{x}^t - f_{s-\mathrm{CNN}}(A_f \mathbf{x}^t, \Theta_2)_{\mathbf{y}} \big) - f_{\mathrm{I-CNN}}(\mathbf{x}^t, \Theta_1)$$

with measured sinogram entries overwritten by actual measured data to guarantee fidelity (Zhang et al., 2020). The paper description emphasizes that both domains are treated equally at every iteration and that the architecture differs from sequential dual-domain pipelines by maintaining strong iterative interaction between the two subnetworks.

MVMS-RCN offers a related dual-domain but non-DSRM-specific case in sparse-view CT. Each stage comprises a projection-domain refinement module and an image-domain multi-scale geometric correction module, yielding a dual-domain deep unfolding framework with end-to-end learnable parameters (Fan et al., 2024). Although it does not use the DSRM label, it reinforces the broader observation that dual-domain architectures commonly pair measurement-space refinement with multi-scale image-space correction.

6. Empirical behavior, advantages, and limitations

For the explicitly named DSRM in defocus deblurring, the supplied ablations show that replacing SRAM with DSRM increases PSNR from 25.49 dB to 26.11 dB, and that DSRM alone outperforms both FIKP-alone and SRAM+FIKP baselines (Zhang et al., 18 Aug 2025). The same source attributes qualitative gains to more effective restoration of details such as edges and textures and stronger suppression of artifacts, particularly in severely blurred regions.

The underlying technical explanation given in the source material is that DSRM leverages both local and global cues: spatial self-attention captures local or high-frequency detail, while frequency-domain enhancement captures global structure (Zhang et al., 18 Aug 2025). The recurrent coarse-to-fine scheme then propagates contextual information from low-resolution stages to higher-resolution stages. This suggests that DSRM is especially suitable for ill-posed restoration problems where locally missing information may still be recoverable through global regularities and staged refinement.

Across the related MRI and CT literature, the principal advantages associated with analogous dual-domain recurrent designs are consistent. These include improved artifact suppression, stronger detail preservation, better use of complementary measurement-space information, and the ability to enforce data consistency after each recurrent update (Zhou et al., 2020, Zhang et al., 2020). In DuDoRNet, this includes preservation of anatomical details and robustness to aliasing artifacts, with PSNR reported as 27.83 dB without T1 and 32.51 dB with T1 for Cartesian sampling, and above 48 dB with spiral sampling (Zhou et al., 2020). In LEARN++, the reported outcome is competitive qualitative and quantitative performance in artifact reduction and detail preservation relative to several state-of-the-art methods (Zhang et al., 2020).

A limitation in discussing DSRM across fields is terminological instability. The acronym is also used for Distribution Shift Risk Minimization, a procedure for adversarial training in NLP that operates by perturbing the probability distribution of clean data rather than embeddings and requires zero adversarial samples for training (Gao et al., 2023). That usage is mathematically and conceptually unrelated to the dual-domain scale-recurrent module in restoration. Any encyclopedia treatment must therefore distinguish acronym reuse from architectural continuity.

7. Terminological ambiguity and conceptual significance

The supplied sources support two complementary conclusions. First, DSRM is a precise module name in the defocus deblurring literature, where it denotes an encoder–DDM–decoder recurrent block that predicts coefficient maps and fuses deconvolution results across scales (Zhang et al., 18 Aug 2025). Second, the same letters are used differently in other areas, and several papers in imaging contain modules that are described as architecturally equivalent or analogous to a DSRM without adopting the exact name (Zhou et al., 2020, Zhang et al., 2020).

This suggests that the most stable conceptual content of DSRM is architectural rather than terminological. The architectural core is the combination of: dual-domain feature processing; recurrent refinement; and, in the most explicit form, scale-wise coarse-to-fine propagation. In inverse problems such as deblurring, MRI reconstruction, and CT reconstruction, these ingredients address complementary deficiencies of single-domain models. Spatial or image-domain processing alone may struggle with non-local artifacts; frequency, k-space, or projection-domain processing alone may not fully recover perceptual structure; and single-pass estimation may be insufficient for severe corruption. DSRM-style designs address these issues by repeatedly exchanging information between complementary representations and progressively correcting errors.

At the same time, the acronym’s reuse outside imaging means that DSRM should not be treated as a universally standardized term. In current arXiv usage reflected by the supplied records, it names both a specific module for dual-domain scale-recurrent deblurring and an unrelated adversarial-training framework based on distribution shift risk minimization (Zhang et al., 18 Aug 2025, Gao et al., 2023). For precision, the full expansion should therefore always be stated on first use.