Subspace Simple Scanning in LF Super-Resolution

• Subspace Simple Scanning (Sub-SS) is a strategy that decomposes a 4D light field into 2D spatial, angular, and epipolar subspaces, applying a fixed unidirectional scan per subspace.
• It replaces complex multi-directional scanning with a simple, raster-like ordering to reduce redundancy and accelerate convergence in Mamba-based processing modules.
• Empirical results show that Sub-SS achieves higher PSNR and faster convergence compared to bi-directional and 4D scanning methods in the LFMT framework.

Subspace Simple Scanning (Sub-SS) is a scanning strategy for light field super-resolution in which a $4$D light field is decomposed into meaningful $2$D subspaces, each subspace is flattened into a $1$D sequence in a fixed order, and the resulting sequences are processed by Mamba-based state-space modules with a single unidirectional scan per subspace (Liu et al., 5 Sep 2025). In the contemporary literature, this name is used explicitly in the LFMT framework for light field image super-resolution, while closely related notions of subspace-wise scanning, probing, or subspace selection also appear in earlier work on efficient light-field modeling, compressive detection, spatial sensing, adaptive subspace detection, and millimeter-wave channel estimation (Gao et al., 2024).

1. Definition, scope, and terminological boundaries

In its explicit, paper-defined sense, Sub-SS denotes the “scanning strategy” proposed for Mamba-based light field super-resolution in the LFMT framework. It has two defining characteristics: “Simple (unidirectional) scanning” and “Subspace coverage”. The former means that it “replaces multi-directional scanning (bi-directional, four-way) with one unidirectional scan per subspace to model correlations”; the latter means that it is “designed to be used across all 2D LF subspaces (spatial, angular, horizontal EPI, vertical EPI) within the overall LFMT pipeline” (Liu et al., 5 Sep 2025).

The relevant feature tensor is

$$F \in \mathbb{R}^{U \times V \times H \times W \times C},$$

where $(u,v)$ index angular coordinates and $(h,w)$ index spatial coordinates. Sub-SS does not process this tensor as a single $U V H W$-length sequence. Instead, it operates on domain-specific $2$D slices: sub-aperture images (SAIs), MacPI angular slices, and horizontal and vertical epipolar plane images (EPIs) (Liu et al., 5 Sep 2025).

The term has a broader interpretive use in adjacent literature. In particular, several papers describe subspace-wise scanning or subspace selection procedures that are not formally named Sub-SS: an “efficient subspace scanning strategy” in MLFSR for light field super-resolution (Gao et al., 2024), a hypothetical “Subspace Simple Scanning” reinterpretation of compressive detection of random subspace signals (Razavi et al., 2015), “subspace scanning” in millimeter-wave MIMO channel estimation (Zhang et al., 2019), and subspace-code decoding or GLR-based scanning over candidate subspaces in spatial sensing and adaptive detection (Mahdavifar et al., 2024). Accordingly, Sub-SS is best understood as a specific LFMT method with a wider family resemblance to earlier subspace-oriented scanning designs.

2. Subspace decomposition and the one-direction scanning rule

The LFMT formulation follows the decomposition of a $4$D light field into $2$D subspaces. For

$2$0

the paper defines the following subspaces (Liu et al., 5 Sep 2025):

• SAI (spatial domain):

$2$1

• MacPI (angular domain):

$2$2

• Horizontal EPIs:

$2$3

• Vertical EPIs:

$2$4

Within each such subspace, Sub-SS uses a “unidirectional raster-like scan”. The paper describes this as flattening each $2$5D map into a $2$6D sequence in a fixed order, for example (Liu et al., 5 Sep 2025): $2$7 for a spatial SAI,

$2$8

for a MacPI slice, and analogous flattenings for EPI subspaces. It also states that “No Reverse / Cross / 4D scanning is used inside a subspace.” This point is central: Sub-SS is defined by restricting each subspace to one deterministic sequence order rather than accumulating forward, backward, cross, or four-way passes (Liu et al., 5 Sep 2025).

The observation-center intuition in LFMT is geometric rather than purely sequential. A chosen pixel can be related to nearby pixels in the spatial domain, to correspondences at the same spatial coordinate in the angular domain, and to slanted structures in horizontal and vertical EPIs. Sub-SS does not collapse these domains into one scan; rather, each Mamba-based module operates in one subspace at a time, and the full model covers all subspaces across stages (Liu et al., 5 Sep 2025).

This subspace restriction is motivated by the structure of light fields. A plausible implication is that the method treats spatial, angular, and epipolar interactions as distinct sequence-construction problems rather than forcing a single ordering to encode all correlations simultaneously.

3. Embedding in LFMT: SSMB, SA-RSMB, EPMB, and EPTB

Sub-SS is implemented inside the Subspace Simple Mamba Block (SSMB), which is the basic Mamba-based module in LFMT. Given

$2$9

SSMB contains two parallel branches (Liu et al., 5 Sep 2025): $1$0 Here, $1$1 denotes Mamba-based sequence modeling with Sub-SS scanning, $1$2 is SiLU, and the two branches split channels from $1$3 to $1$4 before concatenation (Liu et al., 5 Sep 2025).

Two architectural choices distinguish SSMB from a plain visual Mamba block. First, LFMT “remove[s] Mamba’s causal conv and use[s] standard conv”. Second, it adds a “symmetric branch without SSM” so that “sequential modeling (Mamba) plus unidirectional scanning can bias the representation” and a purely convolutional path can “compensat[e] for possible information loss due to sequential constraints” (Liu et al., 5 Sep 2025). Inside $1$5, the map is flattened by Sub-SS,

$1$6

processed by Mamba, and reshaped back (Liu et al., 5 Sep 2025).

SSMB is wrapped by the Residual Subspace Mamba Block (RSMB): $1$7 where $1$8 is layer normalization, $1$9 is channel attention, and $$F \in \mathbb{R}^{U \times V \times H \times W \times C},$$0 are learnable scalar residual weights (Liu et al., 5 Sep 2025).

LFMT then organizes these units into a two-stage design. In Stage I, the Spatial-Angular Residual Subspace Mamba Block (SA-RSMB) performs shallow spatial-angular feature extraction by first processing SAIs and then MacPI slices: $$F \in \mathbb{R}^{U \times V \times H \times W \times C},$$1 Three SA-RSMBs are cascaded: $$F \in \mathbb{R}^{U \times V \times H \times W \times C},$$2 In Stage II, LFMT uses a dual-branch structure. The Epipolar Plane Mamba Block (EPMB) processes horizontal and vertical EPIs with Sub-SS-guided Mamba blocks, while the Epipolar Plane Transformer Block (EPTB) applies Transformer attention in the epipolar domain (Liu et al., 5 Sep 2025). The resulting features are fused by

$$F \in \mathbb{R}^{U \times V \times H \times W \times C},$$3

followed by the reconstruction network $$F \in \mathbb{R}^{U \times V \times H \times W \times C},$$4 (Liu et al., 5 Sep 2025).

A crucial boundary condition is explicit in the paper: Transformer (EPTB) does not use Sub-SS; it uses standard attention. Sub-SS is therefore not a universal LFMT mechanism but the scanning principle inside its Mamba-based modules (Liu et al., 5 Sep 2025).

4. Relation to earlier light-field subspace scanning in MLFSR

Before LFMT, the MLFSR model introduced an “efficient subspace scanning strategy” for Mamba-based light field super-resolution (Gao et al., 2024). MLFSR decomposes a light field

$$F \in \mathbb{R}^{U \times V \times H \times W \times C},$$5

into spatial, angular, and EPI subspace sequences and then performs “bi-directional scanning on each subspace” (Gao et al., 2024). For a feature tensor

$$F \in \mathbb{R}^{U \times V \times H \times W \times C},$$6

the paper defines: $$F \in \mathbb{R}^{U \times V \times H \times W \times C},$$7 for EPI-H and EPI-W sequences, and

$$F \in \mathbb{R}^{U \times V \times H \times W \times C},$$8

for spatial and angular sequences (Gao et al., 2024).

MLFSR’s argument against flattening the entire $$F \in \mathbb{R}^{U \times V \times H \times W \times C},$$9D light field into one $(u,v)$0-length sequence is twofold. First, “Hidden state compression becomes too lossy.” Second, a single long sequence mixes “intra-view spatial structure” and “inter-view angular / epipolar correspondences” in a way that is hard for the SSM to disentangle (Gao et al., 2024). The model therefore uses Bidirectional Subspace Scanning (BiSS) blocks, where the sequence is normalized, scanned forward and backward by Mamba, passed through a second LayerNorm and a Channel Attention MLP, and combined with residual connections (Gao et al., 2024).

Architecturally, MLFSR packages these operations in the Mamba-based Global Interaction (MGI) module and complements them with the Spatial-Angular Modulator (SAM) for local refinement. It also introduces a Transformer-to-Mamba (T2M) loss

$(u,v)$1

with $(u,v)$2, and reports that adding T2M improves average PSNR by $(u,v)$3 dB in ablation (Gao et al., 2024).

The contrast with LFMT is precise. MLFSR uses bi-directional scanning on each subspace, whereas Sub-SS in LFMT is explicitly introduced to replace “current multi-directional scanning strategies” with “one unidirectional scan per subspace” because the earlier strategies lead to “inefficient and redundant feature extraction when applied to complex LF data” (Liu et al., 5 Sep 2025). This suggests a direct methodological progression: efficient subspace scanning in MLFSR established subspace-wise sequence construction as a workable alternative to whole-tensor flattening, and Sub-SS tightened that design by removing multi-directional redundancy.

5. Broader research lineages: detection, sensing, and channel estimation

Although the formal Sub-SS method belongs to light field super-resolution, earlier work in other areas developed closely related subspace-scanning ideas.

In compressive detection of random subspace signals, the measurement matrix is partitioned as

$(u,v)$4

with $(u,v)$5 projecting onto strong left-singular directions of $(u,v)$6 and $(u,v)$7 onto weak ones. Detection is then based on the energy ratio

$(u,v)$8

or, in a fully correlated design, on repeated strongest and weakest directions (Razavi et al., 2015). The source paper does not introduce the name Sub-SS, but the supplied interpretation describes this as a “two-bin subspace scan” in which a detector compares energy in “signal-favorable” and “signal-unfavorable” directions (Razavi et al., 2015).

In millimeter-wave MIMO channel estimation, “subspace scanning” refers to sounding the channel with codebook pairs $(u,v)$9 and selecting

$(h,w)$0

The paper states that “the decision in (3) is highly susceptible to noise” and that sparse subspace scanning performance “starts to deteriorate as the array size grows, especially for the hybrid precoding architecture” (Zhang et al., 2019). It then proposes sparse subspace decomposition (SSD), which minimizes the mismatch

$(h,w)$1

under low-rank structure instead of retaining only the maximum-power sample (Zhang et al., 2019).

In spatial sensing and direction-of-arrival estimation, a sensing subspace code is defined as

$(h,w)$2

so that each DoA configuration maps to a subspace codeword. The interpretation supplied with the paper states that a hypothetical Sub-SS procedure would estimate a signal subspace and then scan over candidate $(h,w)$3, choosing the one with maximum similarity; in that reading, Sub-SS acts as a nearest-neighbor or maximum-likelihood subspace decoder (Mahdavifar et al., 2024).

A similar interpretation appears in adaptive subspace detection with primary and secondary data. There, one can scan candidate subspaces $(h,w)$4 after whitening with secondary data, using GLR-based statistics such as

$(h,w)$5

for known candidate subspaces, or a global eigenvalue-based detector when only the subspace dimension is known (Orlando et al., 2021). Again, the paper does not define Sub-SS as a named method, but it provides a statistically principled backbone for explicit or implicit scanning over subspaces.

Taken together, these lineages show that the phrase “subspace scanning” predates LFMT and spans several meanings: energy contrast between strong and weak directions, codebook search over sounded subspaces, nearest-subspace decoding, and GLR testing over candidate subspaces. The formal novelty of Sub-SS lies in converting this general intuition into a specific unidirectional scanning strategy for Mamba-based light field processing.

6. Empirical behavior, complexity, and recurring misconceptions

LFMT reports a direct ablation of scanning strategies in which Sub-SS is compared with SS2D, Cross-SS2D, and SS4D. The reported values are as follows (Liu et al., 5 Sep 2025):

Scanning strategy	Params (M)	Ave PSNR / SSIM
Sub-SS	2.19	32.66 / 0.9471
SS2D	2.26	32.52 / 0.9468
Cross-SS2D	2.26	32.55 / 0.9470
SS4D	2.34	32.52 / 0.9471

The same paper states that, under similar parameters, replacing Sub-SS with SS2D, Cross-SS2D, or SS4D “decreases PSNR” and “slows convergence”, and that Sub-SS “converges faster to higher PSNR” (Liu et al., 5 Sep 2025). At the full-network level, LFMT reports:

• Params: $(h,w)$6 M
• FLOPs: $(h,w)$7 G
• Ave PSNR: $(h,w)$8 dB

It also reports a tiny configuration:

• Params: $(h,w)$9 M
• FLOPs: $U V H W$0 G
• Ave PSNR: $U V H W$1 dB (Liu et al., 5 Sep 2025).

MLFSR provides complementary evidence on the efficiency of subspace-wise sequence construction. For $U V H W$2 SR on $U V H W$3 light fields, it reports $U V H W$4 ms / $U V H W$5 GB on $U V H W$6 inputs and $U V H W$7 ms / $U V H W$8 GB on $U V H W$9 inputs, while at $2$0 it reports $2$1 s / $2$2 GB and notes that the model still runs on high-resolution inputs where several Transformer baselines are out of memory or substantially slower (Gao et al., 2024).

Three misconceptions recur in discussions of Sub-SS.

First, Sub-SS is not simply any subspace-based method. In the strict sense established by LFMT, it is a unidirectional per-subspace scanning strategy inside Mamba-based light field super-resolution (Liu et al., 5 Sep 2025).

Second, Sub-SS is not a single scan over the full $2$3D tensor. Both MLFSR and LFMT decompose the light field into spatial, angular, and epipolar subspaces precisely to avoid a single $2$4-length sequence (Gao et al., 2024, Liu et al., 5 Sep 2025).

Third, Sub-SS is not synonymous with multi-directional subspace scanning. On the contrary, the method is defined against that family: it “replaces multi-directional scanning (bi-directional, four-way) with one unidirectional scan per subspace” because the earlier designs are argued to induce “coupling and redundancy across subspaces”, “inefficient use of Mamba’s capacity”, and “higher computational cost without proportional gain” in the light-field setting (Liu et al., 5 Sep 2025).

In that sense, Sub-SS occupies a specific position in the evolution of subspace-aware sequence modeling: it preserves the geometric decomposition of light fields into SAI, MacPI, and EPI domains, but reduces the scan within each domain to the simplest deterministic ordering compatible with Mamba-based long-range modeling.