Lightweight frequency-domain super-resolution network based on amplitude-phase collaboration in complex domain

doi:10.3785/j.issn.1008-973X.2026.09.013

Journal of ZheJiang University (Engineering Science)

2026, Vol. 60

Issue (9): 1962-1971 DOI: 10.3785/j.issn.1008-973X.2026.09.013

Lightweight frequency-domain super-resolution network based on amplitude-phase collaboration in complex domain

Peng CUI(

),Chuang GAO,Qinghan MENG

Image Processing Laboratory, Harbin University of Science and Technology, Harbin 150001, China

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Abstract

An amplitude-phase collaborative modeling principle was proposed in order to address the problem that real-valued encoding destroys the integrity of complex structure in frequency-domain super-resolution, leading to phase distortion and degraded geometric fidelity. The coupling relationship between amplitude and phase was directly modeled in the complex domain, with explicit satisfaction of the conjugate symmetry constraint of Fourier transform for real-valued images. A lightweight frequency-domain super-resolution network, namely amplitude-phase network (APNet), was constructed. A frequency-domain amplitude-phase attention (FAPA) mechanism was designed to synchronously learn amplitude scaling and phase calibration in the complex domain, thereby avoiding phase drift caused by the separation of real and imaginary parts. A hierarchical scale-fused kernel block (HSKB) was proposed to enhance the capability of multi-scale and local-global context fusion. Frequency-domain dynamic normalization (FDN) was introduced to adaptively adjust the normalization intensity of the complex space according to the local signal-to-noise ratio. Experiments were conducted on Urban100 and Manga109 datasets with a scale factor of 4. The parameter count of APNet was reduced by 20.9% compared with the state-of-the-art method RepRFN, while the peak signal-to-noise ratio (PSNR) was improved by 0.42 dB and 0.3 dB on the two datasets, respectively.

Key words： single image super-resolution lightweight frequency-domain phase amplitude

Received: 06 October 2025 Published: 20 July 2026

CLC:

TP 391

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Cite this article:

Peng CUI,Chuang GAO,Qinghan MENG. Lightweight frequency-domain super-resolution network based on amplitude-phase collaboration in complex domain. Journal of ZheJiang University (Engineering Science), 2026, 60(9): 1962-1971.

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https://www.zjujournals.com/eng/10.3785/j.issn.1008-973X.2026.09.013 OR https://www.zjujournals.com/eng/Y2026/V60/I9/1962

复数域幅相协同的轻量频域超分辨率网络

针对频域超分辨率中实值化编码破坏复数结构完整性，导致相位失真与几何保真度下降的问题，提出幅相协同建模原则. 在复数域直接建模幅度与相位的耦合关系，显式满足实值图像傅里叶变换的共轭对称性约束. 构建轻量级频域超分辨率网络（APNet）,设计频域幅相注意力机制（FAPA），在复数域同步学习幅度缩放与相位校准，避免实部、虚部分离引起的相位漂移. 提出多尺度融合卷积模块（HSKB），增强多尺度及局部与全局上下文融合能力. 引入频域动态归一化（FDN），依据局部信噪比自适应调节复数空间归一化强度. 实验表明，在比例因子为4的Urban100和Manga109中，相较于最新方法RepRFN在参数量减少20.9%的情况下，PSNR分别提高了0.42、0.3 dB.

关键词： 单幅图像超分辨率, 轻量级, 频域, 相位, 幅度

Fig.1 Overall architecture of proposed APNet

Fig.2 Multi-scale fusion convolution HSKB module

Fig.3 Proposed frequency-domain amplitude-phase attention module

Tab.1 Ablation study of frequency-domain amplitude-phase attention module

Tab.2 Ablation study on multi-scale fusion convolution

Tab.3 Ablation experiment of normalization module

Tab.4 Comparison of various indicators when scale factor is 4

Tab.5 Comparison of L1 error and cosine error for scaling factor of 4

Fig.4 Comparison of SR result from different methods

Fig.5 Performance and complexity comparison on Urban100

方法	尺度因子	N_p/10³	FLOPs/10⁹	Set5		Set14		B100		Urban100		Manga109
方法	尺度因子	N_p/10³	FLOPs/10⁹	PSNR/dB	SSIM	PSNR/dB	SSIM	PSNR/dB	SSIM	PSNR/dB	SSIM	PSNR/dB	SSIM
DBNet^[34]	2	416	84.15	38.00	0.9602	33.43	0.9173	32.22	0.9007	32.07	0.9273	39.00	0.9775
LKDN^[21]	2	291	66.60	38.06	0.9609	34.00	0.9207	32.28	0.9011	32.92	0.9350	39.12	0.9779
RepRFN^[35]	2	386	85.12	38.07	0.9612	33.63	0.9184	32.22	0.9009	32.10	0.9274	39.00	0.9774
SAFMN^[33]	2	228	52.00	38.00	0.9611	33.54	0.9177	32.16	0.8995	31.84	0.9256	38.71	0.9771
OSFFNet^[36]	2	516	83.20	38.10	0.9601	33.72	0.9190	32.29	0.9012	32.67	0.9331	39.09	0.9780
EARFA^[37]	2	1026	229.0	38.04	0.9614	33.98	0.9212	32.32	0.9012	32.88	0.9359	39.16	0.9782
DiMoSR^[38]	2	338	76.00	38.06	0.9607	33.74	0.9194	32.24	0.9006	32.30	0.9295	38.05	0.9782
DSCLoRA^[39]	2	398	77.00	38.02	0.9607	33.72	0.9212	32.26	0.8992	32.81	0.9290	38.01	0.9678
IBMDB^[40]	2	622	92.83	38.06	0.9673	33.66	0.9174	32.16	0.8992	32.17	0.9277	38.81	0.9772
本文方法	2	306	21.00	38.15	0.9612	34.04	0.9218	32.35	0.9015	32.95	0.9353	39.16	0.9783
DBNet^[34]	3	826	70.20	34.46	0.9279	30.42	0.8427	29.18	0.8063	28.51	0.8571	33.99	0.9466
LKDN^[21]	3	311	31.40	34.54	0.9285	30.52	0.8455	29.21	0.8078	28.50	0.8601	34.08	0.9475
RepRFN^[35]	3	392	38.40	34.45	0.9280	30.39	0.8430	29.13	0.8068	28.06	0.8494	33.76	0.9451
SAFMN^[33]	3	233	23.00	34.34	0.9267	30.33	0.8418	29.08	0.8048	27.95	0.8474	33.52	0.9437
OSFFNet^[36]	3	524	37.80	34.58	0.9287	30.48	0.8450	29.21	0.8078	28.50	0.8601	34.08	0.9475
EARFA^[37]	3	1034	102.40	34.53	0.9277	30.51	0.8451	29.29	0.8083	28.87	0.8632	34.18	0.9464
DiMoSR^[38]	3	—	45.00	34.46	0.9279	30.44	0.8429	29.20	0.8073	28.51	0.8574	33.89	0.9469
DSCLoRA^[39]	3	416	25.83	34.51	0.9281	30.43	0.8444	29.06	0.8066	28.33	0.8563	34.04	0.9436
IBMDB^[40]	3	991	67.54	34.45	0.9276	30.44	0.8445	29.15	0.8065	28.37	0.8563	34.08	0.9439
本文方法	3	310	21.00	34.59	0.9286	30.54	0.8455	29.28	0.8081	28.87	0.8631	34.18	0.9476
DBNet^[34]	4	832	51.80	32.29	0.8961	28.71	0.7834	27.66	0.7377	26.34	0.7909	30.83	0.9111
LKDN^[21]	4	322	18.30	32.39	0.8979	28.79	0.7859	27.69	0.7402	26.40	0.7965	30.43	0.9140
RepRFN^[35]	4	402	22.10	32.28	0.8969	28.68	0.7836	27.65	0.7389	26.18	0.7858	30.79	0.9102
SAFMN^[33]	4	240	14.00	32.18	0.8948	28.60	0.7813	27.58	0.7359	25.97	0.7809	30.89	0.9063
OSFFNet^[36]	4	537	22.00	32.39	0.8976	28.75	0.7852	27.66	0.7393	26.36	0.7950	30.84	0.9125
EARFA^[37]	4	1209	11.61	32.38	0.8975	28.76	0.7859	27.65	0.7431	26.60	0.8004	31.07	0.9147
DiMoSR^[38]	4	349	20.00	32.31	0.8962	28.74	0.7844	27.65	0.7384	26.25	0.7889	30.89	0.9061
DSCLoRA^[39]	4	426	27.87	32.19	0.8958	28.63	0.7830	27.61	0.7370	26.13	0.7864	30.60	0.9095
IBMDB^[40]	4	917	43.56	32.23	0.8954	28.61	0.7812	27.55	0.7356	26.10	0.7856	30.71	0.9073
本文方法	4	318	21.00	32.44	0.8979	28.83	0.7864	27.69	0.7428	26.60	0.8004	31.09	0.9146

Tab.6 Comparison of PSNR and SSIM indicator of super-resolution reconstruction models with different scale factors on various test sets

Fig.6 Comparison of visual effect at magnification of four in standard test set


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