Self-Calibrated Subspace Robust PCA for Parameter-Free Removal of Mixed Noise and Line Stripes in Hyperspectral Images

Wenzhe Wang

cs.LGOct 15, 2026

Self-Calibrated Subspace Robust PCA for Parameter-Free Removal of Mixed Noise and Line Stripes in Hyperspectral Images

Authors: Wenzhe Wang

Organizations: Qingdao Preschool Education College, Qingdao 266318, China

Abstract

Hyperspectral images (HSIs) are often corrupted by Gaussian noise, impulses and stripes whose intensities vary across bands. The representative coefficient correlated total variation (RCCTV) model restores HSIs efficiently, but it lacks Gaussian and stripe terms, and its noise-aware extensions require the noise level and a stripe budget to be specified in advance. This article proposes a self-calibrated RCCTV (SC-RCCTV) model, in which the noise parameters are estimated adaptively during the iterations. A band-wise dense term and line-constant column and row stripe terms are introduced into RCCTV. The noise level of each band is initialized by a stripe-invariant median absolute deviation estimator and refined online from the residual, which turns the separation of sparse and dense noise into a band-adaptive Huber loss, and the stripe thresholds follow from a significance test whose false-alarm rate can be predicted analytically. No parameter is tuned for a specific image, and every subproblem of the alternating direction method of multipliers (ADMM) solver is solved in closed form. Under line stripes, SC-RCCTV outperforms the parameter-free FastHyMix by 8.17 dB on native-size cubes, and, without any noise information, it exceeds S3TTV, which is given the true noise parameters, by 1.52 dB while running more than 1,900 times faster. On average, it stays within 0.01 dB of the same model given the true noise levels, and its online calibration improves on a two-stage estimate-then-denoise scheme. Experiments on real Indian Pines and Urban data further delineate its scope for stripes that do not span entire lines.

Figures & tables

Case	Gaussian $\sigma_{k}$	Impulse	Stripes	Seeds	Family
1	0.05	–	–	0–5
2	0.05	5%	–	0–5	G+I
3	0.1	5%	–	0–5
4	–	–	5%	0–5
5	0.05	–	5%	0–5
6	0.1	–	5%	0–5	Str.

TABLE I: Simulated noise cases. Gaussian: standard deviation of the zero-mean Gaussian noise;

\mathcal{U}(0.02,0.18)

: drawn independently for each band. Impulse: fraction of pixels replaced by salt-and-pepper noise. Stripes: fraction of columns in each band that receive a constant offset drawn from

\mathcal{U}(-0.5,0.5)

. Seeds: noise realizations. The rules separate the three noise families used in Table VI .

Pavia University ( $120{\times}120{\times}99$ )
Case	RCCTV	LRTD	E3DTV	t-CTV	FHMix	L1HMD	Ours
1	38.18	37.94	39.38	34.10	41.36	39.78	39.73
2	37.88	37.59	39.21	33.84	39.21	39.52	38.94
3	32.72	34.34	35.76	31.31	36.16	35.17	34.76
4	46.21	42.88	47.00	26.28	33.01	40.47	48.81
5	37.11	37.45	38.71	26.59	32.13	36.47	39.70

TABLE II: MPSNR (dB) on the simulated cubes, mean over the noise realizations of each case (Table I ). Best per row in bold. LRTD: LRTDTV; FHMix: FastHyMix; L1HMD: L1HyMixDe.

Cube	Method	MPSNR $\uparrow$	MSSIM $\uparrow$	SAM $\downarrow$	ERGAS $\downarrow$	Time (s)
Pavia	RCCTV	36.31	0.9042	5.88	15.39	0.8
	LRTDTV	36.60	0.9314	4.05	11.27	18
	E-3DTV	38.29	0.9522	3.46	10.40	4.7
	t-CTV	29.07	0.8193	10.49	28.54	67
	FastHyMix	35.16	0.9155	5.69	15.90	2.6
	L1HyMixDe	36.78	0.9392	4.22	11.92	23

TABLE III: Mean over all cases and realizations of the simulated cubes. Time: one run on case 8 (seed 0). Below the inner rule: S3TTV, which was run on seed 0, cases 1–8 only (about 39 min per cube), and SC-RCCTV on the same eight inputs.

	Pavia University					Beltsville
Case	E-3DTV	FastHyMix	t-CTV	S3TTV	SC-RCCTV	E-3DTV	FastHyMix	t-CTV	S3TTV	SC-RCCTV
1	39.45	41.38	34.07	40.07	39.80	40.54	43.01	35.72	39.93	41.56
2	39.50	39.24	33.81	39.78	38.92	41.11	36.92	35.47	39.40	40.54
3	35.92	36.18	31.27	33.72	34.82	36.40	36.36	32.58	33.74	36.16
4	47.23	32.96	26.22	50.23	48.80	49.56	33.44	26.81	51.09	53.10
5	38.85	31.79	26.37	38.31	39.73	39.18	32.10	27.02	38.31	41.52

TABLE IV: MPSNR (dB) on the official inputs (seed 0, cases 1–8), the only cells on which S3TTV was run.

\times

: the released code stopped with an error.

Fig. 1: Restoration results on Pavia University, case 8 (seed 0), band 50. Top: restored bands with the PSNR of the band; bottom: absolute error maps (display range $[0,0.25]$ ).

Method	OA (%) $\uparrow$	$\kappa\uparrow$	Stripe $\downarrow$	Shift $\downarrow$	Time (s)
Noisy input	72.3 $\pm$ 0.4	0.676	107.8	0	–
RCCTV	74.9 $\pm$ 0.7	0.709	89.5	30.8	2.0
LRTDTV	82.3 $\pm$ 0.3	0.796	38.3	39.4	46
E-3DTV	82.1 $\pm$ 0.3	0.793	20.7	114.7	13
t-CTV	89.2 $\pm$ 0.5	0.875	–	–	270
FastHyMix	80.1 $\pm$ 0.3	0.771	12.2	20.4	3.7

TABLE V: Real data. Indian Pines: overall accuracy (OA, mean

\pm

std over 5 splits) and

\kappa

of an RBF-SVM with 10% training samples per class. Urban (

200{\times}200

): stripe index averaged over the 20 noisiest bands of the input, and largest change of a band mean, both

\times 10^{-3}

. Time: Indian Pines, idle machine; t-CTV was run on Indian Pines only.

Fig. 2: Restoration results on real data. Top: Indian Pines band 109, the noisiest band outside the water-absorption windows; bottom: Urban band 207, a heavily striped band. Display range common to each row: 1st–99th percentile of all restored versions of that band.

Variant	G+I	Str.	B.-v.	All
SC-RCCTV (full)	+1.74	+2.64	+1.94	+2.24
without stripe term $T$	+1.75	+0.08	+1.06	+0.77
without dense term $G$	$-$ 0.01	+1.14	+0.36	+0.65
scalar $\sigma$ instead of $\sigma_{k}$	+1.76	+2.63	+0.43	+1.98
$\hat{\sigma}_{k}^{(0)}$ kept fixed (two-stage)	+1.68	+2.18	+1.80	+1.96
true $\sigma_{k}$ (all else unchanged)	+1.76	+2.65	+1.94	+2.25

TABLE VI: Effectiveness of each component: mean MPSNR gain (dB) over RCCTV in each noise family of Table I (both cubes, all realizations). Last row: the same model with the true

\sigma_{k}

in place of the estimated ones.

Fig. 3: Noise levels

\hat{\sigma}_{k}

estimated by SC-RCCTV on Indian Pines: the stripe-invariant initial estimate

\hat{\sigma}_{k}^{(0)}

and the value after the online refinement (logarithmic scale).

Fig. 4: Accuracy against run time (log scale). (a) Native-size cubes, case 8, mean of both cubes; (b) full Pavia University, mean of cases 8 and 10; (c) Indian Pines, SVM overall accuracy. S3TTV: run time from the per-iteration time.

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Hyperspectral images (HSIs) are often degraded by mixed noise, including band-dependent Gaussian perturbations and structured artifacts such as stripes, dead-lines, and impulse noise. Most deep denoisers regress the clean image directly, entangling signal and structured noise. We instead model HSI denoising as

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