Systematic parameter mapping for Wavelet-Based scatter correction in SPECT: clinical perception versus quantitative metrics

Abstract

Background

Photon scatter significantly degrades Single Photon Emission Computed Tomography (SPECT) image quality, with scattered photons accounting for 30–40% of detected counts within standard energy windows. While conventional scatter correction methods face limitations including noise amplification and computational demands, wavelet transforms offer promising capabilities for sinogram-domain correction. However, comprehensive parameter optimization remains unexplored.

Methods

We evaluated 96 mother wavelets across seven families, implementing three decomposition levels and five thresholding strategies in a Monte Carlo simulation framework. Scatter-contaminated sinograms were processed using discrete wavelet transforms and reconstructed via filtered backprojection. Quantitative assessment employed Universal Image Quality Index (UIQI) with varying block sizes (3 × 3, 25 × 25, 128 × 128) and Root Mean Square Error (RMSE). Three nuclear medicine physicians performed blinded qualitative assessment of the processed images.

Results

Among 94 viable wavelets (excluding outliers db45 and rbio3.1), global optimization identified Rigrsure and Heursure thresholding at decomposition level 1 as optimal for maximizing UIQI (0.559 ± 0.002), while per-slice optimization favored Minimaxi thresholding at level 2. Strong positive correlation existed between UIQI (25 × 25) and UIQI (128 × 128) (r = 0.887, p < 0.01), with both metrics inversely related to RMSE error (r≈ − 0.73, p < 0.01). Despite UIQI optimization, RMSE-optimized images received significantly higher visual quality rankings from physicians (69% improvement, p < 0.001), revealing critical divergence between quantitative metrics and diagnostic utility.

Conclusion

This study establishes wavelet-based scatter correction as a viable approach for SPECT image enhancement through systematic parameter mapping. The marked preference for RMSE-optimized images over UIQI-optimized ones underscores the necessity of aligning algorithmic optimization with clinical perception rather than technical metrics alone. These findings provide a foundation for standardizing wavelet implementation in SPECT scatter correction, directly connecting mathematical optimization to diagnostic relevance in nuclear medicine imaging.

Background

Single Photon Emission Computed Tomography (SPECT) remains pivotal in nuclear medicine for diagnosing and monitoring conditions in oncology, cardiology, and neurology [1]. However, photon scatter—a physical phenomenon where photons deviate from their trajectory due to Compton interactions—compromises image quality by introducing background haze, reducing contrast, and distorting quantitative accuracy [2]. Scattered photons account for 30–40% of detected counts within standard energy windows, limiting diagnostic reliability and dosimetric precision [3, 4].

Conventional energy window-based techniques, such as Dual- and Triple-Energy Window (DEW/TEW) methods, prioritize simplicity but exhibit critical shortcomings. For instance, TEW approaches often over- or underestimate scatter in heterogeneous media, with noise amplification and isotope-specific inefficiencies [5, 6]. While Monte Carlo (MC) simulations provide theoretical accuracy, their computational demands hinder clinical adoption [7, 8]. Model-based methods like Effective Scatter Source Estimation (ESSE) show promise for isotopes such as 177Lu [9], but require intricate calibration. Analytical methods, though improved in contrast (e.g., 52.3% gains via Klein-Nishina models [10]), rely on idealized scatter assumptions. Hardware solutions, including Germanium detectors, offer scatter rejection but increase system complexity, underscoring the need for accessible, software-driven alternatives [11, 12].

Wavelet transforms, renowned for multi-resolution analysis and energy compaction, have demonstrated efficacy in SPECT denoising and feature extraction [13–15]. Applications range from reducing projection-domain noise—such as lowering the Coefficient of Variation (CV) from 27.9% to 15.4% using Daubechies wavelets [14]—to improving the clarity and accuracy of reconstructed images [15]. Their capacity to differentiate low-frequency scatter from high-frequency primary signals remains underexplored for direct sinogram-domain correction—a gap this study addresses.

The efficacy of the wavelet transform is critically dependent on three key parameters. First, the mother wavelet (e.g., Daubechies, Symlet) determines the shape of the basis functions used for decomposition, and its similarity to the signal of interest impacts correction performance. Second, the decomposition level dictates the number of times the signal is decomposed into coarser approximations and details, controlling the scale at which features are analyzed. Third, the thresholding strategy defines the rule used to shrink or eliminate wavelet coefficients identified as noise or scatter [15–17]. Prior studies, however, often limit evaluations to narrow wavelet subsets or ad hoc parameterization. For example, optimal Daubechies levels vary with noise [17], while suboptimal thresholds risk artifact generation [14]. This inconsistency highlights the necessity for comprehensive parameter mapping to unlock wavelet-based scatter correction’s full potential.

This study evaluates discrete wavelet transforms (DWTs) for SPECT scatter correction, employing a 96-wavelet library across seven families, three decomposition levels, and five thresholding strategies. Using simulated SPECT data, we quantify performance via Universal Image Quality Index (UIQI) and Root Mean Square Error (RMSE), identify globally and slice-specific optimal parameters, and compare quantitative metrics against qualitative assessments by nuclear medicine physicians. By bridging the gap between analytic optimization and perceptual quality, this study provides actionable insights for advancing SPECT’s diagnostic and quantitative accuracy.

Materials and methods

Simulation framework

The study employed a Monte Carlo simulation framework using the SimSET package (v2.9) to generate SPECT projection data under controlled scatter conditions. A 4D NURBS-based Cardiac-Torso (NCAT) phantom replicated realistic anatomical and attenuation properties, with two distinct activity distributions: Group 1 (myocardium, liver, lungs, kidneys, spleen) and Group 2 (myocardium, liver, spleen), reflecting clinical uptake patterns. The simulated activity concentrations were set to mimic typical clinical values (Myocardium: 0.8 MBq/mL, Liver: 0.5 MBq/mL, Lungs: 0.1 MBq/mL). A virtual SPECT system modeled a clinical gamma camera equipped with a low-energy high-resolution (LEHR) collimator (NaI(Tl) crystal, 9.5 mm thickness; energy resolution: 9.5% FWHM at 140 keV; collimator hole diameter: 1.4 mm). Projection data comprised 32 angular views over 360°—selected to balance computational tractability with adequate angular sampling for preliminary parameter exploration—yielding 128 × 128 matrices (pixel size: 3.5 mm). Primary (unscattered) and scattered photon contributions were separately tallied across four energy windows (80–160 keV, 110–160 keV, 100–154 keV, 126–154 keV), enabling controlled analysis of scatter dynamics. These windows were chosen to represent a standard clinical window (126–154 keV), wider windows that increase statistics at the expense of higher scatter, and asymmetric windows sometimes employed in other correction schemes.

Scatter-contaminated data generation

Scatter-free reference sinograms were generated using primary photons within the standard 126–154 keV window. Scatter-contaminated datasets incorporated scattered photons (up to fifth order), with scatter fraction (SF) quantified as the ratio of scattered-to-primary photons. Varying energy window configurations modulated SF, allowing systematic evaluation of scatter correction efficacy under clinically relevant noise and contrast conditions.

Wavelet-based scatter correction

Scatter correction was implemented via DWTs applied to sinogram rows. Ninety-six mother wavelets spanning Symlets, Daubechies, Coiflets, Biorthogonal, Reverse Biorthogonal, Haar, and Discrete Meyer families were evaluated. Thresholding strategies included Rigrsure, Heursure, Sqtwolog, Minimaxi, and soft thresholding, applied at decomposition levels 1–3. Briefly, Rigrsure and Heursure are adaptive thresholds based on Stein's Unbiased Risk Estimate; Sqtwolog is a fixed-form universal threshold; Minimaxi uses a minimax principle to find an optimal threshold; and soft thresholding shrinks coefficients towards zero rather than setting them to zero abruptly. Optimal wavelet parameters were determined by maximizing the UIQI or minimizing RMSE relative to scatter-free references.

Image reconstruction and quality assessment

Filtered backprojection (FBP) with a ramp filter (no attenuation correction) was used to reconstruct transverse slices from processed and unprocessed sinograms. FBP was chosen for its computational efficiency and to provide a direct assessment of the wavelet scatter correction's performance without the confounding influence of iterative reconstruction algorithms and their inherent noise modeling. Quantitative evaluation employed UIQI (3 × 3, 25 × 25, 128 × 128 block sizes) and RMSE metrics. Qualitative assessment involved three blinded nuclear medicine physicians scoring five image categories—unprocessed baseline, UIQI-optimized (3 × 3, 25 × 25, 128 × 128), and RMSE-optimized—using Likert scales for overall quality, border definition, and target-to-background ratio. Inter-observer agreement was quantified via Kendall’s W.

Statistical analysis

One-way ANOVA (Welch’s/Brown-Forsythe tests for heteroscedastic data) compared wavelet performances, with post-hoc Games-Howell tests identifying optimal threshold-level combinations. Kruskal–Wallis and Mann–Whitney U tests assessed visual score differences. Pearson correlations linked quantitative metrics. Analyses were executed in SPSS v22.0, with p < 0.05 defining significance.

Results

Energy window influence on scatter

Scatter fraction exhibited a direct proportionality to energy window width. The widest window (80–160 keV) produced the highest scatter fraction (SF) of 45.2%, while the standard clinical window (126–154 keV) had an SF of 33.8%. Subsequent analyses adopted the standard 126–154 keV window to mirror clinical SPECT protocols, highlighting the need for tailored correction in non-standard window designs.

Wavelet parameter optimization

ANOVA revealed significant performance variation (F(93,6015) = 73,330, p < 0.001), with post-hoc Games-Howell tests confirming 94 wavelets achieved non-inferior UIQI within ± 0.01 equivalence margins (α = 0.05). Outliers db45/rbio3.1 exhibited clinically unacceptable artifacts (Supplementary S1). Global optimization achieved mean UIQI = 0.559 ± 0.002 across N = 6,016 sinogram rows processed under varying scatter fractions (Fig. 1A), whereas localized per-slice optimization favored Minimaxi at level 2 (L2), achieving peak UIQI values of 0.78 in high-activity regions (Fig. 1B). Globally optimized parameters demonstrated robustness across anatomical slices (F = 1.24, p = 0.19) and activity distributions (F = 0.37, p = 0.54). Across the 94 viable wavelets, those from the Symlet (sym4-8) and Daubechies (db6-10) families consistently ranked among the top performers in both UIQI and RMSE optimization, while Biorthogonal wavelets (such as bior3.3) showed more variable performance depending on the specific thresholding strategy.

Fig. 1.

Wavelet parameter optimization. A Global UIQI performance of major wavelet families averaged over decomposition levels and thresholding strategies (error bars: Standard Error of the Mean, SEM). B Localized per-slice UIQI optimization outcomes for the Minimaxi strategy, stratified by activity group, illustrating a strong inverse correlation (r = − 0.82) between maximum UIQI and corresponding RMSE error. Level 2 (L2) was predominantly optimal

Correlation between quantitative image quality metrics

Pearson analysis revealed a strong positive correlation between UIQI (25 × 25) and UIQI (128 × 128) (r = 0.887, p < 0.01), with both metrics inversely related to RMSE error (r = − 0.735, p < 0.01; Fig. 2A). UIQI (3 × 3) exhibited weaker correlations with larger block sizes (r =  0.347–0.570, p < 0.01) and minimal association with RMSE (r = − 0.243, p < 0.01), underscoring its reduced utility for global image fidelity assessment.

Fig. 2.

Quantitative metric correlations and qualitative visual assessment. A Heatmap of Pearson correlation coefficients among quantitative metrics (UIQI variants, RMSE error) across all wavelet configurations. Significance: *p < 0.05, **p < 0.01, ***p < 0.001. B Clinician-ranked visual quality (mean ± SEM) across scatter correction methods, contrasting RMSE-optimized (mean rank 4.2 ± 0.3) and various UIQI-optimized outcomes

Qualitative visual assessment by nuclear medicine physicians

RMSE-optimized images achieved superior visual rankings across all criteria (69% higher mean ranks than UIQI-optimized counterparts, p < 0.001; Fig. 2B). Images optimized for UIQI (3 × 3) performed comparably to unprocessed scatter-contaminated data (p > 0.05), while those optimized for UIQI (25 × 25/128 × 128) showed moderate yet statistically inferior improvements. Inter-observer agreement was moderate (Kendall’s W = 0.37–0.42, p < 0.001), confirming reliability in quality ratings.

Organ-specific correction efficacy

Analysis of organ-specific regions revealed that the RMSE-optimized wavelet correction provided notable improvements in both high-uptake regions like the liver and myocardium and low-uptake regions like the lungs. In the liver, background haze was visibly reduced, improving border definition. In the lungs, where scatter from adjacent high-activity organs is problematic, the correction effectively reduced background noise, thereby increasing the target-to-background contrast. Figure 3 demonstrates the visual impact of the correction on the NCAT cardiac phantom. The uncorrected image (Fig. 3A) exhibits characteristic scatter-induced haze and noise. Following correction with the optimal parameters (Reverse Biorthogonal 3.1, Level 2, Heursure thresholding), the myocardium is more clearly defined with a visible reduction in background counts (Fig. 3B).

Fig. 3.

Visual assessment of scatter correction efficacy on the NCAT heart phantom. A Uncorrected tomogram exhibiting characteristic scatter-induced background haze and noise. B The same slice following scatter correction using the RMSE-optimized parameters (Mother Wavelet: Reverse Biorthogonal 3.1, Level: 2, Threshold: Heursure). The myocardium border is sharper and the background is visibly darker. C Representative line intensity profiles from row 22 of the phantom image. The corrected profile (blue solid line) demonstrates signal preservation at peaks and a reduction in background counts (valleys) compared to the uncorrected profile (red dashed line). Note: Intensity values represent reconstructed counts; negative values in low-count regions are attributed to standard filter ringing artifacts inherent to the FBP reconstruction algorithm

Performance of mother wavelet families

The performance of the 96 evaluated mother wavelets varied significantly across the two primary metrics (Fig. 4). As illustrated in Fig. 4A, wavelets from the Symlet and Coiflet families generally yielded higher UIQI scores compared to the Biorthogonal family. Conversely, when analyzing RMSE (Fig. 4B), a distinct cluster of wavelets, particularly the Reverse Biorthogonal family (specifically rbio 3.1) and Discrete Meyer, demonstrated lower error rates, correlating with the superior visual rankings provided by the clinicians.

Fig. 4.

Comparative performance of wavelet families. A Mean UIQI scores for different mother wavelets, highlighting the stability of Symlet and Coiflet families. B Mean RMSE values, identifying the specific wavelets (e.g., rbio 3.1) that minimized error, aligning with clinical preference

Discussion

Scatter correction is essential for improving SPECT image fidelity, as scattered photons constitute 30–40% of detected counts and compromise diagnostic accuracy [6]. This study demonstrates wavelet transforms as an effective sinogram-domain scatter mitigation approach, evaluating 96 mother wavelets across seven families, three decomposition levels, and five thresholding strategies. Although optimized wavelet processing enhanced quantitative metrics such as UIQI, discrepancies with expert visual assessment highlight the importance of incorporating clinical feedback in algorithm design.

Wavelet-based correction circumvents limitations inherent to conventional approaches. Our systematic evaluation demonstrates that wavelet transforms offer a robust and adaptable framework for sinogram-domain scatter correction. While conventional energy window techniques like TEW and DEW, which are widely implemented, they face a well-documented trade-off between noise amplification and scatter underestimation [6, 18]. RMSE-optimized results achieve noticeable background reduction without the significant noise amplification often seen in TEW. Although a direct comparison was not performed, the visual improvements suggest our method is competitive with, and potentially more robust than, standard energy-based methods [6, 8]. Analytical models, such as Klein-Nishina-based approaches [10], improve contrast but require meticulous calibration. In contrast, wavelet processing leverages multi-resolution analysis to differentiate low-frequency scatter from primary signal components directly in the sinogram, offering a data-adaptive solution with inherent noise management. Thresholding strategies like Rigrsure and Heursure proved optimal for global UIQI optimization, achieving metrics surpassing prior wavelet denoising efforts [19], though objectives and baselines varied across studies.

Parameter optimization emerged as a cornerstone of efficacy. While prior studies focused on narrow wavelet subsets [15–17], our comprehensive evaluation identified decomposition levels 2–3 as optimal, balancing scatter suppression with detail preservation. While global optimization favored decomposition level 1 (L1) for top-performing threshold strategies (Rigrsure and Heursure), comprehensive analysis identified levels 2–3 (L2-L3) as optimal for balancing scatter suppression and structural preservation across 91% of wavelet families—consistent with prior findings on resolution-noise tradeoffs in SPECT denoising [14]. Globally optimal parameters demonstrated robustness across phantom configurations, contrasting with complex multi-stage methodologies [19]. Systematic exclusion of underperforming wavelets (db45, rbio3.1) further refines practical implementation strategies.

In recent years, deep learning (DL) methods have emerged as powerful tools for scatter correction [2, 20]. While DL models can learn complex, patient-specific scatter distributions, they often function as "black boxes" and require large, high-quality training datasets. In contrast, wavelet transforms offer a mathematically transparent and data-independent approach. Our findings suggest that wavelet methods provide a strong, interpretable baseline that could be integrated into hybrid models, potentially combining the deterministic signal separation of wavelets with the adaptive power of DL [21, 22].

The divergence between UIQI-optimized and RMSE-minimized outcomes has profound implications for clinical protocol design. Despite strong correlations between UIQI variants (25 × 25 vs. 128 × 128 blocks, r = 0.887) and their inverse relationship with RMSE (r = –0.735), expert evaluators consistently favored RMSE-optimized images. This misalignment echoes findings where wavelet denoising improved SNR but reduced contrast [6], challenging the assumption that technical metrics fully encapsulate diagnostic utility. The superiority of RMSE minimization in aligning with clinical preference highlights the need for perceptually tuned metrics in medical image processing.

A key requirement for any scatter-correction method is its practicality in clinical settings. Although the initial optimization phase—testing 96 wavelet configurations—was computationally intensive, the clinical application of the method is extremely fast. The DWT is inherently efficient and substantially quicker than iterative scatter-estimation approaches such as Monte Carlo or analytical modeling. Once the optimal parameters (such as rbio 3.1, Level 2, Heursure) are determined, the correction can be applied to raw sinograms in near real time—within milliseconds per slice—prior to reconstruction. This enables smooth integration into existing clinical workflows without additional.

While NCAT simulations provide a rigorous ground truth for parameter optimization, there are limitations to this study that must be acknowledged. First, this study focused on optimizing scatter correction for single-energy window acquisitions. Consequently, a direct comparison with DEW/TEW methods was not performed, as those methods require multi-window spectral data that reduces primary window statistics in some legacy systems. Our method provides a viable alternative for systems or protocols restricted to single-window acquisition. Second, the study focused on Tc-99m; results may vary for high-energy isotopes such as Lu-177. Finally, while physiological motion (respiratory or cardiac) was not modeled to isolate scatter effects, future work will integrate motion correction to further validate clinical robustness.

Advanced wavelet methodologies, such as complex transforms for directional selectivity [16] or adaptive thresholding based on local statistics, present promising avenues. Translating optimized parameters to physical phantoms and clinical datasets remains imperative, as does developing perceptually aligned quality metrics.

Conclusion

This study provides a comprehensive framework for optimizing wavelet-based scatter correction in SPECT, establishing robust parameter combinations that enhance image quality. The primary innovation is the demonstration of a significant disconnect between standard quantitative metrics (UIQI) and the perceptual quality valued by clinicians, who strongly preferred images optimized by minimizing RMSE. This key finding challenges the community to develop and validate image quality metrics that better reflect diagnostic utility, ensuring that algorithmic advancements translate into tangible clinical benefits.

Abbreviations

SPECT

Single Photon Emission Computed Tomography

UIQI

Universal Image Quality Index

RMSE

Root Mean Square Error

DEW

Dual-Energy Window

TEW

Triple-Energy Window

MC

Monte Carlo

ESSE

Effective Scatter Source Estimation

CV

Coefficient of Variation

DWTs

Discrete wavelet transforms

NCAT

NURBS-based Cardiac-Torso

LEHR

Low-energy high-resolution

FWHM

Full Width at Half Maximum

SF

Scatter fraction

L2

Level 2

L1

Level 1

L2-L3

Levels 2–3

DL

Deep learning

Author contributions

Sh. Oloomi performed all experiments, analyzed the data, and prepared the manuscript; A. Fathabadi provided useful help and discussion during experiments and data analysis, and helped to prepare the manuscript. All authors read and approved the final manuscript and revisions.

Funding

Not applicable.

Availability of data and materials

The datasets used and/or analyzed during the current study are available from the corresponding author on reasonable request.

Declarations

Ethics approval and consent to participate

Not applicable.

Consent for publication

Not applicable.

Competing interests

The authors declare that they have no competing interests.