MedSaab-US: A Backpropagation-Free Multi-Scale Wavelet-Saab Framework for Thyroid Nodule Segmentation in Ultrasound Images

Abstract: Deep learning (DL) methods dominate thyroid nodule segmentation in ultrasound (US) images, achieving high Dice scores but at the cost of millions of parameters, GPU-dependent training via backpropagation, and limited mathematical tractability. These limitations impede deployment in resource-constrained environments. In this paper, we propose MedSaab-US, a backpropagation-free segmentation framework grounded in the Green Learning paradigm. MedSaab-US extracts multi-scale spatial-frequency features by combining multi-level Discrete Wavelet Transform (DWT) with multi-scale channel-wise Saab (Subspace Approximation with Adjusted Bias) transforms at patch sizes of 5 x 5, 11 x 11, and 21 x 21 pixels. Label-Assisted Greedy (LAG) feature selection retains the most discriminative features, which are fed to an XGBoost classifier for pixel-wise prediction. The Saab transform parameters are determined analytically from data statistics, while XGBoost employs iterative greedy tree construction without requiring backpropagation. Evaluated on the TN3K dataset (2,879 training and 614 test images), MedSaab-US achieves a mean Dice coefficient of 0.4784 +/- 0.2190, precision of 0.5768, and recall of 0.5604, with a model footprint under 500K parameters and CPU-only inference in approximately 0.3 seconds per image. We present this result as an exploratory non-DL baseline for thyroid ultrasound segmentation and analyze the specific challenges posed by isoechoic nodules. An ablation study further quantifies the contribution of each pipeline component, including separate evaluations of LAG feature selection and training-set size.

• The paper introduces MedSaab-US, a backpropagation-free Green Learning pipeline that combines multi-level wavelets, multi-scale Saab features, positional encoding, LAG selection, and XGBoost for thyroid nodule segmentation.
• MedSaab-US achieves a 0.4784 Dice score, 0.3415 IoU, and approximately 0.3-second CPU inference on TN3K, outperforming traditional non-deep-learning baselines but remaining below leading deep networks.
• The paper finds that multi-scale feature extraction provides the largest performance gain, while failures concentrate on isoechoic nodules because local patches lack the global anatomical context captured by deep learning models.

MedSaab-US applies the Green Learning (GL) paradigm — specifically Successive Subspace Learning via the Saab transform — to pixel-level thyroid nodule segmentation in ultrasound, a task previously addressed almost exclusively with deep learning. The paper positions the method explicitly as an exploratory non-DL baseline rather than a competitor to state-of-the-art networks, and it is candid about the resulting performance gap.

Motivation and positioning

Existing DL approaches on TN3K — U-Net variants, TRFE+, SwinE-Net, MADGNet, and the author's prior DeepLabv3+-based model — reach Dice scores between 0.72 and 0.85. The author identifies three drawbacks: opacity of millions of parameters, GPU-dependent training and slow CPU inference, and data hunger without external pre-training. Prior GL work (PixelHop for classification, VoxelHop for MRI classification, RadHop for prostate US grading) had addressed only classification tasks; pixel-level segmentation via GL was unexplored. MedSaab-US fills that gap while targeting resource-constrained, CPU-only deployment.

Method

The pipeline has four stages:

1. Multi-level DWT: each grayscale image is decomposed with a 2-level Daubechies-4 wavelet into seven subbands ($LL_2$, $LH_2$, $HL_2$, $HH_2$, $LH_1$, $HL_1$, $HH_1$), upsampled to full resolution and per-subband normalized.
2. Multi-scale Saab transform: overlapping patches of size $5\times5$, $11\times11$, and $21\times21$ are extracted from every subband; channel-wise PCA retains the top 8 components per (subband, scale), computed analytically from 40,000 sampled patches. This yields 168 features per pixel with no iterative optimization.
3. Positional encoding and LAG selection: three normalized spatial coordinates are appended (encoding a dataset-specific central-inferior nodule prior), then Label-Assisted Greedy selection prunes the 171-dimensional vector to 60 features by mutual information ranking.
4. XGBoost classification: a gradient-boosted tree ensemble (600 estimators, depth 7) performs pixel-wise binary prediction with balanced sampling; the decision threshold is calibrated on a held-out validation split by maximizing Dice.

The paper is careful to note that while the whole system is backpropagation-free, only the Saab and LAG stages are closed-form or purely statistical; XGBoost remains iterative and hyperparameter-tuned. This nuance matters for claims about mathematical tractability.

Results

On TN3K (2,879 train / 614 test, $LH_2$0 images, CPU-only execution at roughly 0.3 s/image), MedSaab-US achieves:

Method	Type	Dice	IoU	Precision	Recall
Otsu+Morph	Non-DL	0.2341	0.1493	0.2817	0.3612
RF+Haralick	Non-DL	0.3518	0.2363	0.3941	0.4227
MedSaab-US	Non-DL	0.4784	0.3415	0.5768	0.5604
SwinE-Net / MADGNet / prior DeepLabv3+ work	DL	0.83–0.85	—	—	—

The +0.127 Dice margin over RF+Haralick supports the claim that learned subspace features outperform hand-crafted texture descriptors. On 104 test cases (16.9%) Dice exceeds 0.70, peaking at 0.9184, showing that strong acoustic contrast permits near-DL-quality segmentation even without gradients.

Ablation findings

The ablation isolates component contributions:

Configuration	Dice
Single scale ($LH_2$1)	0.2594
+ Calibrated threshold	0.2806
Multi-scale ($LH_2$2)	0.4526
+ Positional features (1000 imgs, no LAG)	0.4641
+ LAG selection (1000 imgs)	0.4703
Full (2000 imgs, LAG retained)	0.4784

Multi-scale patch extraction dominates, contributing +0.172 Dice — evidence that thyroid US nodule appearance is intrinsically multi-scale. LAG selection adds +0.006 independently of data volume, and doubling training data from 1000 to 2000 images adds a further +0.008, indicating both effects are real but marginal relative to scale diversity.

Analysis of the gap to deep learning

The 0.37-point Dice deficit is attributed to two causes. First, feature-importance analysis shows $LH_2$3 Saab components dominate (PC5, PC3, PC1 rank highest) while $LH_2$4 boundary features rank low, consistent with the prevalence of isoechoic nodules whose weak high-frequency responses confound boundary detection. Second, the maximum $LH_2$5 receptive field cannot capture image-level context such as gland boundary or trachea position, which DL encoders exploit through stacked convolutions and attention. Per-image Dice scores are bimodal — clustered near 0.0–0.1 (isoechoic cases) and 0.5–0.6 (hypoechoic cases) — motivating a hybrid routing scheme in which an echotexture classifier sends tractable cases to the interpretable GL model and difficult ones to a lightweight DL model.

Limitations and open questions

The paper concedes several constraints directly. The fixed spatial prior in Stage 3 is specific to TN3K's acquisition protocol and may not transfer across probe positions, field-of-view crops, or institutions; cross-institutional validation is required before any deployment. The XGBoost stage introduces tuned hyperparameters, weakening any claim of full closed-form design. The locality limitation of patch-based features remains unresolved within the current framework. Two specific open questions follow: whether GL-compatible global aggregation (e.g., superpixel-level Saab transforms) can close part of the context gap, and whether echotexture-based routing can reliably separate isoechoic from hypoechoic cases in practice.

Conclusion

MedSaab-US establishes a reproducible, backpropagation-free reference point for thyroid nodule segmentation on TN3K, achieving Dice 0.4784 with under 500K parameters and CPU-only inference. Its ablations identify multi-scale feature extraction as the dominant factor, and its error analysis ties residual failures to isoechoic nodule prevalence and limited receptive fields. The contribution is best understood as a characterization of what interpretable Green Learning can and cannot currently achieve in medical image segmentation, rather than as an accuracy-competitive alternative to deep networks.