Learnable Gabor and Wavelet Filters in Deep Learning for Mammographic Breast Cancer Classification: A Systematic Review

Technical Summary: Learnable Gabor and Wavelet Filters in Deep Learning for Mammographic Breast Cancer Classification

Problem Statement
While Convolutional Neural Networks (CNNs) have advanced mammographic breast cancer analysis, their standard kernels learn generic representations that are not explicitly tuned to the specific oriented, multiscale signatures of malignancy, such as spiculated margins, architectural distortion, and clustered microcalcifications. Furthermore, the "black-box" nature of deep learning impedes clinical acceptance, which requires decision support that is both accurate and explainable. Although embedding classical signal-processing operators (Gabor filters for orientation/frequency selectivity and wavelet transforms for multiresolution decomposition) into deep networks offers a path to interpretability and data-driven adaptation, this paradigm has not been systematically appraised. Specifically, there is a lack of evidence regarding the joint integration of learnable Gabor and wavelet operators for multiclass radiological and pathological staging.

Methodology
This study is a systematic review conducted in accordance with the PRISMA 2020 statement.

• Search Strategy: The authors searched PubMed, Scopus, IEEE Xplore, and Web of Science for studies published between January 2010 and May 2026. Search terms combined signal-processing operators (Gabor, wavelet, learnable filters), deep learning paradigms (CNN, DenseNet), and clinical applications (mammography, breast cancer, BI-RADS).
• Selection Criteria: 22 studies met the eligibility criteria. These included:
  1. Studies applying Gabor or wavelet representations directly to mammographic data.
  2. Studies introducing or refining learnable Gabor or wavelet layers within deep neural networks (including foundational studies outside mammography to characterize techniques).
  3. Studies providing deep-learning backbones or multiclass baselines for comparison.
• Quality Assessment: Reporting quality was appraised using the Checklist for Artificial Intelligence in Medical Imaging (CLAIM), and risk of bias was assessed using the Prediction model Risk Of Bias ASsessment Tool (PROBAST).
• Synthesis: Due to heterogeneity in datasets, tasks, and outcome measures (e.g., accuracy, AUC, Dice coefficient), quantitative pooling was deemed inappropriate. Instead, a structured qualitative synthesis was performed, grouping studies by operator type (fixed vs. learnable) and task.

Key Contributions and Findings
The review synthesizes the state of the art regarding learnable signal-processing operators in mammography:

1. Performance Metrics: Reported classification accuracies in the included mammographic studies ranged from 85.4% to 98.7%, with Areas Under the Receiver Operating Characteristic Curve (AUC) ranging from 0.88 to 0.92. Sensitivities for Gabor- and wavelet-based systems clustered between 92% and 96%.
2. Learnable vs. Fixed/Unconstrained: Where compared with fixed-parameter or unconstrained convolutional baselines, learnable formulations (where filter parameters like orientation, frequency, and bandwidth are optimized via backpropagation) matched or exceeded accuracy while consistently reducing the number of trainable parameters. This parameter efficiency is particularly relevant for the small-data regimes typical of annotated mammographic cohorts.
3. Evidence Gaps:
   • Joint Integration: No study reviewed jointly integrated learnable Gabor and learnable wavelet operators within a single backbone.
   • Multiclass Staging: Multiclass radiological and pathological staging (e.g., BI-RADS categories) were addressed only by architectures lacking a parameterized signal-processing front end (e.g., DenseNet, Vision Transformers).
   • Domain Validation: The strongest methodological support for learnable Gabor formulations came from studies validated on hyperspectral, natural-image, and vessel imaging, rather than mammography. The only mammographic study employing learnable wavelet layers addressed binary (benign vs. malignant) classification.
4. Methodological Limitations: The review identified significant reporting deficiencies, including incomplete specification of model architecture and training procedures. External validation on independent data was reported in a minority of studies, and prospective evaluation was absent. Most datasets were retrospective and cancer-enriched.

Significance and Claims
The paper claims that learnable Gabor and wavelet operators embedded within deep neural networks offer a mathematically interpretable and parameter-efficient approach to mammographic breast cancer analysis, with performance comparable to contemporary deep-learning methods.

However, the authors maintain a modest stance regarding the current state of the field. They assert that the current evidence is confined to single-operator designs and predominantly binary tasks. The specific intersection of jointly using learnable Gabor and wavelet operators for multiclass mammographic classification and pathological staging remains an unaddressed evidence gap. The authors conclude that while the theoretical advantages (interpretability, efficiency, robustness to density variations) are clear, future work must evaluate unified, constrained learnable-filter architectures on prospectively assembled, externally validated, and stage-annotated cohorts to confirm these advantages in clinically meaningful settings.