SVD and Decision Trees Combine to Strip Salt-and-Pepper Noise from Digital Images

Digital images have become indispensable across medicine, remote sensing, security, and everyday communication, yet their usefulness collapses when unwanted artifacts corrupt the underlying data. One of the most stubborn forms of contamination is salt-and-pepper noise, which scatters pixels to extreme values of pure white or pure black across an otherwise clean picture. Unlike gentle random fluctuations that blur contrast slightly, impulse noise of this kind completely overwrites individual pixel values, meaning the original information at those locations is genuinely lost rather than merely obscured. A new study published in Multimedia Tools and Applications by Rasyida Md Saad, Ahmad Kadri Junoh, and Wan Zuki Azman Wan Muhamad of Universiti Malaysia Perlis, together with Achmad Abdurrazzaq of Indonesia Defense University, presents an extended machine learning framework that tackles this problem by combining classical matrix mathematics with a decision tree classifier and a purpose-built median filter.

The core insight of the work is that noise identification and noise removal are two distinct problems that benefit from different tools. The first stage of the proposed pipeline applies singular value decomposition, a fundamental technique of linear algebra that factors any matrix into a product of three simpler matrices. When an image is treated as a matrix of pixel intensities, SVD exposes its underlying structure through singular values, which capture the dominant energy of the image content. Salt-and-pepper corruption disturbs this structure in characteristic ways, because impulsive pixels contribute abrupt, high-magnitude outliers that the singular spectrum does not smoothly accommodate. By examining the decomposition, the researchers can flag pixels whose behavior deviates from the structured representation of the scene, effectively producing a map of suspected noise locations.

What distinguishes this method from earlier hybrid designs is what happens to the SVD output next. Rather than using the decomposition results solely as a direct detection criterion, the team converts them into a structured dataset that can be learned from. Each sample in the dataset encodes the diagnostic information generated by the singular value analysis for a given pixel, together with its known true status as noisy or clean. This transformation of a deterministic mathematical procedure into training data is the step that brings machine learning into the loop. A decision tree classifier is then trained on this dataset. Decision trees are among the most interpretable models in machine learning: they partition the feature space through a hierarchy of binary decisions, each learned automatically from the training examples, and they ultimately classify each new pixel as corrupted or uncorrupted with a chain of transparent rules.

The choice of a decision tree is significant for a denoising application. Deep neural networks, which dominate much of the modern image restoration literature, can deliver impressive results but demand enormous training sets, substantial computational resources, and careful architectural tuning, and their decisions remain largely opaque. A decision tree, by contrast, trains rapidly on a modest dataset, requires no specialized hardware, and yields a model whose reasoning can be inspected. For deployment scenarios where processing must occur on ordinary hardware, or where practitioners need to understand and trust why a pixel was flagged, this simplicity becomes a genuine advantage rather than a compromise. The classifier inherits the discriminating power of the SVD features while adding the adaptivity that a fixed threshold rule lacks.

Once the decision tree has identified which pixels are corrupted, the second half of the pipeline takes over: replacing the flagged values with plausible estimates. For this, the authors propose an improved median filter that they call the Frequency Deviation Median Filter, or FDMF. Median filtering is the classical remedy for impulse noise because the median of a neighborhood is inherently robust to extreme outliers; a scattering of pure black and pure white values does not drag the median the way it drags a mean. Conventional median filters, however, apply their operation indiscriminately and can smooth away fine detail. Variants developed over decades, from the standard median filter to adaptive, directional, and decision-based medians, have sought to limit filtering to corrupted pixels and to choose replacement values more intelligently. The FDMF continues this lineage by using the deviation of frequencies within a processing window to guide the replacement of noisy pixels, aiming to preserve edges and textures while filling in the damaged values.

A particularly valuable contribution of the paper extends beyond the algorithm itself: the researchers explicitly document the factors that influence how well such a machine learning based denoising system performs. Two factors receive detailed attention. The first is the number of images selected to construct the training dataset. Because the decision tree learns the signature of noise exclusively from the examples it sees, an insufficient or unrepresentative training pool limits generalization, while the study shows that dataset composition plays a direct role in optimizing the method’s performance. The second factor is the direction of training the dataset, meaning the orientation in which training data are extracted and presented to the classifier. These findings matter for anyone reproducing or adapting the method, because two implementations of the same algorithm can yield noticeably different results depending on how these design choices are made.

To validate the approach, the authors carried out experiments on a diverse set of images: a black image, a white image, eleven natural images, and additionally medical and satellite imagery. Testing across such varied content is essential, because a filter that works well on landscapes may falter on the smooth gradients of medical scans or the repetitive textures of aerial views. The images were subjected to salt-and-pepper noise at multiple densities, allowing the team to evaluate performance not just in mild conditions but in the high-density regimes where most classical filters break down. Both qualitative visual inspection and quantitative metrics were used, with comparisons against existing denoising methods drawn from the extensive literature on median filter variants, adaptive algorithms, and earlier SVD-based hybrid techniques.

The reported results show that the proposed method delivers promising outcomes relative to the competing approaches, with the advantage becoming most pronounced as noise density increases. This pattern makes intuitive sense. At low noise levels, even simple filters can restore images adequately, and differences between methods are marginal. At high densities, where a large fraction of pixels has been overwritten and clean neighborhoods are scarce, the ability to detect corruption reliably before filtering becomes decisive. The SVD-driven detection feeding a trained decision tree provides exactly that discriminative first stage, allowing the FDMF to operate on a precisely identified set of corrupted pixels rather than spreading its efforts across the whole image. The researchers note that the method was validated through these experiments and that comparisons, both qualitative and quantitative, supported its effectiveness, especially for higher noise densities.

The study also situates itself within a long trajectory of research. The lineage includes landmark work on directional weighted median filters, pixel-density based methods, trimmed and winsorized mean filters, adaptive frequency medians, and algebraic approaches using tropical mathematics, several of which involve overlapping author groups. Earlier efforts already incorporated machine learning, including decision-tree-based denoising and directional switching median filters combined with learning methods, and more recent literature has explored convolutional neural networks for magnetic resonance images, encoder-decoder networks for mixed Gaussian and impulse noise, and PDE-informed models. What the new work adds is a careful articulation of the dataset creation process itself, treating the construction of training data from SVD outputs, and the choice of how many images to use and in which direction to train, as first-class design decisions whose effects are measured rather than assumed.

The practical implications reach across the fields where image quality is critical. Medical diagnostics cannot afford artifacts that obscure anatomical structure; satellite and aerial imagery underpins environmental monitoring and security; and industrial vision systems rely on clean inputs for accurate measurement. A denoising pipeline that is computationally light, interpretable, and robust at high noise densities offers a credible alternative to heavyweight deep learning models in such settings. The authors’ demonstration that training-set size and training direction materially affect performance gives practitioners concrete guidance for tuning the system. The datasets analyzed in the study were drawn from publicly available repositories, including the USC-SIPI Image Database, supporting reproducibility. As digital imaging continues to expand into noisier acquisition environments, hybrid frameworks of this kind, marrying the mathematical rigor of decomposition methods with the adaptive judgment of machine learning, suggest a productive middle path between classical filtering and modern deep networks.

Subject of Research: Machine learning based image denoising of salt-and-pepper noise using singular value decomposition and median filtering

Article Title: Extended machine learning method and factors that influence the performance of image denoising process

Article References: Extended machine learning method and factors that influence the performance of image denoising process. (n.d.). https://doi.org/10.1007/s11042-026-21904-4

Image Credits: AI Generated

DOI: 10.1007/s11042-026-21904-4

Keywords: image denoising, salt-and-pepper noise, singular value decomposition, decision tree, machine learning, median filter, Frequency Deviation Median Filter, digital image processing, noise detection, grayscale images, medical imaging, satellite imagery