Image Denoising via RBF Neural Network Learning with Projected Original Images

Image denoising is a common task in computer vision and image processing, where RBF (Radial Basis Function) neural networks combined with Supervised Principal Component Analysis (SPCA) provide an effective solution. The core concept involves dimensionality reduction to extract key features, followed by RBF network learning to map relationships between noisy and clean data, ultimately achieving high-quality reconstruction.

The first stage is feature extraction. While traditional PCA is an unsupervised dimensionality reduction method, SPCA incorporates label information (such as clean images as supervisory signals) to preserve more denoising-relevant features. The projected low-dimensional data both compresses information volume and filters out certain noise components. In code implementation, SPCA can be achieved by modifying the covariance matrix calculation to include class information, typically using libraries like scikit-learn's decomposition module with custom supervision extensions.

The RBF neural network serves as a nonlinear mapper in this pipeline. Its hidden layer's radial basis functions perform nonlinear transformations on input features, learning complex relationships from noisy principal components to clean ones through supervised training. Compared to standard fully-connected networks, RBF's localized response characteristics make it more suitable for capturing spatial correlations between image patches. Implementation typically involves setting Gaussian kernel functions with tunable bandwidth parameters, and training can utilize gradient descent or specialized solvers for radial basis networks.

The final reconstruction phase reprojects the network output back to the original image space. Since SPCA preserves primary structural information, combined with detail components restored by the RBF network, this approach achieves better interpretability than direct end-to-end denoising methods. This technique is particularly effective for images with regular noise patterns (like Gaussian noise) and requires less training data than deep learning approaches. The reconstruction process involves inverse PCA transformation using the preserved eigenvectors from the SPCA stage.

The advantage of this methodology lies in combining traditional dimensionality reduction with modern neural networks—SPCA reduces computational complexity while RBF provides nonlinear expressive power. Practical applications require careful attention to selection of basis function widths and the impact of SPCA-retained dimensions on final results. Code implementation would typically involve parameter tuning through cross-validation and performance evaluation using metrics like PSNR (Peak Signal-to-Noise Ratio).