Adaptive Image Reconstruction via Gradient-Based Regularization

The patent applies the dynamics principle by making the regularization parameter adaptive rather than fixed. The parameter dynamically adjusts based on the gradient magnitude of the image estimate, allowing different regularization strengths in different image regions. This is achieved through the Huber regularization term which automatically transitions between linear and quadratic regularization based on local gradient characteristics, resolving the contradiction between adaptability and complexity.

The patent implements parameter changes by modifying the regularization parameter based on image gradient information. The Huber regularization term uses a parameter that changes according to the gradient magnitude, switching between different regularization behaviors (linear for large gradients, quadratic for small gradients). This allows the system to adapt to different image features without requiring complex manual parameter adjustment.

The patent applies the local quality principle by using different regularization types in different image regions based on gradient magnitude. In regions with large gradients (edges), linear regularization is applied to preserve edge sharpness. In regions with small gradients (smooth areas), quadratic regularization is applied to provide stronger noise reduction. This local adaptation resolves the contradiction between edge preservation and noise reduction.

The patent implements a composite regularization approach by combining linear and quadratic regularization terms through the Huber regularization function. The composite nature of this regularization term allows it to exhibit linear behavior in some regions and quadratic behavior in others, depending on the local gradient characteristics. This composite approach simultaneously achieves edge preservation and noise reduction, resolving the contradiction between these two opposing requirements.