This paper introduces a supervised dictionary learning approach that combines discriminative and reconstructive components for signal representation and classification. The proposed model learns a shared dictionary and multiple decision functions for different signal classes, enabling effective classification while maintaining reconstruction accuracy. The linear variant of the model admits a simple probabilistic interpretation, while the more general variant can be interpreted in terms of kernels. The optimization framework for learning all components of the model is presented, along with experimental results on standard handwritten digit and texture classification tasks. The supervised dictionary learning (SDL) approach is formulated to simultaneously learn a dictionary and decision functions for classification. The model incorporates both reconstruction and classification objectives, with the reconstruction term ensuring fidelity to the input data and the classification term ensuring discriminative power. The model is trained using a mixed formulation that balances the generative and discriminative aspects, allowing for better performance in classification tasks. The model is evaluated on two tasks: handwritten digit recognition using the MNIST and USPS datasets, and texture classification using the Brodatz dataset. The results show that the SDL-D model, which incorporates discriminative learning, outperforms other approaches in both tasks. The linear model performs well in digit recognition, while the bilinear model is more effective in texture classification, especially when the training set is small or the data is noisy. The paper also provides a probabilistic interpretation of the linear model and a kernel-based interpretation of the bilinear model. These interpretations help in understanding the model's behavior and its effectiveness in different scenarios. The optimization procedure is detailed, and the model is shown to be effective in both generative and discriminative settings. The results demonstrate that the proposed approach is a powerful method for supervised dictionary learning, with potential applications in various image processing and classification tasks.This paper introduces a supervised dictionary learning approach that combines discriminative and reconstructive components for signal representation and classification. The proposed model learns a shared dictionary and multiple decision functions for different signal classes, enabling effective classification while maintaining reconstruction accuracy. The linear variant of the model admits a simple probabilistic interpretation, while the more general variant can be interpreted in terms of kernels. The optimization framework for learning all components of the model is presented, along with experimental results on standard handwritten digit and texture classification tasks. The supervised dictionary learning (SDL) approach is formulated to simultaneously learn a dictionary and decision functions for classification. The model incorporates both reconstruction and classification objectives, with the reconstruction term ensuring fidelity to the input data and the classification term ensuring discriminative power. The model is trained using a mixed formulation that balances the generative and discriminative aspects, allowing for better performance in classification tasks. The model is evaluated on two tasks: handwritten digit recognition using the MNIST and USPS datasets, and texture classification using the Brodatz dataset. The results show that the SDL-D model, which incorporates discriminative learning, outperforms other approaches in both tasks. The linear model performs well in digit recognition, while the bilinear model is more effective in texture classification, especially when the training set is small or the data is noisy. The paper also provides a probabilistic interpretation of the linear model and a kernel-based interpretation of the bilinear model. These interpretations help in understanding the model's behavior and its effectiveness in different scenarios. The optimization procedure is detailed, and the model is shown to be effective in both generative and discriminative settings. The results demonstrate that the proposed approach is a powerful method for supervised dictionary learning, with potential applications in various image processing and classification tasks.