Facial Expression Recognition Using Compressive Sensing Algorithms

Compressive sensing is a signal processing technique that leverages signal sparsity for efficient sampling and reconstruction, demonstrating unique advantages in facial expression recognition applications. Unlike traditional methods requiring high-dimensional image data processing, compressive sensing reconstructs original signals from a small number of measurements, significantly reducing computational complexity. In code implementation, this typically involves creating measurement matrices (e.g., random Gaussian matrices) and optimization solvers for signal recovery.

In our JAFFE database implementation for expression recognition, we first extract Gabor features through multi-scale and multi-orientation Gabor wavelet transforms. Gabor filters effectively capture facial texture and directional information by simulating the human visual system's sensitivity to local frequency and orientation. The implementation involves convolving facial images with Gabor filter banks at different scales (typically 5 scales) and orientations (usually 8 directions), converting face images into highly discriminative feature vectors. The code would include parameters for wavelength, orientation, and bandwidth adjustments to optimize feature extraction.

The core of compressive sensing lies in utilizing the sparsity of these Gabor features. Facial expression variations primarily concentrate in key regions (such as eyebrows and mouth corners), where Gabor features exhibit sparsity under specific bases like Discrete Cosine Transform (DCT) or wavelet bases. Through random measurement matrices (implemented using functions like randn() in MATLAB), we perform dimensionality reduction by projecting high-dimensional Gabor features into a lower-dimensional space while preserving essential information with minimal measurements.

During the reconstruction phase, optimization algorithms such as Orthogonal Matching Pursuit (OMP) or LASSO are employed to recover sparse coefficients from compressed measurements. The OMP algorithm iteratively selects the most correlated atoms from the dictionary, while LASSO uses L1-norm regularization for sparse solutions. Finally, classifiers like Support Vector Machines (SVM) with kernel functions or neural networks with specific architectures perform expression classification. This approach achieves an optimal balance between data efficiency and recognition accuracy on the JAFFE database, making it particularly suitable for resource-constrained real-time applications where memory and computational power are limited.