Scalable Framework for Multivariate Time Series Applied to Audio Processing
Development of an innovative Convolutional Dictionary Learning (CDL) framework capable of processing large-scale audio datasets while significantly reducing computational complexity and memory footprint. The framework aims to enable real-time audio processing through efficient sparse coding and dictionary learning algorithms.
Implemented implicit matrix operations using LinearOperators to avoid explicit matrix construction, reducing memory usage from 132GB to 4MB for 2-hour audio signals. This approach enables efficient computation of convolution and correlation operations without storing large matrices.
Developed optimized Conjugate Gradient and BiCGStab solvers for the sparse coding problem, achieving a 17.6x speedup through JIT compilation. The solvers efficiently handle the optimization problem: min½‖Y - D*Z‖₂² + λ‖Z‖₁.
Leveraged the high sparsity of activation matrices (99% zeros) through intelligent encoding and sparse operations, enabling efficient storage and computation while maintaining signal quality.