Band-Limited Proximal FISTA for Efficient Sparse Harmonic Recovery on MCU

Compressed sensing (CS) enables signal reconstruction from fewer measurements when the signal is sparse in a transform domain. However, executing ${\ell }_1$-regularized recovery on MCU-class hardware is challenging due to limited compute resources and the cost of repeated forward and adjoint operator evaluations. This paper presents a band-limited proximal variant of FISTA that enforces known spectral support during thresholding, restricting the effective optimization domain without changing the measurement model. We implement a complete CS reconstruction pipeline on an STM32F407 (Cortex-M4) using CMSIS-DSP FFT/IFFT kernels and evaluate it using ECG waveforms acquired through an AD8232 front end as benchmark signals. With $M=340$ measurements (33% of uniform sampling), the embedded implementation achieves a PRDN of 24.38%, closely matching MATLAB references (CVX: 22.64%, FISTA: 22.39%) under identical hyperparameters. Cycle-accurate profiling shows that FFT/IFFT-based forward/adjoint operators dominate the per-iteration runtime. Under a 60 Hz band-limited setting, the required iterations are reduced from 30 to 16 with an acceptable PRDN, demonstrating a practical trade-off between reconstruction accuracy and computational cost on MCU-class devices.