Mixed Precision ℓ₁ Solver for Compressive Depth Reconstruction: An ADMM Case Study

This paper presents a mixed precision framework for compressive depth reconstruction using a compact Alternating Direction Method of Multipliers (ADMM) solver tailored for the ℓ₁-norm regularized least squares problem. The proposed approach dynamically adjusts the precision of arithmetic operations during iterative optimization to balance performance and resource utilization.

Key contributions include:

• Compact ADMM Solver: Development of an efficient ADMM algorithm optimized for FPGA architectures, enabling real-time depth reconstruction.

• Mixed Precision Strategy: Implementation of a mixed precision scheme that varies the bit-width of arithmetic operations, achieving significant reductions in hardware resource usage and power consumption.

• FPGA Implementation: Realization of the proposed solver on an FPGA platform, demonstrating over 55% savings in hardware resources and 78% reduction in power consumption compared to single-precision floating-point implementations, with minimal degradation in depth reconstruction quality.

Recommended citation: Wu, Y., Wallace, A. M., Aßmann, A., & Stewart, B. (2021). Mixed Precision ℓ₁ Solver for Compressive Depth Reconstruction: An ADMM Case Study. In *Proceedings of the 2021 IEEE Workshop on Signal Processing Systems (SiPS 2021)* (pp. 70–75). IEEE. https://doi.org/10.1109/SiPS52901.2021.9595141
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