Photoplethysmogram (PPG) is a noninvasive technique to estimate heart rate and respiration rate with advantages over electrocardiogram (ECG) in terms of ease of sensing. In the realm of energy-efficient health monitoring, compressive sensing (CS) is gaining prominence, particularly for signals that exhibit sparsity. This study explores to find the best sparse recovery algorithm for a fixed sparsifying matrix including impulse (I), discrete cosine (C), discrete sine (S) [I C S] and deterministic binary block diagonal (DBBD) sensing matrix for the reconstruction of the CS PPG signal, with a focus on quality metrics and potential very large scale integration (VLSI) implementations. At a compression ratio (CR) of 3, the orthogonal matching pursuit (OMP) algorithm, DBBD and [I C S] combination outperform other recovery algorithms, achieving an average percentage root mean square difference (PRD) of 1.86%, maximum absolute error (MaxAE) of 0.0976 and signal-to-noise ratio (SNR) of 36.07 dB. However, as CR increases, the approximate message passing (AMP) algorithm, DBBD and [I C S] combination often surpass OMP, achieving an average PRD value of 9.79% at a CR of 5. Additionally, AMP is computationally simpler than OMP for lower CRs. Although OMP is recommended for its accuracy across various CRs, AMP often matches or even outperforms it at higher CRs with the fixed combination of DBBD and [I C S] in compressed PPG signal recovery. The results emphasize the importance of finding suitable sparse recovery algorithms for specific CRs, sparsifying matrices, sensing matrices and the trade-offs between compression, distortion and complexity. © 2023 IEEE.