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Precise heart rate (HR) estimation of individuals during physical exercise from PPG sensors using direct methods often produces erroneous output due to the occurrence of exceedingly high motion artifacts (MAs). The effect of MAs can be neutralized using non-direct algorithms such as optimization techniques using some a priori about MA. In this paper, we propose a dual-optimization technique using adaptive Fourier decomposition in conjunction with sparse spectral reconstruction (AFODSS) using a multiple measurement vectors (MMVs) model and a regularized bi-conjugate gradient focal underdetermined system solver (BCG-FOCUSS) algorithm. Using AFODSS, the average absolute error (AAE) of HR obtained on the dataset recorded from 23 subjects during their intense exercise is 1.35 beats/min. The BCG-FOCUSS algorithm used in this paper helps to speed up the convergence rate and reduce time complexity when compared with other FOCUSS algorithms. [ABSTRACT FROM AUTHOR]