Heart Rate (HR) estimation is of utmost importance due to its applicability in diverse fields. Conventional methods for HR estimation require skin contact and are not suitable in certain scenarios such as sensitive skin or prolonged unobtrusive HR monitoring. Therefore remote photoplethysmography (rPPG) methods have become an active area of research. These methods utilize the facial videos acquired using a camera followed by extracting the Blood Volume Pulse (BVP) signal for heart rate calculation. The existing rPPG methods either utilized a single color channel or weighted color differences, which has certain limitations dealing with motion and illumination artifacts. This study considered BVP extraction as an undercomplete problem and proposed a method resistant to motion and illumination variation artifacts. This method is based on an undercomplete independent component analysis, aiming to estimate the unmixing matrix using a non-linear Cumulative Density Function (CDF) that has been optimized using the customized Levenberg-Marquardt algorithm. Therefore, the method is named U-LMA. The proposed method was tested under three scenarios: constrained, motion, and illumination variations scenarios. High Pearson correlation coefficient values and smaller lower-upper statistical limits of Bland-Altman plots justified the outstanding performance of the proposed U-LMA. Furthermore, its comparative analysis with the state-of-the-art methods demonstrated its efficacy and reliability, which was proven by the lowest error and highest correlation values (0.01 significance level). Additionally, higher accuracy satisfying the clinically accepted error differences also justified its clinical relevance.