In modern decades, a human socioeconomic lifestyle has been disrupted by their stress levels. Normally, the stress levels were measured based on the Electrodermal Activity (EDA) analysis that analyses the changes in the Skin Conductance Response (SCR) level. As a result, different sensors were designed to analyze the changes in human emotional levels using the EDA signals. During analysis, the unwanted noise components in the signals were removed by using a Compressed Sensing-based Decomposition (CSD) approach. Conversely, this approach has high computational complexity. Therefore in this article, a Modified CSD (MCSD) for EDA signal is proposed that may vary the shape of the impulse response with time and varied noise models. The key aim of this model is to improve the recovery accuracy of EDA signal decomposition and enhance the human stress monitoring system. In this modified model, a computationally efficient decomposition method is proposed by using matrix-free convex optimization modeling that exploits the Toeplitz structure to allow decomposition of EDA signals with provable bounds on the recovery of true SCR events by using the computationally efficient algorithm and guarantee a better recovery accuracy. Finally, this approach is tested on Wearable Stress and Affect Detection (WESAD) dataset to exhibit that the proposed MCSD approach achieves a recovery accuracy of 92.4% which is 2.55% higher than the existing CSD approach.