Gradient Profile Estimation Using Exponential Cubic Spline Smoothing in a Bayesian Framework

Attaining reliable gradient profiles is of utmost relevance for many physical systems. In situations, the estimation inaccurate due to noise. It common practice first estimate underlying system and then compute profile by taking subsequent analytic derivative estimated system. The often fitting or smoothing data using other techniques. Taking an function can be ill-posed. This becomes worse as noise in increases. As a result, uncertainty generated this paper, theoretical framework method discrete noisy presented. was developed within Bayesian framework. Comprehensive numerical experiments were conducted on synthetic at different levels accuracy proposed quantified. Our findings suggest that outperforms state-of-the-art methods.