Numerical Methods for Information Tracking of Noisy and Non-smooth Data in Large-scale Statistics

In our universe, there is a presence of random bit of disorder in every field that has to be contemplated and understood clearly. This random bit of disorder in a physical system is known as noise. Noise in the field of statistics can be defined as an additional meaningless information that cannot be clearly interpreted which is present in the entire dataset. In large-scale statistics, noisy data has an adverse effect on the results and it can lead to skewness in any data analysis process, if not properly understood or handled. The adverse effect on the results is mainly due to uncorrelated (zero autocorrelation) property of noise. This makes it completely unpredictable at any given point in time, hence thorough investigation and removal of noise plays a vital role in data analysis process. In the field of engineering, measurement of experimental data obtained by using scientific instruments consists of some values that are independent of the experimental setup. One of most widely technique is the optimization methods viz, gradient descent, conjugate gradient, Newton’s method etc. Most of these methods require the determination of derivative of a function specified by the dataset (using finite-difference approximation). If the noisy data is approximated using a specific finite difference method this results in the amplification of noise present in the data. In order to overcome the aforementioned problem of amplification of noise in the derivative of a function, various regularization methods are employed. The parameter that plays a vital role in these methods are termed as regularization parameter. One of the most important technique used in the field of regularization is known as total variation regularization. This review aimed at gathering the disperse literature on the current state of various noises and their regularization methods.