In this thesis, the problem of data denoising is studied, and two new denoising approaches are proposed. Using statistical properties of the additive noise, the methods provide adaptive data-dependent soft thresholding techniques to remove the additive noise.The proposed methods, Point-wise Noise Invlaidating Soft Thresholding (PNIST) and Accumulative Noise Invalidation Soft Thresholding (ANIST), are based on Noise Invalidation. The invalidation exploits basic properties of the additive noise in order to remove the noise effects as much as possible. There are similarities and differences between ANIST and PNIST. While PNIST performs better in the case of additive white Gaussian noise, ANIST can be used with both Gaussian and non Gaussian additive noise. As part of a data denoising technique, a new noise variance estimation is also proposed. The thresholds proposed by NIST approaches are comparable to the shrinkage methods, and our simulation results promise that the new methods can outperform the existing approaches in various applications.We also explore the area of image denoising as one of the main applications of data denoising and extend the proposed approaches to two dimensional applications. Simulations show that the proposed methods outperform common shrinkage methods and are comparable to the famous BayesShrink method in terms of Mean Square Error and visual quality.