Recently, a novel wavelet method to reduce speckle noise in synthetic aperture radar images was presented. The method, based on the thresholding of the wavelet coefficients of the transformed image, is computationally efficient and maintains sharp image features. The application of a similar method is explored to reduce speckle noise in TV holography fringes, which is a very important problem in the quantitative analysis of transient phenomena. Several thresholding approaches are used to test the noise reduction algorithm on computer-simulated fringes and results are assessed through the evaluation of two comparative parameters: the image fidelity and the speckle index. It is shown that the method achieves the highest speckle reduction when speckle grains have the same average size of the image pixels.