Many real word images are often contaminated by noise. Noise reduction techniques aim to improve image quality and can be used to facilitate further image processing. This work proposes an alternative method for spatial, additive, Gaussian noise reduction based on a discrete wavelet transform. A new undecimated and shift invariant filter bank has been sued to decompose the image into components. The basic filters are extrapolated from a biorthogonal wavelet basis. Reconstruction is obtained by simply summing the image components. The noise reduction on the components is obtained by applying thresholding functions on the pixel values of each component. Each thresholding function is a member of a scheme and is characterised by a number of parameters. The scheme describes the shape of a parameterised family of thresholding functions. The parameters select the member of the family to be applied to each component. A new thresholding scheme, obtained from Bayesian optimal estimator theory, is designed. The parameters for each component are dependent on the level of the contaminating noise and are selected using a preliminary training procedure based on a set of video images. The cost function utilised for the training is a weighted version of mean square error designed to reflect the human visual system. An estimation of the standard deviation level of the noise is required by the technique. Three techniques using the highest frequency band to estimate the level on all the bands are presented and a combined estimator is used. The method has been tested on large sets of images and levels of additive, Gaussian, white and coloured noises. The method compares favourably with other wavelet based noise reduction techniques and demonstrates significantly increased noise reduction and visual quality.