Wavelet shrinkage is usually performed using one of two predominant thresholding schemes.  The hard threshold filter Hh removes coefficients below a threshold value t0, determined by the noise variance.  This is sometimes referred to as the “keep or kill” method [1].  The soft threshold filter Hs shrinks the wavelet coefficients above and below the threshold.  Soft thresholding reduces coefficients toward zero [3].  The process of denoising is necessarily lossy in that the denoised signal is irreversibly different than the noisy signal.  Thresholding is the cause of this loss of information.

It has been shown that if we desire the resulting signal to be smooth, the soft threshold filter should be used.  However, the hard threshold filter performs better.  Both methods result in error within a logarithmic factor of the ideal ris, a performance measure  of the ideal shrinkage scheme [5].  Choosing a threshold value can also be difficult.  In practical situations, where the noise-free signal is unknown, we seek an approximation of the signal that is smooth and fits the input well.  A small threshold value creates a noisy result near the input, while a large threshold value introduces bias.  The optimal threshold is somewhere in-between [4].

Experimental studies have shown that for certain applications, the optimal threshold is simply computed as a constant c times the noise variance [5].  The Universal method assigns a threshold level equal to the variance times (sqrt(2log(n))), where n is the sample size [2].  Another approach utilizes Generalized Cross Validation (GCV), a function of the threshold value which is minimized to minimize the mean square error [4].