1. An adaptive method for reducing signal dependent noise including speckle noise mixed with a true signal in a coherent imaging system signals such as medical ultrasound imaging signals comprising: dividing the imaging system signal into an equal number of subintervals; transforming each of said subintervals using discrete wavelet transform to provide wavelet transform coefficients; identifying for each of said transformed subintervals which of said wavelet transform coefficients come from said noise or from said true signal through the use of adaptive non-linear thresholding; selecting those wavelet transform coefficients which are identified as related to said true signal; and passing said true signal wavelet transform coefficients through an inverse discrete wavelet transform to provide an enhanced true signal with reduced noise.