Speckle reduction on ultrasound image by variational methods and adaptive Lagrangian multipliers

Ultrasound images are corrupted by a multiplicative noise, the speckle, which makes high level analysis difficult. Within each resolution cell a number of elementary scatterers reflects the incident wave towards the sensor. The backscattered coherent waves with different phases undergo a constructive or a destructive interference in a random manner. This paper proposes a method of restoration based on variational principles applied to wavelet coefficients. The idea of this process is to avoid the various difficulties caused by wavelet coefficients thresholding, substituting it by a total variation-based technique. The method is based on orthogonal wavelets and uses the conventional separable two-dimensional discrete wavelet transform (DWT) scheme. The coefficients of the different levels are filtered by the total variation algorithm. Nevertheless, in order to comply with ultrasound images statistics, we have adapted the constraints commonly applied to Euler-Lagrange equations. After stating first results on synthetic image, we will validate our model on real images.