The mathematical majorize-minimize principle is applied in various ways to process the image data to provide a more reliable image from the backscatter data using a reduced amount of memory and processing resources. A processing device processes the data set by creating an estimated image value for each voxel in the image by iteratively deriving the estimated image value through application of a majorize-minimize principle to solve a maximum a posteriori (MAP) estimation problem associated with a mathematical model of image data from the data. A prior probability density function for the unknown reflection coefficients is used to apply an assumption that a majority of the reflection coefficients are small. The described prior probability density functions promote sparse solutions automatically estimated from the observed data.