Laser Speckle Contrast Imaging (LSCI) is a minimally invasive full field optical technique used to generate blood flow maps with high spatial and temporal resolution. The lack of quantitative accuracy and the inability to predict flows in the presence of static scatterers such as an intact or thinned skull have been the primary limitation of LSCI. We present a new Multi-Exposure Speckle Imaging (MESI) instrument that has potential to obtain quantitative baseline flow measures. We show that the MESI instrument extends the range over which relative flow measurements are linear. We also present a new speckle model which can discriminate flows in the presence of static scatters. We show that in the presence of static scatterers the new model used along with the new MESI instrument can predict correlation times of flow consistently to within 10% of the value without static scatterers compared to an average deviation of more than 100% from the value without static scatterers using traditional LSCI. We also show that the new speckle model used with the MESI instrument can maintain the linearity of relative flow measurements in the presence of static scatterers.