I just want to add a bit to what has been depicted above. 1) The SPI observation stations shouldn't be less than 6-7; otherwise, the interpolated values will lack accuracy. 2) When you interpolate the data, it is better to set the same cell size as satellite images. 3) If you want to correlate your interpolated values with the image pixel values (such as NDVI, EVI or others), you can create a random points shapefile containing 1000 to 5000 points (depending on the scope of your study area), and then extract both SPI and image values of the same pixels. You can now correlate them by using regression analysis. 

Hi,

Firstly, you must have your values in a "point" form (point shapefile).Then, you can use ArcMap (Geostatistical wizard tool)  and the variety of interpolation methods are provided in this tool.

Alternatively, you can use QGIS (its freeware) and the menu (raster -->interpolation). where you can choose intepolation method and the cell size of final raster file. 

thank you all

Hi Hamed,  Just to complement the previous suggestions: we have used GRASS GIS software to generate interpolated maps of precipitation and temperature from meteorological stations data using regularized splines.  The method in GRASS is based on this article: http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.71.4351&rep=rep1&type=pdf .   On the other hand, something that it is convienient to take in account is the influence of the topography. If elevation and some other relief influences (like rain shadow), are important, it might be very convienient to consider some other variables, besides the X,Y (point) location of the stations.

thank you so much jose...

To my opinion, R is a good choice if you are familiar with geostats or sp package.

The book ''applied spatial data analysis with R" has detail information about spatial interpolation as you need.