Compressive sensing (CS) is a popular technique used to reconstruct a signal from few training examples, a problem which arises in many machine learning applications. In this paper, we introduce a technique to guarantee that our data obeys certain isometric properties. In addition, we introduce a bayesian approach to compressive sensing, which we call ABCS, allowing us to obtain complete statistics for estimated parameters. We apply these ideas to fMRI classification and find that by isometrically transforming our data, significant improvements in classification accuracy can be achieved using the LASSO and Dantzig selector methods, two standard techniques used in CS. In addition, applying the ABCS method offers improvements in classification accuracy over both LASSO and Dantzig. Finally, we find that applying both the ABCS method together with isometric transformations, we are able to achieve an error rate of 0.0%.