Reconstructing original data points from t-SNE output

I have been trying to understand t-SNE for a while now and I have this very basic question on the comparison of PCA and t-SNE, on which I would really appreciate some help. In case of PCA suppose the Eigen vectors (say first $m$ PCs are retained) are $U_{n\times m}$ and your data matrix is $X_{n\times p}$ with covariance matrix $C_{n\times n}=XX^T$, then the reduced data set is obtained by performing a projection $X_r=U^TX$. From this $X_r$ one can get back $X$ by simply multiplying $X_r$ with $U$. Thus $U$ acts as the basis functions on which the data is projected. I was wondering what would be the basis function for t-SNE type dimensionality reduction algorithm. I know it's non-linear so such a linear projection would not be available, but is there a way to get back the original data set from the reduced data set as obtained as the output of t-SNE algorithm? Apologies if this is too intuitive or fundamental and is simply because of my lack of understanding t-SNE. Any links to material related to this would be appreciated