what is the intuitive understanding of 2n x 2m interpolation

[cliff0412]

in section 5, the full data matrix is composed of D^{in}, D^{rows}, D^{cols}, D^{both}. My understanding is that d^{in} is the original raw data, D^{rows} is corresponding to the 1D row coefficinets C^{rows}, while D^{cols} is corresponding to the 1D col coefficinets C^{cols}. D^{both} is corresponding to both rows and cols. the fomulae is given in 24, 25, 26. Is my shallow understanding correct?

Is there an intuitive understanding here? why the original raw data (n,m) is converted to one of size (2n,2m)?

[ImmanuelSegol]

@yuvalingo

[yuvalingo]

All D^{} matrices are evaluations, not coefficients. D^{in} is the original data. D^{rows} are the row-wise x2 interpolated evaluations. D^{cols} are the column-wise. D^{both} are the evaluations for both rows and cols (bottom-right quadrant). They can be calculated as interpolations of D^{rows} or D^{cols}.

The reason to interpolate is to add data redundancy such that it is probabilistically easy to recover any data from a few samples. Read about data availability sampling...