we have 4*4 integer dct kernel matrix and DCT coefficients,we want to perform inverse DCT in order to get input coeffients.How to do that?
HEVC specifies four transform units (TUs) sizes of 4x4, 8x8, 16x16, and 32x32 to code the prediction residual.A CTB may be recursively partitioned into 4 or more TUs.TUs use integer basis functions that are similar to the discrete cosine transform (DCT).In addition 4x4 luma transform blocks that belong to an intra coded region are transformed using an integer transform that is derived from discrete sine transform (DST).This provides a 1% bit rate reduction but was restricted to 4x4 luma transform blocks due to marginal benefits for the other transform cases.Chroma uses the same TU sizes as luma so there is no 2x2 transform for chroma.
You can refer:
http://lib.mdp.ac.id/ebook/Karya%20Umum/Video-Compression-Video-Coding-for-Next-generation-Multimedia.pdf
For implementing you can refer
http://in.mathworks.com/matlabcentral/fileexchange/45151-h-264-baseline-codec--reading-and-writing-videos-
If you want for HEVC in particular then refer opensource HEVC codecs like HM, openHEVC or FFmpeg's x265.
The HEVC applied two types of transforms: the Integer Discrete Sine Transform (Int-DST) and the integer Discrete Cosine Transform (Int-DCT). The Int-DST 4x4 is used for TUs while the DCT is utilized for TUs with sizes from 64x64 down to 8x8.
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If you have DCT kernel matrix then IDCT is just transpose of that matrix. IDCT matrix holds all the properties of DCT matrix. In HEVC a 32-point DCT kernel is used and all the lower order DCT/IDCT matrix can be derived from that as the coefficients of lower order matrices are just subset of higher order matrices.
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