Real sparse fast DCT for vectors with short support

Abstract

In this paper we present a new fast and deterministic algorithm for the inverse discrete cosine transform of type II for reconstructing a real input vector of length N with short support of length m from its discrete cosine transform of type II if an upper bound M on the support length m is known. The resulting algorithm only uses real arithmetic, has a sublinear runtime of O(Mlog⁡M+mlog2⁡NM) and requires O(M+mlog2⁡NM) samples. For m and M approaching the vector length, the runtime and sampling requirements approach those of a regular IDCT-II for vectors with full support.