Sparse Recovery Using the Discrete Cosine Transform

This note considers the problem of sparse recovery in R-n from linear measurements associated with a discrete cosine transform. The main theorem shows that an s-sparse vector in R-n can be recovered from the first 2s coefficients of its discrete cosine transform. This theorem is a real-valued analog of a result in Foucart and Rauhut (A mathematical introduction to compressive sensing, applied and numerical harmonic analysis, Birkhauser/Springer, New York, 2013) concerned with sparse recovery in C-n based on linear measurements via the discrete Fourier transform.