As the data compression methods based on sparse representation （SR） have the problems of low compression ratio and reconstruction accuracy， a dual-iteration concentrated dictionary learning algorithm is proposed. This algorithm maps high-dimensional signals to low-dimensional feature spaces. If features of the high-dimensional original signal are retained by the low-dimensional feature space， higher accuracy will be achieved when the high-dimensional signal is reconstructed from the low-dimensional feature space. To keep more principal components of high-dimensional dictionaries in low-dimensional dictionaries， a new transformation algorithm named ? transformation is proposed. It can improve the energy concentration of the high-dimensional dictionary. Further， aiming at the coupling relationship between the high-dimensional dictionary and the low-dimensional dictionary， a dual-iteration training method is established to improve the energy concentration and the expressive ability of the dictionary. Experiments show that， compared with the traditional algorithms， the convergence speed of the proposed algorithm is improved by more than three times. In addition， a higher compression ratio and a higher quality reconstructed signal are obtained.