In this paper we present a novel speech feature extraction algorithm based on sparse auditory coding and regression techniques in a reproducing kernel Hilbert space (RKHS). The features known as sparse kernel cepstral coefficients (SKCC) are extracted under the hypothesis that the noise-robust information in speech signal is embedded in a subspace spanned by overcomplete, regularized and normalized gamma-tone basis functions. After identifying the information bearing subspace, noise-robustness is achieved by sparsifying the SKCC features using simple thresholding. We show that computing the SKCC features involves correlating the speech signal with a pre-computed matrix, thus making the algorithm amenable to DSP based implementation. Speech recognition experiments using AURORA 2 dataset demonstrate that the SKCC features delivers consistent improvements in recognition performance over the state-of-the-art features under different noisy recording conditions.