As a promising technique,sparse coding can be widely used for representation,compression,denoising and separation of signals.This technique has been introduced into noisy speech processing,where enhancing speech itself or speech feature remains a challenge.Unlike other fields where noises are dense,the noises in speech are often sparse or partly sparse over the speech dictionary,resulting in performance degradation.It is necessary to understand the noise conditions of speech environments and the applied range of sparse coding.This paper analyzes the assumptions of sparse coding and provides the bounds of reconstruction error for two sparse coding methods which are widely used.Based on this analysis,the performance of the two methods under different conditions are compared.The results show that the performance of sparse coding can be improved by a well-prepared noise dictionary.Experiments on speech enhancement and recognition are conducted,and the results coincide with the theoretical analysis well. As a promising technique, sparse coding can be widely used for representation, compression, denoising and separation of signals. This technique has been introduced into noisy speech processing, where enhancing speech itself or speech features remains a challenge. Unlike other fields where noises are dense , the noises in speech are often sparse or partly sparse over the speech dictionary, resulting in performance degradation. It is necessary to understand the noise conditions of speech environments and the applied range of sparse coding. This paper analyzes the assumptions of sparse coding and Provides the bounds of reconstruction error for two sparse coding methods which are widely used. Based on this analysis, the performance of the two methods under different conditions are compared. The results show that the performance of sparse coding can be improved by a well-prepared noise dictionary. Experiments on speech enhancement and recognition are conducted, and the results coincide with the theoretical analysis well.