Latent fingerprint identification plays an important role for identifying and convicting criminals in law enforcement agencies. Latent fingerprint images are usually of poor quality with unclear ridge structure and various overlapping patterns. Although significant advances have been achieved on developing automated fingerprint identification system, it is still challenging to achieve reliable feature extraction and identification for latent fingerprints due to the poor image quality. Prior to feature extraction, fingerprint enhancement is necessary to suppress various noises, and improve the clarity of ridge structures in latent fingerprints. Motivated by the recent success of sparse representation in image denoising, this paper proposes a latent fingerprint enhancement algorithm by combining the total variation model and multiscale patch-based sparse representation. First, the total variation model is applied to decompose the latent fingerprint into cartoon and texture components. The cartoon component with most of the nonfingerprint patterns is removed as the structured noise, whereas the texture component consisting of the weak latent fingerprint is enhanced in the next stage. Second, we propose a multiscale patch-based sparse representation method for the enhancement of the texture component. Dictionaries are constructed with a set of Gabor elementary functions to capture the characteristics of fingerprint ridge structure, and multiscale patch-based sparse representation is iteratively applied to reconstruct high-quality fingerprint image. The proposed algorithm cannot only remove the overlapping structured noises, but also restore and enhance the corrupted ridge structures. In addition, we present an automatic method to segment the foreground of latent image with the sparse coefficients and orientation coherence. Experimental results and comparisons on NIST SD27 latent fingerprint database are presented to show the effectiveness of the proposed algorithm and its superiority over existing algorithms.