Due to the limitation of the spatial resolution of hyperspectral sensors, in real hyperspectral remote sensing images, targets of interest usually only occupy a few pixels (or even subpixels). Under such circumstances, we hope that the output of the detection algorithm is sparse. However, the existing detection algorithms seldom restrict this sparsity. Among the developed detection algorithms, the constrained energy minimization (CEM) and the adaptive coherence/cosine estimator (ACE) are two famous and widely used algorithms. In this letter, based on the CEM and the ACE, we propose the novel sparse CEM (SparseCEM) and sparse ACE (SparseACE) using the $\ell_{1}$-norm regularization term to restrict the output to be sparse. Furthermore, we convert our detection models to second-order cone program problems, which can be efficiently solved by using the interior point method. The experiments on two real hyperspectral images demonstrate the effectiveness of the proposed algorithms.