In this paper, we establish stable recovery conditions for k-sparse signals under two types of noise models via the l(p) - beta l(q) minimization method with parameters 0 < p <= 1, 1 <= q <= 2 (p not equal q) and 0 < beta <= 1. First, within the Restricted Isometry Property (RIP) framework, we derive a new sufficient condition under l(infinity)-bounded noise. Sec-ond, using the mutual coherence framework, we propose a uniform sufficient condition under both l(2)-bounded noise and l(infinity)-bounded noise. Furthermore, we provide several important remarks, showing that our derived con-dition improves upon existing ones. Finally, we propose a new DCA-based algorithm for l(p) - beta l(q) minimization problem, and experimental results show that the algorithm achieves satisfactory performance.
