In recent years, using compressed sensing (CS) as a cryptosystem has drawn more and more attention since this cryptosystem can perform compression and encryption simultaneously. However, this cryptosystem is vulnerable to known-plaintext attack (KPA) under multi-time-sampling (MTS) scenario due to the linearity of its encoding process. In this paper, a privacy-preserving CS scheme for image compression-encryption applications is proposed, which embeds a non-linear operation called noise injected negative-positive transformation (NINPT) in the CS encoding process with the purpose of withstanding KPA. The encoding procedures of the proposed scheme include three steps. First, the original image is encrypted by using NINPT operation. Second, the intermediate ciphertext is re-encrypted and compressed by using CS simultaneously. Third, the final compressed ciphertext is quantized into bits via scalar quantization (SQ). Since the introduction of NINPT operation in the CS encoding process breaks the linearity of the CS sampling process, the proposed scheme can withstand KPA under MTS scenario. For image signal reconstruction, a projected Landweber with embedding decryption (PL-ED) algorithm is proposed. Simulation results demonstrate that the proposed scheme can withstand KPA under MTS scenario at the cost of slightly sacrificing the compression performance.