Chaotic systems have been extensively applied in image encryption as a source of randomness. However, dynamical degradation has been pointed out as an important limitation of this procedure. To overcome this limitation, this paper presents a novel image encryption scheme based on the pseudo-orbits of 1D chaotic maps. We use the difference of two pseudo-orbits to generate a random sequence. The generated sequence has been successful in all NIST tests, which implies it has adequate randomness to be employed in encryption process. Confusion and diffusion requirements are also effectively implemented. The usual low-key space of 1D maps has been improved by a novelty procedure based on multiple perturbations in the transient time. A factor using the plain image is one of the perturbation conditions, which ensures a new and distinct secret key for each image to be encrypted. The proposed encryption scheme has been efficaciously verified using the Lena, Baboon, and Barbara test images.