Imaging with partial apertures is suitable for applications where compact, light-weight, and cost-effective optical systems are desired. The feasibility of a partial aperture imaging system (PAIS) with a single annular coded-phase aperture was first studied for future space and ground-based telescopic systems. The concept of PAIS is based on the interferenceless coded aperture correlation holography (I-COACH) technique. Since I-COACH is an incoherent and interferenceless technique, it is compatible with telescopic applications. Although, in PAIS, only a small fraction of light is modulated by the coded aperture the image resolution of PAIS is similar to that of full-aperture imaging systems. In this study, the design and the reconstruction technique of PAIS are modified to provide higher image quality with improved resolution, lower noise, and higher visibility. The upgraded design makes use of sparse-response holograms and a nonlinear reconstruction. Far-field imaging usually suffers from lower power signals at the sensor plane, causing a lower signal-to-noise ratio (SNR) and degradation in the image quality. To improve the SNR, it is crucial to use a power-efficient system, with higher signal intensity per camera pixel. This goal can be achieved by accumulating all the incoming power to a small sensor area, and distributing the light between several randomly distributed dots on the sensor, instead of inefficiently spreading the light over the entire camera plane. The results of the modified PAIS (M-PAIS) are reconstructed by a nonlinear correlation to provide well-resolved images which are compared with full aperture direct imaging results.