In this paper, we propose a new design for single sensor compressive HDR light field cameras, combining multi-ISO photography with coded mask acquisition, placed in a compressive sensing framework. The proposed camera model is based on a main lens, a multi-ISO sensor and a coded mask located in the optical path between the main lens and the sensor that projects the coded spatio-angular information of the light field onto the 2D sensor. The model encompasses different acquisition scenarios with different ISO patterns and gains. Moreover, we assume that the sensor has a built-in color filter array (CFA), making our design more suitable for consumer-level cameras. We propose a reconstruction algorithm to jointly perform color demosaicing, light field angular information recovery, HDR reconstruction, and denoising from the multi-ISO measurements formed on the sensor. This is achieved by enabling the sparse representation of HDR light fields using an overcomplete HDR dictionary. We also provide two HDR light field data sets: one synthetic data set created using the Blender rendering software with two baselines, and a real light field data set created from the fusion of multi-exposure low dynamic range (LDR) images captured using a Lytro Illum light field camera. Experimental results show that, with a sampling rate as low as 2.67%, using two shots, our proposed method yields a higher light field reconstruction quality compared to the fusion of multiple LDR light fields captured with different exposures, and with the fusion of multiple LDR light fields captured with different ISO settings.