The recently proposed framework of ultrasound compressive deconvolution offers the possibility of decreasing the acquired data while improving the image spatial resolution. By combining compressive sampling and image deconvolution, the direct model of compressive deconvolution combines random projections and 2D convolution with a spatially invariant point spread function. Considering the point spread function known, existing algorithms have shown the ability of this framework to reconstruct enhanced ultrasound images from compressed measurements by inverting the forward linear model. In this paper, we propose an extension of the previous approach for compressive blind deconvolution, whose aim is to jointly estimate the ultrasound image and the system point spread function. The performance of the method is evaluated on both simulated and in vivo ultrasound data.