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Image subtraction is an effective method used in astronomy to search transient objects or identify objects that have time-varying brightness. The state-of-the-art astronomical image subtraction methods work by taking two aligned images of the same observation area, calculating a space-varying convolution kernel for the two images, and finally obtaining the difference image using the convolution kernel. With the need for fast image subtraction in astronomy projects, we study the parallelization of HOTPANTS, a popular astronomical image subtraction package by Andrew Becker, on multicore CPUs and GPUs. Specifically, we identify the components in HOTPANTS that are data parallel and parallelize these components on the GPU and multicore CPU. We divide the work between the CPU and the GPU to minimize the overall time. In the GPU-based components, we investigate the suitable setup of the GPU thread structure for the computation, and optimize data access on the GPU memory hierarchy. Consequently, P-HOTPANTS (our parallel zed HOTPANTS), achieves a 4-times speedup over the original HOTPANTS running on a desktop with an Intel i7 CPU and an NVIDIA GTX580 GPU.