Compressed sensing is an arisen and significant theory, which has been widely used in infrared image reconstruction and many methods based on compressed sensing have been proposed. However, the existing methods can hardly accurately reconstruct infrared images. Considering that the sparsity of an infrared image plays a crucial role in compressed sensing to accurately reconstruct image, this paper presents a new sparse representation (MBFSF) that integrates the multiscale bilateral filter with shearing filter to overcome the above disadvantage. Firstly, one approximation subband image and a series of detail subband images at different scales and directions are obtained by the MBFSF. Then, in view of the feature that the most information is preserved in the approximation subband image, the proposed method only measures the detail subband images and preserves the approximation subband image. Subsequently, a very sparse random measurement matrix is used for the measurement at the detail subband images to reduce the computation cost and storage of large random measurement matrices in compressed sensing. Finally, an accelerated iterative hard thresholding algorithm is employed to reconstruct the infrared image. Experimental results show that the proposed method has superior performance in terms of reconstruction accuracy and compares favorably with existing compressed sensing methods, which is an effective method in high-resolution infrared imaging based on compressed sensing.