Infrared camera systems may be made dramatically smaller by simultaneously collecting several low-resolution images with multiple narrow aperture lenses rather than collecting a single high-resolution image with one wide aperture lens. Conventional imaging systems consist of one or more optical elements that image a scene on the focal plane. The resolution depends on the wavelength of operation and the f-number of the lens system, assuming a diffraction limited operation. An image of comparable resolution may be obtained by using a multi-channel camera that collects multiple low-resolution measurements of the scene and then reconstructing a high-resolution image. The proposed infrared sensing system uses a three-by-three lenslet array with an effective focal length of 1.9mm and overall system length of 2.3mm, and we achieve image resolution comparable to a conventional single lens system having a focal length of 5.7mm and overall system length of 26mm. The high-resolution final image generated by this system is reconstructed from the noisy low-resolution images corresponding to each lenslet; this is accomplished using a computational process known as superresolution reconstruction. The novelty of our approach to the superresolution problem is the use of wavelets and related multiresolution method within a Expectation-Maximization framework to improve the accuracy and visual quality of the reconstructed image. The wavelet-based regularization reduces the appearance of artifacts while preserving key features such as edges and singularities. The processing method is very fast, making the integrated sensing and processing viable for both time-sensitive applications and massive collections of sensor outputs.