Modern digital cameras include an image processing pipeline that converts raw sensor data to a rendered RGB image. Several key steps in the pipeline operate on spatially localized data (demosaicking, noise reduction, color conversion). We show how to derive a collection of local, adaptive linear filters (kernels) that can be applied to each pixel and its neighborhood; the adaptive linear calculation approximates the performance of the modules in the conventional image processing pipeline. We also derive a set of kernels from images rendered by expert photographers. In both cases, we evaluate the accuracy of the approximation by calculating the difference between the images rendered by the camera pipeline with the images rendered by the local, linear approximation. The local, linear and learned (L³) kernels approximate the camera and expert processing pipelines with a mean S-CIELAB error of ΔE < 2. A value of the local and linear architecture is that the parallel application of a large number of linear kernels works well on modern hardware configurations and can be implemented efficiently with respect to power.