I develop a novel nonlinear image representation based on multiscale local orientation measurements. Specifically, an image is first decomposed using a two-orientation Steerable Pyramid, a multiscale wavelet type transform where the basis functions are derivative operators. Transforming these multiscale image gradients into polar coordinates partitions the image data into local magnitudes and local orientations. I show that it is possible to reconstruct the original image from only the orientation measurements. An algorithm for reconstructing the original image is developed based on projection onto convex sets. Additionally, I demonstrate the robustness of the representation to quantization of the orientation measurements.

Following, I describe a pair of statistical models for images that explicitly capture variations in local orientation and contrast. The first model describes patches of image coefficients as samples of a fixed Gaussian process that are rotated and scaled by hidden variables controlling the local contrast and orientation. The second introduces an additional hidden variable that mediates adaptation to the orientedness of the local signal. I develop optimal Bayesian least squares error estimators for these models that function by conditioning upon and integrating over the hidden variables. The resulting denoising procedures give results that are visually superior to those obtained with a Gaussian scale mixture model that does not explicitly incorporate local orientation. An alternate method for constructing a spatially adaptive denoising method by combining two distinct local denoising methods is explored using machine learning methodology. Interpolation between the two methods is controlled by a spatially varying decision function that may be learned from example data. I use weighted kernel ridge regression to solve this learning problem for the Gaussian scale mixture and the orientation adapted Gaussain scale mixture methods described above, yielding an improved performance "hybrid" denoiser.