This chapter describes a novel algorithm for image denoising which seeks to capture nonlocal image regularity while leveraging established transform-based techniques. It explores a class of hybrid weighted graphs which smoothly mix the nonlocal image graph with local connectivity structure. With the spectral graph wavelet transform (SGWT), this produces a hybrid local/nonlocal wavelet transform. The chapter examines two methods for image denoising, the scaled Laplacian method based on a simple thresholding rule, and a method based on l1 minimization. It introduces a novel image model based on describing the wavelet coefficients under a new nonlocal image graph wavelet transform. The chapter constructs an overcomplete frame of wavelets on this graph using the SGWT, and shows that the nonlocal graph wavelet coefficients of images are well modeled by a scaled Laplacian probability model. It details a way for building local oriented wavelets with the SGWT, enabling the construction of hybrid local/nonlocal graph wavelets.