Super-resolution (SR) is the process of combining multiple aliased low-quality images to produce a high-resolution high-quality image. Aside from registration and fusion of low-resolution images, a key process in SR is the restoration and denoising of the fused images. We present a novel extension of the combined Fourier-wavelet deconvolution and denoising algorithm ForWarD to the multiframe SR application. Our method first uses a fast Fourier-base multiframe image restoration to produce a sharp, yet noisy estimate of the high-resolution image. Our method then applies a space-variant nonlinear wavelet thresholding that addresses the nonstationarity inherent in resolution-enhanced fused images. We describe a computationally efficient method for implementing this space-variant processing that leverages the efficiency of the fast Fourier transform (FFT) to minimize complexity. Finally, we demonstrate the effectiveness of this algorithm for regular imagery as well as in digital mammography.