A very fast noniterative algorithm is proposed for denoising or smoothing one-dimensional discrete signals, by solving the total variation regularized least-squares problem or the related fused lasso problem. A C code implementation is available on the web page of the author.

The fusion of multispectral (MS) and panchromatic (PAN) images is a useful technique for enhancing the spatial quality of low-resolution MS images. Liu recently proposed the smoothing-filter-based intensity modulation (SFIM) fusion technique. This technique upscales MS images using bicubic interpolation and introduces high-frequency information of the PAN image into the MS images. However, this fusion technique is plagued by blurred edges if the upscaled MS images are not accurately coregistered with the PAN image. In the first part of this letter, we propose the use of the Induction scaling technique instead of bicubic interpolation to obtain sharper, better correlated, and hence better coregistered upscaled images. In the second part, we propose a new fusion technique derived from induction, which is named ldquoIndusion.rdquo In this method, the high-frequency content of the PAN image is extracted using a pair of upscaling and downscaling filters. It is then added to an upscaled MS image. Finally, a comparison of SFIM (with both bicubic interpolation and induction scaling) is presented along with the fusion results obtained by IHS, discrete wavelet transform, and the proposed Indusion techniques using Quickbird satellite images.

We propose a new definition for the gradient field of a discrete image defined on a twice finer grid. The differentiation process from an image to its gradient field is viewed as the inverse operation of linear integration, and the proposed mapping is nonlinear. Then, we define the total variation of an image as the $\ell_1$ norm of its gradient field amplitude. This new definition of the total variation yields sharp edges and has better isotropy than the classical definition.

The development of multisensor systems in recent years has led to great increase in the amount of available remote sensing data. Image fusion techniques aim at inferring high quality images of a given area from degraded versions of the same area obtained by multiple sensors. This paper focuses on pansharpening, which is the inference of a high spatial resolution multispectral image from two degraded versions with complementary spectral and spatial resolution characteristics: 1) a low spatial resolution multispectral image and 2) a high spatial resolution panchromatic image. We introduce a new variational model based on spatial and spectral sparsity priors for the fusion. In the spectral domain, we encourage low-rank structure, whereas in the spatial domain, we promote sparsity on the local differences. Given the fact that both panchromatic and multispectral images are integrations of the underlying continuous spectra using different channel responses, we propose to exploit appropriate regularizations based on both spatial and spectral links between panchromatic and fused multispectral images. A weighted version of the vector total variation norm of the data matrix is employed to align the spatial information of the fused image with that of the panchromatic image. With regard to spectral information, two different types of regularization are proposed to promote a soft constraint on the linear dependence between the panchromatic and fused multispectral images. The first one estimates directly the linear coefficients from the observed panchromatic and low-resolution multispectral images by linear regression while the second one employs the principal component pursuit to obtain a robust recovery of the underlying low-rank structure. We also show that the two regularizers are strongly related. The basic idea of both regularizers is that the fused image should have low-rank and preserve edge locations. We use a variation of the recently proposed split augmented Lagrangian shrinkage algorithm to effectively solve the proposed variational formulations. Experimental results on simulated and real remote sensing images show the effectiveness of the proposed pansharpening method compared with the state-of-the-art.