The injection scheme provides an efficient way for CS- and MRA-based pansharpening approaches. Within this paradigm, the estimation of injection gains is one of the keys to pansharpening outcomes, which has attracted much attention in the community. Most of the existing models are derived from the regression methodology. Hence, the reference is indispensable for the estimation. However, the reference is unavailable in practice, and therefore, the estimation is usually performed at a degraded scale. This article is devoted to the estimation of injection gains without reference. A hybrid-scale (HS) estimation, which involves both the high-resolution and low-resolution data, is proposed, along with three HS models. The proposed method features a context-based and fast implementation with fewer tunable parameters. Experimental results show that the HS models yield more accurate and robust results compared with the typical regression-based models, and they are also competitive with the state-of-the-art approaches.

The fusion of Panchromatic (PAN) and Hyperspectral image (HSI) aims at improving resolution in spatial and spectral domain simultaneously. Multiresolution analysis is a widely used method for Mutispectral or HSI pansharpening. However, only detail information from PAN is considered while ignoring the detail information from HSI. In this paper, an improved approach based on multiresolution analysis is proposed, which extracts detail information from both PAN and HSI by choosing optimal multiresolution layers. Another contribution is that we discuss the weight when fusing the detail information. The experimental results demonstrate that the proposed method can provide better quality metrics and visual effects when compared with some existing methods.

When airborne lidar is used to produce digital elevation models, the random error of airborne lidar systems is often the limiting factor. To improve the overall 3-D expected accuracy of airborne lidar systems, we develop random error models of airborne lidar systems. First, we present a footprint geolocation equation for the airborne lidar that describes an ideal system, followed by a modified footprint geolocation equation that contains systematic and random errors. To better constrain these uncertainties, we describe the mathematical characteristics of the random error in detail by modeling it as a stochastic process. The probabilistic random error models are developed by analyzing the differences between the errorless equation and the equation with errors. This paper also addresses the issue of recovering the errors and presents an error recovery model. Finally, based on a linear scanner and a new coordinate system, we simulate the geometric processes of point positioning of airborne lidar systems and study the impacts of the random measurement errors on the 3-D coordinate accuracy of airborne lidar systems.

This paper is devoted to the study of a directional lifting transform for wavelet frames. A nonsubsampled lifting structure is developed to maintain the translation invariance as it is an important property in image denoising. Then, the directionality of the lifting-based tight frame is explicitly discussed, followed by a specific translation invariant directional framelet transform (TIDFT). The TIDFT has two framelets ψ1, ψ2 with vanishing moments of order two and one respectively, which are able to detect singularities in a given direction set. It provides an efficient and sparse representation for images containing rich textures along with properties of fast implementation and perfect reconstruction. In addition, an adaptive block-wise orientation estimation method based on Gabor filters is presented instead of the conventional minimization of residuals. Furthermore, the TIDFT is utilized to exploit the capability of image denoising, incorporating the MAP estimator for multivariate exponential distribution. Consequently, the TIDFT is able to eliminate the noise effectively while preserving the textures simultaneously. Experimental results show that the TIDFT outperforms some other frame-based denoising methods, such as contourlet and shearlet, and is competitive to the state-of-the-art denoising approaches.

In this paper, we present the lifting factorization and construction of wavelet bi-frames with arbitrary generators and scaling. We show that an arbitrary polyphase matrix of a wavelet bi-frame can be factorized into a series of lifting steps. Based on the proposed factorization, we present a general construction of bi-frames. Especially, we give an explicit formula to construct the bi-frames of two scaling and two generators with symmetry and one vanishing moment. This paper does not involve many theories of wavelet frames in mathematics, but focuses on the algebraic issues related to Laurent polynomials, which are efficient expressions in redundant filter banks associated with wavelet frames. As an extension of the classical two-channel filter bank, the redundant filter bank is more complicated but also more flexible. Furthermore, we present an algorithm to increase the number of vanishing moments to arbitrary order by lifting, which is iterated and is straightforward in implementation.

In this paper, we present the lifting scheme of wavelet bi-frames along with theory analysis, structure, and algorithm. We show how any wavelet bi-frame can be decomposed into a finite sequence of simple filtering steps. This decomposition corresponds to a factorization of a polyphase matrix of a wavelet bi-frame. Based on this concept, we present a new idea for constructing wavelet bi-frames. For the construction of symmetric bi-frames, we use generalized Bernstein basis functions, which enable us to design symmetric prediction and update filters. The construction allows more efficient implementation and provides tools for custom design of wavelet bi-frames. By combining the different designed filters for the prediction and update steps, we can devise practically unlimited forms of wavelet bi-frames. Moreover, we present an algorithm of increasing the number of vanishing moments of bi-framelets to arbitrary order via the presented lifting scheme, which adopts an iterative algorithm and ensures the shortest lifting scheme. Several construction examples are given to illustrate the results.