This paper presents a novel remote sensing image fusion algorithm, which implements the intensity-hue-saturation (IHS) transform on panchromatic sharpening of multispectral data and the dual-tree compactly supported shearlet transform (DT CSST) during fusion. Shearlet transforms can provide almost optimal representation of the anisotropic features of an image. The spatial domain discrete implem...

in this paper, g-dual function-valued frames in l2(0;1) are in-troduced. we can achieve more reconstruction formulas to ob-tain signals in l2(0;1) by applying g-dual function-valued framesin l2(0;1).

Shearlab is a Matlab toolbox for digital shearlet transformation of two-D (image) data we developed following a rational design process. The Pseudo-Polar FFT fits very naturally with the continuum theory of the Shearlet transform and allows us to translate Shearlet ideas naturally into a digital framework. However, there are still windows and weights which must be chosen. We developed more than...

In this paper, we first briefly review the directional properties of the Dual-Tree complex wavelet transform and we investigate how the directional selectivity of the transform can be increased (i.e., to obtain more than 6 orientations per scale). To this end, we describe a new augmented Lagrangian optimization algorithm to jointly perform the 2D spectral factorization of a set of 2D directiona...

Hilbert frames theory have been extended to frames in Hilbert $C^*$-modules. The paper introduces equivalent $*$-frames and presents ordinary duals of a constructed $*$-frame by an adjointable and invertible operator. Also, some necessary and sufficient conditions are studied such that $*$-frames and ordinary duals or operator duals of another $*$-frames are equivalent under these conditions. W...

Segmentation plays an important role in many preprocessing stages in image processing. Recently, convex relaxation methods for image multi-labeling were proposed in the literature. Often these models involve the total variation (TV) semi-norm as regularizing term. However, it is well-known that the TV functional is not optimal for the segmentation of textured regions. In recent years directiona...

The shearlet representation has gained increasing recognition in recent years as a framework for the efficient representation of multidimensional data. This representation consists of a countable collection of functions defined at various locations, scales and orientations, where the orientations are obtained through the use of shearing matrices. While shearing matrices offer the advantage of p...

in this paper we introduce and study besselian $g$-frames. we show that the kernel of associated synthesis operator for a besselian $g$-frame is finite dimensional. we also introduce $alpha$-dual of a $g$-frame and we get some results when we use the hilbert-schmidt norm for the members of a $g$-frame in a finite dimensional hilbert space.

Segmentation plays an important role in many preprocessing stages in image processing. Recently, convex relaxation methods for image multi-labeling were proposed in the literature. Often these models involve the total variation (TV) semi-norm as regularizing term. However, it is well-known that the TV functional is not optimal for the segmentation of textured regions. In recent years directiona...

‎We present an application of the dual Gabor frames to image‎ ‎processing‎. ‎Our algorithm is based on finding some dual Gabor‎ ‎frame generators which reconstructs accurately the elements of the‎ ‎underlying Hilbert space‎. ‎The advantages of these duals‎ ‎constructed by a polynomial of Gabor frame generators are compared‎ ‎with their canonical dual‎.