In recent years directional multiscale transformations like the curveletor shearlet transformation have gained considerable attention. The reason for this is that these transforms are unlike more traditional transforms like wavelets able to efficiently handle data with features along edges. The main result confirming this property for shearlets is contained in [21] where it is shown that for ve...

Abstract. We study efficient and reliable methods of capturing and sparsely representing anisotropic structures in 3D data. As a model class for multidimensional data with anisotropic features, we introduce generalized three-dimensional cartoon-like images. This function class will have two smoothness parameters: one parameter β controlling classical smoothness and one parameter α controlling a...

In this paper, we first introduce the concept of an adaptive MRA (AMRA) structure which is a variant of the classical MRA structure suited to the main goal of a fast flexible decomposition strategy adapted to the data at each decomposition level. We then study this novel methodology for the general case of affine-like systems, and derive a Unitary Extension Principle (UEP) for filter design. Fi...

Based on image sparse representation in the shearlet domain, we proposed a 2 1 L sparsity regularized unconvex variation model for image super-resolution. The 2 1 L regularizer term constrains the underlying image to have a sparse representation in shearlet domain. The fidelity term restricts the consistency with the measured imaged in terms of the data degradation model. Then, the variable spl...

The use of the Hilbert transform for time/frequency analysis of signals is briefly considered. While the Hilbert transform is based on arbitrary continuous signals, most practical signals are digitially sampled and time-limited. To avoid aliasing in the sampling process the signals must also be bandlimited. It is argued that it is reasonable to consider such sampled signals as periodic (this is...

3B şekil oluşturulma sürecinde herhangi ek donanım gerektirmeyen Odaktan Şekil (Shape From Focus - SFF) en çok tercih edilen stratejilerdendir. SFF stratejisi, oluşturma farklı odaklı 2B görüntü serisi kullanmakta ve üç temel aşamadan oluşmaktadır: (1) Farklı serisinin elde edilmesi, (2) Görüntü piksellerinin odaklama değerlerinin hesaplanması (3) Maksimum pikselin seçilmesi. Yüksek doğruluk da...

The field $Q_{p}$ of $p$-adic numbers is defined as the completion of the field of the rational numbers $Q$ with respect to the  $p$-adic norm $|.|_{p}$. In this paper, we study the continuous and discrete $p-$adic shearlet systems on $L^{2}(Q_{p}^{2})$. We also suggest discrete $p-$adic shearlet frames. Several examples are provided.