Spectral-Smoothness and Non-Local Self-Similarity Regularized Subspace Low-Rank Learning Method for Hyperspectral Mixed Denoising

During the imaging process, hyperspectral image (HSI) is inevitably affected by various noises, such as Gaussian noise, impulse noise, stripes or deadlines. As one of the pre-processing steps, the removal of mixed noise for HSI has a vital impact on subsequent applications, and it is also one of the most challenging tasks. In this paper, a novel spectral-smoothness and non-local self-similarity regularized subspace low-rank learning (termed SNSSLrL) method was proposed for the mixed noise removal of HSI. First, under the subspace decomposition framework, the original HSI is decomposed into the linear representation of two low-dimensional matrices, namely the subspace basis matrix and the coefficient matrix. To further exploit the essential characteristics of HSI, on the one hand, the basis matrix is modeled as spectral smoothing, which constrains each column vector of the basis matrix to be a locally continuous spectrum, so that the subspace formed by its column vectors has continuous properties. On the other hand, the coefficient matrix is divided into several non-local block matrices according to the pixel coordinates of the original HSI data, and block-matching and 4D filtering (BM4D) is employed to reconstruct these self-similar non-local block matrices. Finally, the formulated model with all convex items is solved efficiently by the alternating direction method of multipliers (ADMM). Extensive experiments on two simulated datasets and one real dataset verify that the proposed SNSSLrL method has greater advantages than the latest state-of-the-art methods.

An Efficient Local Block Sobolev Gradient and Laplacian Approach for Elimination of Atmospheric Turbulence

A long range observing systems can be sturdily affected by scintillations. These scintillations are caused by changes in atmospheric conditions. In recent years, various turbulence mitigation approaches for turbulence mitigation have been exhibiting a promising nature. In this paper, we propose an effectual method to alleviate the effects of atmospheric distortion on observed images and video sequences. These sequences are mainly affected through floating air turbulence which can severely degrade the image quality. The existing algorithms primarily focus on the removal of turbulence and provides a solution only for static scenes, where there is no moving entity (real motion). As in the traditional SGL algorithm, the updated frame is iteratively used to correct the turbulence. This approach reduces the turbulence effect. However, it imposes some artifacts on the real motion that blurs the object. The proposed method is an alteration of the existing Sobolev Gradient and Laplacian (SGL) algorithm to eliminate turbulence. It eliminates the ghost artifact formed on moving object in the existing approach. The proposed method alleviates turbulence without harming the moving objects in the scene. The method is demonstrated on significantly distorted sequences provided by OTIS and compared with the SGL technique. The information conveyed in the scene becomes clearly visible through the method on exclusion of turbulence. The proposed approach is evaluated using standard performance measures such as MSE, PSNR and SSIM. The evaluation results depict that the proposed method outperforms the existing state-of-the-art approaches for all three standard performance measures.

The Flora Motif as Design Identity in Local Traditional Block Batik

This study discusses that floral motifs as the dominant traditional motifs in Malaysian block batik. In the 20th century, the block makers created any motif with purpose—the traditional block batik motifs not revealed due to lack of secure identity upon the development of high-tech modernisation. Based on the sequence of this issue, this study aims to classify the various types of local block motifs and designs. The classification base on their features using a suitable procedure. The crucial outcomes where the motifs of block batik still show the elements and innovation of the local motif identity. Keywords: Block Batik; Design; Motif; Identity eISSN: 2398-4287© 2020. The Authors. Published for AMER ABRA cE-Bsby e-International Publishing House, Ltd., UK. This is an open access article under the CC BYNC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer–review under responsibility of AMER (Association of Malaysian Environment-Behaviour Researchers), ABRA (Association of Behavioural Researchers on Asians) and cE-Bs (Centre for Environment-Behaviour Studies), Faculty of Architecture, Planning & Surveying, Universiti Teknologi MARA, Malaysia. DOI: https://doi.org/10.21834/ebpj.v5iSI3.2542

Unitary signings and induced subgraphs of Cayley graphs of $\mathbb{Z}_2^{n}$

Boolean functions play an important role in many different areas of computer science. The _local sensitivity_ of a Boolean function $f:\{0,1\}^n\to \{0,1\}$ on an input $x\in\{0,1\}^n$ is the number of coordinates whose flip changes the value of $f(x)$, i.e., the number of i's such that $f(x)\not=f(x+e_i)$, where $e_i$ is the $i$-th unit vector. The _sensitivity_ of a Boolean function is its maximum local sensitivity. In other words, the sensitivity measures the robustness of a Boolean function with respect to a perturbation of its input. Another notion that measures the robustness is block sensitivity. The _local block sensitivity_ of a Boolean function $f:\{0,1\}^n\to \{0,1\}$ on an input $x\in\{0,1\}^n$ is the number of disjoint subsets $I$ of $\{1,..,n\}$ such that flipping the coordinates indexed by $I$ changes the value of $f(x)$, and the _block sensitivity_ of $f$ is its maximum local block sensitivity. Since the local block sensitivity is at least the local sensitivity for any input $x$, the block sensitivity of $f$ is at least the sensitivity of $f$. The next example demonstrates that the block sensitivity of a Boolean function is not linearly bounded by its sensitivity. Fix an integer $k\ge 2$ and define a Boolean function $f:\{0,1\}^{2k^2}\to\{0,1\}$ as follows: the coordinates of $x\in\{0,1\}^{2k^2}$ are split into $k$ blocks of size $2k$ each and $f(x)=1$ if and only if at least one of the blocks contains exactly two entries equal to one and these entries are consecutive. While the sensitivity of the function $f$ is $2k$, its block sensitivity is $k^2$. The Sensitivity Conjecture, made by Nisan and Szegedy in 1992, asserts that the block sensitivity of a Boolean function is polynomially bounded by its sensivity. The example above shows that the degree of such a polynomial must be at least two. The Sensitivity Conjecture has been recently proven by Huang in [Annals of Mathematics 190 (2019), 949-955](https://doi.org/10.4007/annals.2019.190.3.6). He proved the following combinatorial statement that implies the conjecture (with the degree of the polynomial equal to four): any subset of more than half of the vertices of the $n$-dimensional cube $\{0,1\}^n$ induces a subgraph that contains a vertex with degree at least $\sqrt{n}$. The present article extends this result as follows: every Cayley graph with the vertex set $\{0,1\}^n$ and any generating set of size $d$ (the vertex set is viewed as a vector space over the binary field) satisfies that any subset of more than half of its vertices induces a subgraph that contains a vertex of degree at least $\sqrt{d}$. In particular, when the generating set consists of the $n$ unit vectors, the Cayley graph is the $n$-dimensional hypercube.

Convergence of Slice-Based Block Coordinate Descent Algorithm for Convolutional Sparse Coding

Convolutional sparse coding (CSC) models are becoming increasingly popular in the signal and image processing communities in recent years. Several research studies have addressed the basis pursuit (BP) problem of the CSC model, including the recently proposed local block coordinate descent (LoBCoD) algorithm. This algorithm adopts slice-based local processing ideas and splits the global sparse vector into local vector needles that are locally computed in the original domain to obtain the encoding. However, a convergence theorem for the LoBCoD algorithm has not been given previously. This paper presents a convergence theorem for the LoBCoD algorithm which proves that the LoBCoD algorithm will converge to its global optimum at a rate of O1/k. A slice-based multilayer local block coordinate descent (ML-LoBCoD) algorithm is proposed which is motivated by the multilayer basis pursuit (ML-BP) problem and the LoBCoD algorithm. We prove that the ML-LoBCoD algorithm is guaranteed to converge to the optimal solution at a rate O1/k. Preliminary numerical experiments demonstrate the better performance of the proposed ML-LoBCoD algorithm compared to the LoBCoD algorithm for the BP problem, and the loss function value is also lower for ML-LoBCoD than LoBCoD.

Terrestrial kaolin deposits trapped in Miocene karstic sinkholes on planation surface remnants, Transdanubian Range, Pannonian Basin (Hungary)

In the Transdanubian Range, Pannonian Basin, Hungary, karstic sinkholes on a planation surface of Triassic carbonates are filled by grey clayey–silty kaolin deposits. The provenance and accumulation age of these strongly altered terrestrial karst-filling sediments are constrained by X-ray powder diffraction, heavy mineral analysis and zircon U–Pb dating. The heavy minerals of the Southern Bakony Mountains samples are dominated by the ultra-stable zircon–rutile–tourmaline association. Zircon U–Pb data indicate accumulation between 20 and 16 Ma. Furthermore, Archaean to Palaeogene grains were also determined, reflecting the principally fluvial recycling of Eocene bauxites and their cover sequences. In contrast, the sample from the Keszthely Hills consists almost exclusively of airborne material including zircons of 18–14 Ma, reflecting a dominant contribution from the Carpathian–Pannonian Neogene volcanism. The shift in the Miocene age components is inferred to have been caused by the landscape evolution and burial history of the planation surface remnants controlled by local block tectonics.