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NASA's Solar Dynamics Observatory (SDO) mission collects extensive data to monitor the Sun's daily activity. In the realm of space mission design, data compression plays a crucial role in addressing the challenges posed by limited telemetry rates. The primary objective of data compression is to facilitate efficient data management and transmission to work within the constrained bandwidth, thereby ensuring that essential information is captured while optimizing the utilization of available resources. This paper introduces a neural video compression technique that achieves a high compression ratio for the SDO's image data collection. The proposed approach focuses on leveraging both temporal and spatial redundancies in the data, leading to a more efficient compression. In this work, we introduce an architecture based on the Transformer model, which is specifically designed to capture both local and global information from input images in an effective and efficient manner. Additionally, our network is equipped with an entropy model that can accurately model the probability distribution of the latent representations and improves the speed of the entropy decoding step. The entropy model leverages a channel-dependent approach and utilizes checkerboard-shaped local and global spatial contexts. By combining the Transformer-based video compression network with our entropy model, the proposed compression algorithm demonstrates superior performance over traditional video codecs like H.264 and H.265, as confirmed by our experimental results.

While replacing Gaussian decoders with a conditional diffusion model enhances the perceptual quality of reconstructions in neural image compression, their lack of inductive bias for image data restricts their ability to achieve state-of-the-art perceptual levels. To address this limitation, we adopt a non-isotropic diffusion model at the decoder side. This model imposes an inductive bias aimed at distinguishing between frequency contents, thereby facilitating the generation of high-quality images. Moreover, our framework is equipped with a novel entropy model that accurately models the probability distribution of latent representation by exploiting spatio-channel correlations in latent space, while accelerating the entropy decoding step. This channel-wise entropy model leverages both local and global spatial contexts within each channel chunk. The global spatial context is built upon the Transformer, which is specifically designed for image compression tasks. The designed Transformer employs a Laplacian-shaped positional encoding, the learnable parameters of which are adaptively adjusted for each channel cluster. Our experiments demonstrate that our proposed framework yields better perceptual quality compared to cutting-edge generative-based codecs, and the proposed entropy model contributes to notable bitrate savings., Comment: Accepted by CVPR2024

Studying the solar system and especially the Sun relies on the data gathered daily from space missions. These missions are data-intensive and compressing this data to make them efficiently transferable to the ground station is a twofold decision to make. Stronger compression methods, by distorting the data, can increase data throughput at the cost of accuracy which could affect scientific analysis of the data. On the other hand, preserving subtle details in the compressed data requires a high amount of data to be transferred, reducing the desired gains from compression. In this work, we propose a neural network-based lossy compression method to be used in NASA's data-intensive imagery missions. We chose NASA's SDO mission which transmits 1.4 terabytes of data each day as a proof of concept for the proposed algorithm. In this work, we propose an adversarially trained neural network, equipped with local and non-local attention modules to capture both the local and global structure of the image resulting in a better trade-off in rate-distortion (RD) compared to conventional hand-engineered codecs. The RD variational autoencoder used in this work is jointly trained with a channel-dependent entropy model as a shared prior between the analysis and synthesis transforms to make the entropy coding of the latent code more effective. Our neural image compression algorithm outperforms currently-in-use and state-of-the-art codecs such as JPEG and JPEG-2000 in terms of the RD performance when compressing extreme-ultraviolet (EUV) data. As a proof of concept for use of this algorithm in SDO data analysis, we have performed coronal hole (CH) detection using our compressed images, and generated consistent segmentations, even at a compression rate of $\sim0.1$ bits per pixel (compared to 8 bits per pixel on the original data) using EUV data from SDO., Comment: Accepted for publication in IEEE Transactions on Aerospace and Electronic Systems (TAES). arXiv admin note: text overlap with arXiv:2210.06478

Despite the advances in the field of Face Recognition (FR), the precision of these methods is not yet sufficient. To improve the FR performance, this paper proposes a technique to aggregate the outputs of two state-of-the-art (SOTA) deep FR models, namely ArcFace and AdaFace. In our approach, we leverage the transformer attention mechanism to exploit the relationship between different parts of two feature maps. By doing so, we aim to enhance the overall discriminative power of the FR system. One of the challenges in feature aggregation is the effective modeling of both local and global dependencies. Conventional transformers are known for their ability to capture long-range dependencies, but they often struggle with modeling local dependencies accurately. To address this limitation, we augment the self-attention mechanism to capture both local and global dependencies effectively. This allows our model to take advantage of the overlapping receptive fields present in corresponding locations of the feature maps. However, fusing two feature maps from different FR models might introduce redundancies to the face embedding. Since these models often share identical backbone architectures, the resulting feature maps may contain overlapping information, which can mislead the training process. To overcome this problem, we leverage the principle of Information Bottleneck to obtain a maximally informative facial representation. This ensures that the aggregated features retain the most relevant and discriminative information while minimizing redundant or misleading details. To evaluate the effectiveness of our proposed method, we conducted experiments on popular benchmarks and compared our results with state-of-the-art algorithms. The consistent improvement we observed in these benchmarks demonstrates the efficacy of our approach in enhancing FR performance., Comment: Accepted to 22$^{nd}$ IEEE International Conference on Machine Learning and Applications 2023 (ICMLA)

Transform and entropy models are the two core components in deep image compression neural networks. Most existing learning-based image compression methods utilize convolutional-based transform, which lacks the ability to model long-range dependencies, primarily due to the limited receptive field of the convolution operation. To address this limitation, we propose a Transformer-based nonlinear transform. This transform has the remarkable ability to efficiently capture both local and global information from the input image, leading to a more decorrelated latent representation. In addition, we introduce a novel entropy model that incorporates two different hyperpriors to model cross-channel and spatial dependencies of the latent representation. To further improve the entropy model, we add a global context that leverages distant relationships to predict the current latent more accurately. This global context employs a causal attention mechanism to extract long-range information in a content-dependent manner. Our experiments show that our proposed framework performs better than the state-of-the-art methods in terms of rate-distortion performance., Comment: Accepted to IEEE 22$^nd$ International Conference on Machine Learning and Applications 2023 (ICMLA) - Selected for Oral Presentation

Missions studying the dynamic behaviour of the Sun are defined to capture multi-spectral images of the sun and transmit them to the ground station in a daily basis. To make transmission efficient and feasible, image compression systems need to be exploited. Recently successful end-to-end optimized neural network-based image compression systems have shown great potential to be used in an ad-hoc manner. In this work we have proposed a transformer-based multi-spectral neural image compressor to efficiently capture redundancies both intra/inter-wavelength. To unleash the locality of window-based self attention mechanism, we propose an inter-window aggregated token multi head self attention. Additionally to make the neural compressor autoencoder shift invariant, a randomly shifted window attention mechanism is used which makes the transformer blocks insensitive to translations in their input domain. We demonstrate that the proposed approach not only outperforms the conventional compression algorithms but also it is able to better decorrelates images along the multiple wavelengths compared to single spectral compression., Comment: Accepted to IEEE 22$^{nd}$ International Conference on Machine Learning and Applications 2023 (ICMLA)

NASA's Solar Dynamics Observatory (SDO) mission collects large data volumes of the Sun's daily activity. Data compression is crucial for space missions to reduce data storage and video bandwidth requirements by eliminating redundancies in the data. In this paper, we present a novel neural Transformer-based video compression approach specifically designed for the SDO images. Our primary objective is to efficiently exploit the temporal and spatial redundancies inherent in solar images to obtain a high compression ratio. Our proposed architecture benefits from a novel Transformer block called Fused Local-aware Window (FLaWin), which incorporates window-based self-attention modules and an efficient fused local-aware feed-forward (FLaFF) network. This architectural design allows us to simultaneously capture short-range and long-range information while facilitating the extraction of rich and diverse contextual representations. Moreover, this design choice results in reduced computational complexity. Experimental results demonstrate the significant contribution of the FLaWin Transformer block to the compression performance, outperforming conventional hand-engineered video codecs such as H.264 and H.265 in terms of rate-distortion trade-off., Comment: Accepted to IEEE 22$^{nd}$ International Conference on Machine Learning and Applications 2023 (ICMLA) - Selected for Oral Presentation

The design of a neural image compression network is governed by how well the entropy model matches the true distribution of the latent code. Apart from the model capacity, this ability is indirectly under the effect of how close the relaxed quantization is to the actual hard quantization. Optimizing the parameters of a rate-distortion variational autoencoder (R-D VAE) is ruled by this approximated quantization scheme. In this paper, we propose a feature-level frequency disentanglement to help the relaxed scalar quantization achieve lower bit rates by guiding the high entropy latent features to include most of the low-frequency texture of the image. In addition, to strengthen the de-correlating power of the transformer-based analysis/synthesis transform, an augmented self-attention score calculation based on the Hadamard product is utilized during both encoding and decoding. Channel-wise autoregressive entropy modeling takes advantage of the proposed frequency separation as it inherently directs high-informational low-frequency channels to the first chunks and conditions the future chunks on it. The proposed network not only outperforms hand-engineered codecs, but also neural network-based codecs built on computation-heavy spatially autoregressive entropy models., Comment: Accepted to 30$^{th}$ IEEE International Conference on Image Processing (ICIP 2023)

Currently available face datasets mainly consist of a large number of high-quality and a small number of low-quality samples. As a result, a Face Recognition (FR) network fails to learn the distribution of low-quality samples since they are less frequent during training (underrepresented). Moreover, current state-of-the-art FR training paradigms are based on the sample-to-center comparison (i.e., Softmax-based classifier), which results in a lack of uniformity between train and test metrics. This work integrates a quality-aware learning process at the sample level into the classification training paradigm (QAFace). In this regard, Softmax centers are adaptively guided to pay more attention to low-quality samples by using a quality-aware function. Accordingly, QAFace adds a quality-based adjustment to the updating procedure of the Softmax-based classifier to improve the performance on the underrepresented low-quality samples. Our method adaptively finds and assigns more attention to the recognizable low-quality samples in the training datasets. In addition, QAFace ignores the unrecognizable low-quality samples using the feature magnitude as a proxy for quality. As a result, QAFace prevents class centers from getting distracted from the optimal direction. The proposed method is superior to the state-of-the-art algorithms in extensive experimental results on the CFP-FP, LFW, CPLFW, CALFW, AgeDB, IJB-B, and IJB-C datasets., Comment: IEEE/CVF Winter Conference on Applications of Computer Vision (WACV23)

NASA's Solar Dynamics Observatory (SDO) mission gathers 1.4 terabytes of data each day from its geosynchronous orbit in space. SDO data includes images of the Sun captured at different wavelengths, with the primary scientific goal of understanding the dynamic processes governing the Sun. Recently, end-to-end optimized artificial neural networks (ANN) have shown great potential in performing image compression. ANN-based compression schemes have outperformed conventional hand-engineered algorithms for lossy and lossless image compression. We have designed an ad-hoc ANN-based image compression scheme to reduce the amount of data needed to be stored and retrieved on space missions studying solar dynamics. In this work, we propose an attention module to make use of both local and non-local attention mechanisms in an adversarially trained neural image compression network. We have also demonstrated the superior perceptual quality of this neural image compressor. Our proposed algorithm for compressing images downloaded from the SDO spacecraft performs better in rate-distortion trade-off than the popular currently-in-use image compression codecs such as JPEG and JPEG2000. In addition we have shown that the proposed method outperforms state-of-the art lossy transform coding compression codec, i.e., BPG., Comment: Accepted to IEEE 21$^{st}$ International Conference on Machine Learning and Applications 2022 (ICMLA) - Selected for Oral Presentation

The problem of determining resolving sets in graph theory has a long history, as it has many applications in chemistry, robot navigation, combinatorial optimization and utilization of the idea in pattern recognition and processing of images that also provide motivation for founding the theory. Especially, it is well known that these problems are NP hard. In the present work, first we define the structure of the crystal cubic carbon $CCC(n)$ by a new method, and we will find the minimum number of doubly resolving sets and strong resolving sets for the crystal cubic carbon $CCC(n)$. Also, we construct a new class of graphs of order $n+ \Sigma_{p=2}^{k}n^2(n-1)^{p-2}$, is denoted by $LCG(n, k)$ and recall that the layer cycle graph with parameters $n$ and $k$. Moreover, we will compute the minimum number of some resolving sets for the layer cycle graph $LCG(n, k)$.

A subset $Q = \{q_1, q_2, ..., q_l\}$ of vertices of a connected graph $G$ is a doubly resolving set of $G$ if for any various vertices $x, y \in V(G)$ we have $r(x|Q)-r(y|Q)\neq\lambda I$, where $\lambda$ is an integer, and $I$ indicates the unit $l$- vector $(1,..., 1)$. A doubly resolving set of vertices of graph $G$ with the minimum size, is denoted by $\psi(G)$. In this work, we will consider the computational study of some resolving sets with the minimum size for $(C_n\Box P_k)\Box P_m$., Comment: arXiv admin note: substantial text overlap with arXiv:2103.15560

A resolving set for a graph $G$ is a set of vertices $Q = \{q_1, ..., q_k\}$ such that, for all $p\in V(G)$ the $k$-tuple $(d(p, q_1), ..., d(p, q_k ))$ uniquely determines $p$, where $d(p, q_i)$ is considered as the minimum length of a shortest path from $p$ to $q_i$ in graph $G$. In this paper, we consider the computational study of some resolving sets with the minimum size for the $m$-cylinder graph $(C_n\Box P_k)\Box P_m$. The Boolean lattice $BL_n$, $n\geq 1$, is the graph whose vertex set is the set of all subsets of $[n]=\{1,2,...,n\}$, where two subsets $X$ and $Y$ are adjacent if their symmetric difference has precisely one element. In the graph $BL_n$, the layer $L_i$ is the family of $i$-subsets of $[n]$. The subgraph $BL_n(i,i+1)$ is the subgraph of $BL_n$ induced by layers $L_i$ and $L_{i+1}$. Usually the graph $BL_n(1,2)$ is denoted by $H(n)$. We study the minimum size of a resolving set, doubly resolving set and strong resolving set for the graph $L(n)$, which is the line graph of $H(n)$., Comment: For personal reasons, Professor Liu asked us not to mention his name in the article and to thank him only in the acknowledgments section

Let $G$ be a finite, connected graph of order of at least 2, with vertex set $V(G)$ and edge set $E (G)$. A set $S$ of vertices of the graph $G$ is a doubly resolving set for $G$ if every two distinct vertices of $G$ are doubly resolved by some two vertices of $S$. The minimal doubly resolving set of vertices of graph $G$ is a doubly resolving set with minimum cardinality and is denoted by $\psi(G)$. In this paper, first, we construct a class of graphs of order $2n+ \Sigma_{r=1}^{k-2}nm^{r}$, denoted by $LSG(n,m, k)$, and call these graphs as the layer Sun graphs with parameters $n$, $m$ and $k$. Moreover, we compute minimal doubly resolving sets and the strong metric dimension of layer Sun graph $LSG(n,m, k)$ and the line graph of the layer Sun graph $LSG(n,m, k)$.

Let $\Gamma$ be a simple connected undirected graph with vertex set $V(\Gamma)$ and edge set $E(\Gamma)$. The metric dimension of a graph $\Gamma$ is the least number of vertices in a set with the property that the list of distances from any vertex to those in the set uniquely identifies that vertex. For an ordered subset $W = \{w_1, w_2, ..., w_k\}$ of vertices in a graph $\Gamma$ and a vertex $v$ of $\Gamma$, the metric representation of $v$ with respect to $W$ is the $k$-vector $r(v | W) = (d(v, w_1), d(v, w_2), ..., d(v, w_k ))$. If every pair of distinct vertices of $\Gamma$ have different metric representations then the ordered set $W$ is called a resolving set of $\Gamma$. It is known that the problem of computing this invariant is NP-hard. In this paper, we consider the problem of determining the cardinality $\psi(\Gamma)$ of minimal doubly resolving sets of $\Gamma$, and the strong metric dimension for jellyfish graph $JFG(n, m)$ and cocktail party graph $CP(k+1)$., Comment: arXiv admin note: substantial text overlap with arXiv:1905.10525, arXiv:1908.07854

Resolving parameters is a fundamental area of combinatorics with applications not only to many branches of combinatorics but also to other sciences. In this article, we construct a class of Toeplitz graphs, and will be denoted by $T_{2n}(W)$, so that they are Cayley graphs. First, we review some of the features of this class of graphs. In fact, this class of graphs are vertex transitive, and by calculating the spectrum of the adjacency matrix related with them, we show that this class of graphs cannot be edge transitive. Moreover, we show that this class of graphs cannot be distance regular, and since the computing resolving parameters of a class of graphs such that are not distance regular is more difficult, then we regard this as justification for our focus on some resolving parameters. In particular, we determine the minimal resolving set, doubly resolving set and strong metric dimension for this class of graphs., Comment: arXiv admin note: substantial text overlap with arXiv:1905.10527

If all the eigenvalues of the adjacency matrix of a graph $\Gamma$ are integers, then we say that $\Gamma$ is an integral graph. It seems hard to prove a graph to be determined by its spectrum. In this paper, we investigate some new classes of multicone graphs determinable by their spectra, such as: $K_v \bigtriangledown O_k$, $K_v \bigtriangledown mO_k$, $K_v \bigtriangledown \Box_n$ and $K_v \bigtriangledown m\Box_n$, where $O_k$ denoted the Odd graph $O_{d+1}$ and, $\Box_n$ denoted the folded $2d+1$ cube. Also, the notation of the folded graph of $2.O_k$ will be defined and denoted by $F(2.O_k)$. Moreover, we study some algebraic properties of the graph $F(2.O_k)$, in fact we show that $F(2.O_k)$ is an integral graph., Comment: arXiv admin note: substantial text overlap with arXiv:1905.10525

Let $\Gamma=(V,E)$ be a graph. If all the eigenvalues of the adjacency matrix of the graph $\Gamma$ are integers, then we say that $\Gamma$ is an integral graph. A graph $\Gamma$ is determined by its spectrum if every graph cospectral to it is in fact isomorphic to it. In this paper, we investigate some algebraic properties of the Cayley graph $\Gamma=Cay(\mathbb{Z}_{n}, S)$, where $n=p^m$, ($p$ is a prime integer, $m\in\mathbb{N}$) and $S=\{{a}\in\mathbb{Z}_{n}\,|\,\, (a, n)=1\}$. First, we show that $\Gamma$ is an integral graph. Also we determine the automorphism group of $\Gamma$. Moreover, we show that $\Gamma$ and $K_v \bigtriangledown\Gamma$ are determined by their spectrum.

Let $n$ and $k$ be integers with $n> k\geq1$ and $[n] = \{1, 2, ... , n\} $. The $bipartite \ Kneser \ graph$ $H(n, k)$ is the graph with the all $k$-element and all ($n-k$)-element subsets of $[n] $ as vertices, and there is an edge between any two vertices, when one is a subset of the other. In this paper, we show that $H(n, k)$ is an arc-transitive graph. Also, we show that $H(n,1)$ is a distance-transitive Cayley graph. Finally, we determine the automorphism group of the graph $H(n, 1)$ and show that $Aut(H(n, 1)) \cong Sym([n] )$ $\times \mathbb{Z}_2$, where $\mathbb{Z}_2$ is the cyclic group of order $2$. Moreover, we pose some open problems about the automorphism group of the bipartite Kneser graph $H(n, k)$., Comment: To appear in Ars Combinatoria. arXiv admin note: text overlap with arXiv:1803.02524