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This paper introduces sparse coding and dictionary learning for Symmetric Positive Definite (SPD) matrices, which are often used in machine learning, computer vision and related areas. Unlike traditional sparse coding schemes that work in…
We find that the overlapping of a topological quantum color code state, representing a quantum memory, with a factorized state of qubits can be written as the partition function of a 3-body classical Ising model on triangular or Union Jack…
We define linear and semilinear isometry for general subspace codes, used for random network coding. Furthermore, some results on isometry classes and automorphism groups of known constant dimension code constructions are derived.
Coherence has been used as a resource for optical communications since its earliest days. It is widely used for multiplexing of data, but not for encoding of data. Here we introduce a coding scheme, which we call \textit{mutual coherence…
Semantic image understanding is a challenging topic in computer vision. It requires to detect all objects in an image, but also to identify all the relations between them. Detected objects, their labels and the discovered relations can be…
We consider the locality of encoding and decoding operations in distributed storage systems (DSS), and propose a new class of codes, called locally encodable and decodable codes (LEDC), that provides a higher degree of operational locality…
This fourth and last tome is focusing on describing the envisioned works for a project that has been presented in the preceding tome. It is about a new approach dedicated to the coding of still and moving pictures, trying to bridge the…
This paper presents a collaborative implicit neural simultaneous localization and mapping (SLAM) system with RGB-D image sequences, which consists of complete front-end and back-end modules including odometry, loop detection, sub-map…
A `whole-part' theory is developed for a set of finite quantum systems $\Sigma (n)$ with variables in ${\mathbb Z}(n)$. The partial order `subsystem' is defined, by embedding various attributes of the system $\Sigma (m)$ (quantum states,…
In this paper we explore the use of spatial clustering algorithms as a new computational approach for modeling the cosmic web. We demonstrate that such algorithms are efficient in terms of computing time needed. We explore three distinct…
Change point detection (CPD) and anomaly detection (AD) are essential techniques in various fields to identify abrupt changes or abnormal data instances. However, existing methods are often constrained to univariate data, face scalability…
This paper investigates the design of spatially coupled low-density parity-check (SC-LDPC) codes constructed from connected-chain ensembles for bit-interleaved coded modulation (BICM) schemes. For short coupling lengths, connecting multiple…
In this paper, we investigate the impact of spatial coupling on the thresholds of turbo-like codes. Parallel concatenated and serially concatenated convolutional codes as well as braided convolutional codes (BCCs) are compared by means of…
A new formulation of lateral imaging process of point-scanning optical coherence tomography (OCT) and a new differential contrast method designed by using this formulation are presented. The formulation is based on a mathematical sample…
The statistical description of Giant Molecular Cloud (GMC) properties relies heavily on the performance of automatic identification algorithms, which are often seriously affected by the survey design. The algorithm we designed, SCIMES…
In computer vision and medical imaging, the problem of matching structures finds numerous applications from automatic annotation to data reconstruction. The data however, while corresponding to the same anatomy, are often very different in…
SAM is a segmentation model recently released by Meta AI Research and has been gaining attention quickly due to its impressive performance in generic object segmentation. However, its ability to generalize to specific scenes such as…
Over-the-air computation (OAC) harnesses the natural superposition of wireless signals to compute aggregate functions during transmission, thereby collapsing communication and computation into a single step and significantly reducing…
The immense amount of daily generated and communicated data presents unique challenges in their processing. Clustering, the grouping of data without the presence of ground-truth labels, is an important tool for drawing inferences from data.…
Sparse coding has shown its power as an effective data representation method. However, up to now, all the sparse coding approaches are limited within the single domain learning problem. In this paper, we extend the sparse coding to cross…