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Simulation of quantum systems is challenging due to the exponential size of the state space. Tensor networks provide a systematically improvable approximation for quantum states. 2D tensor networks such as Projected Entangled Pair States…

This book serves as an introductory yet thorough guide to tensor networks and their applications in quantum computation and quantum information, designed for advanced undergraduate and graduate-level readers. In Part I, foundational topics…

Image segmentation, the process of partitioning an image into meaningful regions, plays a pivotal role in computer vision and medical imaging applications. Unsupervised segmentation, particularly in the absence of labeled data, remains a…

Dynamic mode decomposition (DMD) is a data-driven method for estimating the dynamics of a discrete dynamical system. This paper proposes a tensor-based approach to DMD for applications in which the states can be viewed as tensors.…

Tensor network methods have progressed from variational techniques based on matrix-product states able to compute properties of one-dimensional condensed-matter lattice models into methods rooted in more elaborate states such as projected…

Particle competition and cooperation (PCC) is a graph-based semi-supervised learning approach. When PCC is applied to interactive image segmentation tasks, pixels are converted into network nodes, and each node is connected to its k-nearest…

State Space Models (SSMs), especially Mamba, have shown great promise in medical image segmentation due to their ability to model long-range dependencies with linear computational complexity. However, accurate medical image segmentation…

Deep networks can be trained to map images into a low-dimensional latent space. In many cases, different images in a collection are articulated versions of one another; for example, same object with different lighting, background, or pose.…

In medical imaging analysis, deep learning has shown promising results. We frequently rely on volumetric data to segment medical images, necessitating the use of 3D architectures, which are commended for their capacity to capture interslice…

Segmentation is one of the most significant steps in image processing. Segmenting an image is a technique that makes it possible to separate a digital image into various areas based on the different characteristics of pixels in the image.…

Medical imaging plays a crucial role in modern healthcare by providing non-invasive visualisation of internal structures and abnormalities, enabling early disease detection, accurate diagnosis, and treatment planning. This study aims to…

Compression is a standard procedure for making convolutional neural networks (CNNs) adhere to some specific computing resource constraints. However, searching for a compressed architecture typically involves a series of time-consuming…

Recent progress in encoder-decoder neural network architecture design has led to significant performance improvements in a wide range of medical image segmentation tasks. However, state-of-the-art networks for a given task may be too…

Tensor networks (TNs) enable compact representations of large tensors through shared parameters. Their use in probabilistic modeling is particularly appealing, as probabilistic tensor networks (PTNs) allow for tractable computation of…

High resolution (HR) 3D images are widely used nowadays, such as medical images like Magnetic Resonance Imaging (MRI) and Computed Tomography (CT). However, segmentation of these 3D images remains a challenge due to their high spatial…

Tensor network states (TNS) are a promising but numerically challenging tool for simulating two-dimensional (2D) quantum many-body problems. We introduce an isometric restriction of the TNS ansatz that allows for highly efficient…

This study introduces a novel unsupervised medical image feature extraction method that employs spatial stratification techniques. An objective function based on weight is proposed to achieve the purpose of fast image recognition. The…

Deep learning has shown promising results in medical image analysis, however, the lack of very large annotated datasets confines its full potential. Although transfer learning with ImageNet pre-trained classification models can alleviate…

Strongly correlated layered 2D systems are of central importance in condensed matter physics, but their numerical study is very challenging. Motivated by the enormous successes of tensor networks for 1D and 2D systems, we develop an…

In this paper, we propose a novel medical image segmentation using iterative deep learning framework. We have combined an iterative learning approach and an encoder-decoder network to improve segmentation results, which enables to precisely…