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Principal components analysis (PCA) is a standard tool for identifying good low-dimensional approximations to data in high dimension. Many data sets of interest contain private or sensitive information about individuals. Algorithms which…

The Karhunen-Lo\`eve transform (KLT) is often used for data decorrelation and dimensionality reduction. The KLT is able to optimally retain the signal energy in only few transform components, being mathematically suitable for image and…

Multimodal medical image fusion helps to increase efficiency in medical diagnosis. This paper presents multimodal medical image fusion by selecting relevant features using Principle Component Analysis (PCA) and Particle Swarm Optimization…

The discrete cosine transform (DCT), introduced by Ahmed, Natarajan and Rao, has been used in many applications of digital signal processing, data compression and information hiding. There are four types of the discrete cosine transform. In…

Transformer has achieved great success in computer vision, while how to split patches in an image remains a problem. Existing methods usually use a fixed-size patch embedding which might destroy the semantics of objects. To address this…

Transformers are very powerful tools for a variety of tasks across domains, from text generation to image captioning. However, transformers require substantial amounts of training data, which is often a challenge in biomedical settings,…

Sparse principal component analysis (PCA) and sparse canonical correlation analysis (CCA) are two essential techniques from high-dimensional statistics and machine learning for analyzing large-scale data. Both problems can be formulated as…

Recent video codecs such as VVC and AV1 apply a Non-rectangular (NR) partitioning to combine prediction signals using a smooth blending around the boundary, followed by a rectangular transform on the whole block. The NR signal…

The robust PCA of covariance matrices plays an essential role when isolating key explanatory features. The currently available methods for performing such a low-rank plus sparse decomposition are matrix specific, meaning, those algorithms…

In this paper we analyze approximate methods for undertaking a principal components analysis (PCA) on large data sets. PCA is a classical dimension reduction method that involves the projection of the data onto the subspace spanned by the…

We present a novel approach for adaptive, differentiable parameterization of large-scale random fields. If the approach is coupled with any gradient-based optimization algorithm, it can be applied to a variety of optimization problems,…

We present a new technique called contrastive principal component analysis (cPCA) that is designed to discover low-dimensional structure that is unique to a dataset, or enriched in one dataset relative to other data. The technique is a…

Convolutional Neural Network is good at image classification. However, it is found to be vulnerable to image quality degradation. Even a small amount of distortion such as noise or blur can severely hamper the performance of these CNN…

As an extension of the 2D fractional Fourier transform (FRFT) and a special case of the 2D linear canonical transform (LCT), the gyrator transform was introduced to produce rotations in twisted space/spatial-frequency planes. It is a useful…

Dimensionality reduction is a fundamental technique in machine learning and data analysis, enabling efficient representation and visualization of high-dimensional data. This paper explores five key methods: Principal Component Analysis…

We study the distributed computing setting in which there are multiple servers, each holding a set of points, who wish to compute functions on the union of their point sets. A key task in this setting is Principal Component Analysis (PCA),…

Principal component analysis (PCA) has been widely used in analyzing high-dimensional data. It converts a set of observed data points of possibly correlated variables into a set of linearly uncorrelated variables via an orthogonal…

Corner detection is a vital operation in numerous computer vision applications. The Chord-to-Point Distance Accumulation (CPDA) detector is recognized as the contour-based corner detector producing the lowest localization error while…

We propose a practical approach to JPEG image decoding, utilizing a local implicit neural representation with continuous cosine formulation. The JPEG algorithm significantly quantizes discrete cosine transform (DCT) spectra to achieve a…

With the rapid advancements in digital imaging systems and networking, low-cost hand-held image capture devices equipped with network connectivity are becoming ubiquitous. This ease of digital image capture and sharing is also accompanied…