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Transformer-based models have recently shown success in representation learning on graph-structured data beyond natural language processing and computer vision. However, the success is limited to small-scale graphs due to the drawbacks of…
Data-dependent secondary transforms, which aim to decorrelate coefficients of a separable primary transform, can improve residual coding efficiency; however, their deployment is often constrained by computational complexity. Recent video…
In image compression, classical block-based separable transforms tend to be inefficient when image blocks contain arbitrarily shaped discontinuities. For this reason, transforms incorporating directional information are an appealing…
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…
The discrete cosine transform (DCT) is the key step in many image and video coding standards. The 8-point DCT is an important special case, possessing several low-complexity approximations widely investigated. However, 16-point DCT…
Discrete cosine transform (DCT) and other Fourier-related transforms have broad applications in scientific computing. However, off-the-shelf high-performance multi-dimensional DCT (MD DCT) libraries are not readily available in parallel…
Video coding standards are primarily designed for efficient lossy compression, but it is also desirable to support efficient lossless compression within video coding standards using small modifications to the lossy coding architecture. A…
In this paper, we introduce low-complexity multidimensional discrete cosine transform (DCT) approximations. Three dimensional DCT (3D DCT) approximations are formalized in terms of high-order tensor theory. The formulation is extended to…
Modern compression systems use linear transformations in their encoding and decoding processes, with transforms providing compact signal representations. While multiple data-dependent transforms for image/video coding can adapt to diverse…
Low-rank optimization has emerged as a promising direction in training large language models (LLMs) to improve running time and reduce the memory usage of adaptive optimizers by constraining learning to a lower-dimensional space. Prior work…
The discrete Hartley transform (DHT) is a useful tool for medical image coding. The three-dimensional DHT (3D DHT) can be employed to compress medical image data, such as magnetic resonance and X-ray angiography. However, the computation of…
This paper introduced a matrix parametrization method based on the Loeffler discrete cosine transform (DCT) algorithm. As a result, a new class of eight-point DCT approximations was proposed, capable of unifying the mathematical formalism…
A multiplierless pruned approximate 8-point discrete cosine transform (DCT) requiring only 10 additions is introduced. The proposed algorithm was assessed in image and video compression, showing competitive performance with state-of-the-art…
A fast Discrete Cosine Transform (DCT) algorithm is introduced that can be of particular interest in image processing. The main features of the algorithm are regularity of the graph and very low arithmetic complexity. The 16-point version…
The 2-D discrete wavelet transform (DWT) can be found in the heart of many image-processing algorithms. Until recently, several studies have compared the performance of such transform on various shared-memory parallel architectures,…
In recent years, the integration of advanced imaging techniques and deep learning methods has significantly advanced computer-aided diagnosis (CAD) systems for breast cancer detection and classification. Transformers, which have shown great…
For the last few decades, the application of signal-adaptive transform coding to video compression has been stymied by the large computational complexity of matrix-based solutions. In this paper, we propose a novel parametric approach to…
Visual tracking usually requires an object appearance model that is robust to changing illumination, pose and other factors encountered in video. In this paper, we construct an appearance model using the 3D discrete cosine transform…
The Karhunen-Lo\`eve transform (KLT) is often used for data decorrelation and dimensionality reduction. Because its computation depends on the matrix of covariances of the input signal, the use of the KLT in real-time applications is…
The two-dimensional discrete cosine transform (DCT) can be found in the heart of many image compression algorithms. Specifically, the JPEG format uses a lossy form of compression based on that transform. Since the standardization of the…