Related papers: Performance Analysis of DCT, Hadamard, and PCA in …
Modern image compression methods are typically optimized for the rate--distortion--perception trade-off, whereas their robustness to bit-level corruption is rarely examined. We show that diffusion-based compressors built on the Reverse…
Discrete Cosine Transform (DCT) is very important in image compression. Classical 1-D DCT and 2-D DCT has time complexity O(NlogN) and O(N²logN) respectively. This paper presents a quantum DCT iteration, and constructs a quantum 1-D…
We consider the problem of decomposing a large covariance matrix into the sum of a low-rank matrix and a diagonally dominant matrix, and we call this problem the "Diagonally-Dominant Principal Component Analysis (DD-PCA)". DD-PCA is an…
Principal component analysis (PCA) is widely used for feature extraction and dimensionality reduction, with documented merits in diverse tasks involving high-dimensional data. Standard PCA copes with one dataset at a time, but it is…
Continuing our previous research on color image compression, we move towards spectral image compression. This enormous amount of data needs more space to store and more time to transmit. To manage this sheer amount of data, researchers have…
Self-attention is central to the success of Transformer architectures; however, learning the query, key, and value projections from random initialization remains challenging and computationally expensive. In this paper, we propose two…
Principal component analysis (PCA) is a widespread technique for data analysis that relies on the covariance-correlation matrix of the analyzed data. However to properly work with high-dimensional data, PCA poses severe mathematical…
Block frames called directional analytic discrete cosine frames (DADCFs) are proposed for sparse image representation. In contrast to conventional overlapped frames, the proposed DADCFs require a reduced amount of 1) computational…
Dimensionality reduction represents a critical preprocessing step in order to increase the efficiency and the performance of many hyperspectral imaging algorithms. However, dimensionality reduction algorithms, such as the Principal…
Data compression can be achieved by reducing the dimensionality of high-dimensional but approximately low-rank datasets, which may in fact be described by the variation of a much smaller number of parameters. It often serves as a…
Recent video codecs with multiple separable transforms can achieve significant coding gains using asymmetric trigonometric transforms (DCTs and DSTs), because they can exploit diverse statistics of residual block signals. However, they add…
The block Discrete Cosine Transform (DCT) is commonly used in image and video compression due to its good energy compaction property. The Saab transform was recently proposed as an effective signal transform for image understanding. In this…
A general method for recovering missing DCT coefficients in DCT-transformed images is presented in this work. We model the DCT coefficients recovery problem as an optimization problem and recover all missing DCT coefficients via linear…
We present an unsupervised learning analysis of correlation hierarchies in the quarter-filled simple and extended Hubbard models by applying principal component analysis (PCA) to exact-diagonalization (ED) data on 3x4 and 4x4 cylindrical…
The usage of linear transformations has great relevance for data decorrelation applications, like image and video compression. In that sense, the discrete Tchebichef transform (DTT) possesses useful coding and decorrelation properties. The…
A novel coding strategy for block-based compressive sens-ing named spatially directional predictive coding (SDPC) is proposed, which efficiently utilizes the intrinsic spatial cor-relation of natural images. At the encoder, for each block…
Image Compression has become an absolute necessity in today's day and age. With the advent of the Internet era, compressing files to share among other users is quintessential. Several efforts have been made to reduce file sizes while still…
Contemporary lossy image and video coding standards rely on transform coding, the process through which pixels are mapped to an alternative representation to facilitate efficient data compression. Despite impressive performance of…
Despite the unprecedented compression efficiency achieved by deep learned image compression (LIC), existing methods usually approximate the desired bitrate by adjusting a single quality factor for a given input image, which may compromise…
This paper studies computationally efficient methods and their minimax optimality for high-dimensional clustering and signal recovery under block signal structures. We propose two sets of methods, cross-block feature aggregation PCA…