Related papers: Data-independent Low-complexity KLT Approximations…
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 Karhunen-Lo\`eve transform (KLT) stands as a well-established discrete transform, demonstrating optimal characteristics in data decorrelation and dimensionality reduction. Its ability to condense energy compression into a select few…
The discrete cosine transform (DCT) is a central tool for image and video coding because it can be related to the Karhunen-Lo\`eve transform (KLT), which is the optimal transform in terms of retained transform coefficients and data…
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…
Discrete trigonometric transforms (DTTs), such as the DCT-2 and the DST-7, are widely used in video codecs for their balance between coding performance and computational efficiency. In contrast, data-dependent transforms, such as the…
Transform coding to sparsify signal representations remains crucial in an image compression pipeline. While the Karhunen-Lo\`{e}ve transform (KLT) computed from an empirical covariance matrix $\bar{C}$ is theoretically optimal for a…
It is well-known for transform coding of multivariate Gaussian sources, that the Karhunen-Lo\`eve transform (KLT) minimizes the mean square error distortion. However, finding the optimal transform for general non-Gaussian sources has been…
Linear block transform coding remains a fundamental component of image and video compression. Although the Discrete Cosine Transform (DCT) is widely employed in all current compression standards, its sub-optimality has sparked ongoing…
Discrete transforms play an important role in many signal processing applications, and low-complexity alternatives for classical transforms became popular in recent years. Particularly, the discrete cosine transform (DCT) has proven to be…
In this work, we propose a new method of computing the Karhunen-Lo\`{e}ve Transform (KLT) applied to complex voltage data for the detection and noise level reduction in astronomical signals. We compared this method with the standard KLT…
Particle picking is currently a critical step in the cryo-EM single particle reconstruction pipeline. Despite extensive work on this problem, for many data sets it is still challenging, especially for low SNR micrographs. We present the KLT…
The discrete cosine transform (DCT) is a relevant tool in signal processing applications, mainly known for its good decorrelation properties. Current image and video coding standards -- such as JPEG and HEVC -- adopt the DCT as a…
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…
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…
As communication channels are increasing in number, reliability of faithful communication is reducing. Hacking and tempering of data are two major issues for which security should be provided by channel. This raises the importance of…
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…
The Karhunen-Loeve (KL) transform can compactly represent the information contained in large, complex datasets, cleanly eliminating noise from the data and identifying elements of the dataset with extreme or inconsistent characteristics. We…
In many state-of-the-art compression systems, signal transformation is an integral part of the encoding and decoding process, where transforms provide compact representations for the signals of interest. This paper introduces a class of…
Learned wavelet image and video coding approaches provide an explainable framework with a latent space corresponding to a wavelet decomposition. The wavelet image coder iWave++ achieves state-of-the-art performance and has been employed for…
Application of Karhunen-Loeve decomposition (KLD, or singular value decomposition) is presented for analysis of the spatio-temporal dynamics of wide-aperture vertical cavity surface emitting laser (VCSEL), considered as a thin-layer system.…