Fast Transforms in Image Processing: Compression, Restoration, and Resampling

Yaroslavsky, Leonid P.

doi:10.1155/2014/276241

Cited by 13 publications

(7 citation statements)

References 62 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…Fourier transforms have also been extensively utilized in many image-processing applications. For example, it can be used for image transformation and compression [42,43]. Shi et al [44] used 2D Fourier transforms that also employed a hash function to take advantage of the sparsity in the frequency domain to estimate the largest k coefficients.…”

Section: Related Workmentioning

confidence: 99%

An Attentive Fourier-Augmented Image-Captioning Transformer

2021

View full text Add to dashboard Cite

Many vision–language models that output natural language, such as image-captioning models, usually use image features merely for grounding the captions and most of the good performance of the model can be attributed to the language model, which does all the heavy lifting, a phenomenon that has persisted even with the emergence of transformer-based architectures as the preferred base architecture of recent state-of-the-art vision–language models. In this paper, we make the images matter more by using fast Fourier transforms to further breakdown the input features and extract more of their intrinsic salient information, resulting in more detailed yet concise captions. This is achieved by performing a 1D Fourier transformation on the image features first in the hidden dimension and then in the sequence dimension. These extracted features alongside the region proposal image features result in a richer image representation that can then be queried to produce the associated captions, which showcase a deeper understanding of image–object–location relationships than similar models. Extensive experiments performed on the MSCOCO dataset demonstrate a CIDER-D, BLEU-1, and BLEU-4 score of 130, 80.5, and 39, respectively, on the MSCOCO benchmark dataset.

show abstract

Section: Related Workmentioning

confidence: 99%

An Attentive Fourier-Augmented Image-Captioning Transformer

2021

View full text Add to dashboard Cite

show abstract

“…In this study, we present a methodology to derive the columns of matrix B from DCT basis functions [38] as they can be used to enforce a predefined temporal structure for the subspace on which the data are projected. To model low frequency information in fMRI data, DCT provides a continuous periodic signal structure, which has the benefit of compactness [39]. DCT basis functions b k (n) are defined for 0 ≤ n < (N − 1) time points as:…”

Section: Selection Of Basesmentioning

confidence: 99%

A Projection CCA Method for Effective fMRI Data Analysis

Qadar

Seghouane

2019

IEEE Trans. Biomed. Eng.

View full text Add to dashboard Cite

Objective: Canonical correlation analysis (CCA) is a data driven method that has been successfully used in functional magnetic resonance imaging (fMRI) data analysis. Standard CCA extracts meaningful information from a pair of data sets by seeking pairs of linear combinations from two sets of variables with maximum pairwise correlation. So far, however, this method has been used without incorporating prior information available for fMRI data. In this paper, we address this issue by proposing a new CCA method named pCCA (for projection CCA). Methods: The proposed method is obtained by projection onto a set of basis vectors that better characterize temporal information in the fMRI data set. A methodology is presented to describe the basis selection process using discrete cosine transform (DCT) basis functions. Employing DCT guides the estimated canonical variates, yielding a more computationally efficient CCA procedure. Results: The performance gain of the proposed pCCA algorithm over standard and regularized CCA is illustrated on both simulated and real fMRI datasets from resting state, block paradigm task-related and event-related experiments. The results show that pCCA can successfully extract the task as well restingstate latent components with increased specificity. Conclusion: In addition to offering a new CCA approach, when applied on fMRI data, the proposed algorithm adapts to variations of brain activity patterns and reveals the functionally connected brain regions. Significance: The proposed method can be seen as a regularized CCA method where regularization is introduced via basis expansion, which has the advantage of enforcing smoothness on canonical components.

show abstract

“…It is a separable transform and due to its energy compaction properties it is commonly used for image and video compression in widely used JPEG and MPEG formats. DCT is one of the transformation methods with the best energy compaction properties on natural images [39]. Karhunen-Loève transform is considered to be optimal in signal decorrelation, however it transforms signal via unique basis functions that are not separable and need to be estimated for every image.…”

Section: Discrete Cosine Transformmentioning

confidence: 99%

Harmonic Networks: Integrating Spectral Information into CNNs

Uličný¹,

Krylov²,

Dahyot³

2018

Preprint

View full text Add to dashboard Cite

Convolutional neural networks (CNNs) learn filters in order to capture local correlation patterns in feature space. In contrast, in this paper we propose harmonic blocks that produce features by learning optimal combinations of spectral filters defined by the Discrete Cosine Transform. The harmonic blocks are used to replace conventional convolutional layers to construct partial or fully harmonic CNNs. We extensively validate our approach and show that the introduction of harmonic blocks into state-of-the-art CNN baseline architectures results in comparable or better performance in classification tasks on small NORB, CIFAR10 and CIFAR100 datasets.

show abstract

Fast Transforms in Image Processing: Compression, Restoration, and Resampling

Cited by 13 publications

References 62 publications

An Attentive Fourier-Augmented Image-Captioning Transformer

An Attentive Fourier-Augmented Image-Captioning Transformer

A Projection CCA Method for Effective fMRI Data Analysis

Harmonic Networks: Integrating Spectral Information into CNNs

Contact Info

Product

Resources

About