Image Compression Based on a Partially Rotated Discrete Cosine Transform With a Principal Orientation

Abstract

Image transforms are necessary for image and video compression. Analytic transforms are powerful in compacting natural signals for wider exploitation. Various methods have been introduced to represent such data as a small number of bases, and several of these methods use machine learning, usually based on sparse coding, to outperform analytic transforms. They show sufficient data compaction abilities. However, these methods focus only on data compaction and reconstruction performance, without considering computational issues during implementation. We introduce a new framework for a more efficient transform based on a two-dimensional discrete cosine transform (DCT) and its characteristics. We aimed to improve the data compaction ability of transforms to levels better or similar to that of the DCT and other data-driven transforms, with fast and efficient implementation. We focused on the properties of the DCT, including horizontal and vertical directional information, and approximated its direction using the transform. Our framework was designed by rotating some of the DCT bases to fit this direction. As expected, our framework achieves a transform design with minimized computation for efficient implementation. It does not require an iterative algorithm or brute-force methods to find the best transform matrix or other parameters, thereby making it much faster than other methods. Our framework is 10 times faster than the steerable DCT (SDCT) and twice as fast as the eight-level SDCT with minimum performance reduction. Experimental validation with various images indicates that the proposed method sufficiently approaches the performance of the other transforms despite faster implementation.INDEX TERMS Directional discrete cosine transform, discrete cosine transform, image transformation, image compression, sparse coding transform.

Extracting the most important Discrete Cosine Transform (DCT) Coefficients for Image Compression using Deep Learning

“…G. Lee and Y. Choe [17] presented a new model for more effective and specific transform which is built on a 2D DCT. Authors tried to increase the data compaction capability of transforms to balance what another discrete cosine transforms with effective and speedy implementation.…”

“…They examine the discrete cosine transform properties and characteristics which include the vertical and horizontal direction information in order to approximate the DCT direction. The model proposed by G.Lee and Y.Choe [17] was constructed by changing the direction of few discrete cosine transforms bases to fix the direction.…”

Watermark Embedding Scheme with Variance of Chromatic Components

“…The watermark is embedded as binary data using DFT, which bears the Joint Photographic Experts Group (JPEG) compression [8]. Many algorithms have been developed by using discrete wavelet transform (DWT) [9] and discrete cosine transform (DCT) [10]. Due to its less computational cost and simplicity of the transform, Walsh-Hadamard transform is used in watermarking [11].…”