Multiplier-less discrete sinusoidal and lapped transforms using sum-of-powers-of-two (SOPOT) coefficients

This paper proposes a new family of multiplier-less discrete cosine and sine transforms called the SOPOT DCTs and DSTs. The fast algorithm of Wang [10] is used to parameterize all the DCTs and DSTs in terms of certain (2×2) matrices, which are then converted to SOPOT representation using a method previously proposed by the authors [7]. The forward and inverse transforms can be implemented with the same set of SOPOT coefficients. A random search algorithm is also proposed to search for these SOPOT coefficients. Experimental results show that the (2×2) basic matrix can be implemented, on the average, in 6 to 12 additions. The proposed algorithms therefore require only O(N log2N) additions, which is very attractive for VLSI implementation. Using these SOPOT DCTs/DSTs, a family of SOPOT Lapped Transforms (LT) is also developed. They have similar coding gains but much lower complexity than their real-valued counterparts.published_or_final_versio

Lossless Image and Intra-Frame Compression With Integer-to-Integer DST

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 simple approach is to skip transform and quantization, and simply entropy code the prediction residual. However, this approach is inefficient at compression. A more efficient and popular approach is to skip transform and quantization but also process the residual block in some modes with differential pulse code modulation ( DPCM), along the horizontal or vertical direction, prior to entropy coding. This paper explores an alternative approach based on processing the residual block with integer-to-integer (i2i) transforms. I2i transforms can map integer pixels to integer transform coefficients without increasing the dynamic range and can be used for lossless compression. We focus on lossless intra coding and develop novel i2i approximations of the odd type-3 discrete sine transform (ODST-3). Experimental results with the high efficiency video coding (HEVC) reference software show that when the developed i2i approximations of the ODST-3 are used along the DPCM method of HEVC, an average 2.7% improvement of lossless intra frame compression efficiency is achieved over HEVC version 2, which uses only the DPCM method, without a significant increase in computational complexity

Study of machine learning techniques for image compression

In the age of the Internet and cloud-based applications, image compression has become increasingly important. Moreover, image processing has recently sparked the interest of technology companies as autonomous machines powered by artificial intelligence using images as input are rapidly growing. Reducing the amount of information needed to represent an image is key to reducing the amount of storage space, transmission bandwidth, and computation time required to process the image, which in turn saves resources, energy, and money. This study aims to investigate machine learning techniques (Fourier, wavelets, and PCA) for image compression. Several Fourier and wavelet methods are included, such as the wellknown Cooley-Tukey algorithm, the discrete cosine transform, and the Mallart algorithm, among others. To comprehend each step of image compression, an object-oriented Matlab code has been developed in-house. To do so, extensive research in machine learning techniques, not only in terms of theoretical understanding, but also in the mathematics that support it. The developed code is used to compare the performance of the different compression techniques studied. The findings of this study are consistent with the advances in image compression technologies in recent years, with the dominance of the JPEG compression method (Fourier) and later JPEG2000 (wavelets) reigning supreme