Integer Cosine Research Articles

ECG data compression using the formation of QRS-complex segment bank and integer DCT-based plateau region processing

Electrocardiogram (ECG) data is essential for evaluating cardiac health conditions. Long-term ECG signal monitoring needs a considerable amount of memory for storage, impacting data bandwidth allocation. The ECG data compression is challenging in preserving significant features, using low computational resources, and achieving a higher compression ratio at lower reconstruction error. This paper proposes an innovative QRS-complex and plateau (Non-QRS) region segregation for QRS-complex subsegment bank formation and integer cosine transform-based ECG data compression. An adaptive QRS-complex subsegment template bank is formed by: (i) QRS and Non-QRS region segmentation; (ii) QRS region identification; (iii) QRS region alignment; (iv) Dc equalization and sub-template formation of the QRS region. A discrete integer cosine transform, quantization, and grouping with a significance map are used on the non-QRS segment of the ECG. Both the QRS and non-QRS regions are coded by lossless arithmetic encoding. Experiments are enumerated on the MIT BIH arrhythmia database, which validates the potential of the proposed approach by achieving an average value equal to 31.51, 0.84, and 28.57 for compression ratio, percentage-root-mean-square-difference, and quality-score, respectively. The average distortion measure for the proposed ECG compressor is less than 2%, which is within the clinically acceptable limit. The proposed method is also compared to existing state-of-the-art ECG compression techniques. It performs better in terms of compression ratio and preservation of ECG features. Additionally, this method typically requires less computational resources and is easy to implement, which is an advantage over other ECG compression methods.

Integer Modified Sine-Cosine Transforms Type VII. A construction Method and Separable Directional Adaptive Transforms for Intra Prediction with 8 × 8 Chroma Blocks in Image/Video Coding

A matrix method for constructing a modified order-8 integer sine-cosine transform type VII is proposed. Based on the method, two order-8 integer modified sine-cosine transforms type VII are constructed and algorithms for fast computing of these transforms are developed, which require only integer operations. These algorithms are of low multiplicative complexity, which is 7 and 10.5 times less, and they require 23.3 and 44.2% less additional operations than the well-known algorithm of the discrete sine transform type VII. These transforms have higher coding gain performance for quality and compression ratio compared to the well-known sine transforms. Algorithms for fast computing of 2D separate directional integer cosine and modified sine-cosine type VII adaptive transforms for intra prediction with 8 × 8 chroma blocks are developed. These algorithms have low multiplicative complexity, which is 6.6 and 16.5 times less than that of the well-known algorithms.

Modified Integer Sine Transforms. Construction Method and Separable Directional Adaptive Transforms for Intra Prediction in Image/Video Coding

The author proposes a matrix method for constructing a modified order 8 integer sine type VII transform. Based on the method, two modified order 8 integer sine type VII transforms are constructed and algorithms for fast implementation of 8-point modified integer sine type VII transforms are developed, which require only integer operations. These algorithms have low computational complexity that is 4.5 and 10.9 times less than that of the known algorithm. These transforms have higher coding performance in terms of quality and compression ratio than the known sine transforms do. Algorithms for fast implementation of 2D 8-point separable directional integer cosine and modified adaptive sine transforms for intra prediction with low computational complexity are developed, and their computational complexity is 4.62 and 8.24 times lower than that of the known algorithms.

Algorithms for Fast Implementation of 4-Point Integer Sine Type Vii Transformswithout Multiplication and Separable Directional Adaptive Transforms for Intra Prediction in Image/Video Coding

The separable directional adaptive integer cosine and sine type VII transforms with 4×4 blocks are proposed for intra prediction in image and video coding. Algorithms for fast implementation of 2D 4-point separable directional integer cosine and sine transforms are developed. These algorithms require 7 times fewer multiplication operations and provide higher compression ratio than the well-known algorithms. Two order-4 integer sine type VII transforms are proposed, and algorithms are developed for fast implementation of 4-point integer sine type VII transforms, which require integer operations only. As compared to the known algorithm, these algorithms can significantly reduce the number of multiplication operations or avoid them at all. These integer sine transforms are very close to discrete sine type VII transform and have a higher compression ratio than the well-known sine transform accepted in standard H.265 does.

Low-Complexity Order-64 Integer Cosine Transform Design and its Application in HEVC

In high efficiency video coding (HEVC) standard, residuals are partitioned into variable-size transform units, and integer cosine transforms (ICTs) of order-4, 8, 16, and 32 are adopted to optimize the coding performance. Order-64 ICT is not used due to its high complexity and limited gain in general coding applications. This paper proposes a set of low-complexity ICTs (LCICTs), from order-8 to order-64, which have fully factorizable structures. LCICTs achieve similar coding performance as the state-of-art methods on HEVC Test Model 13 while requiring lower complexity, e.g., 71% fewer multiplications than the partially factorizable ICTs in the order-64 case. Moreover, we find that order-64 ICTs achieve around 1% average bitrate reduction at high quantization parameters.

Simple High-Order Integer Cosine Transform for High-Resolution Video Coding

A matrix method is proposed for constructing a simple order-32 integer cosine transform. Based on the method, a one-norm simple order-32 integer transform is constructed and its fast algorithms of low computational complexity are developed that require only integer operations and whose computational complexity is 4.9 times less than that of well-known algorithms and is 21.6 times less than that of the standard H.265. This transform is close to the discrete cosine transform and has good coding performance.

High-Order Integer Cosine Transform: Construction Method and Fast Algorithms for High-Resolution Image and Video Coding

Matrix method of constructing one-norm high-order integer cosine transform is proposed. The one-norm order-32 integer transform is constructed and its fast algorithms of low computing complexity are developed. Its computing complexity is 3.24 times less than that in the well-known algorithms and 15.6 times less than in standard H.265 and requires integer operations only. This transform is not only very close to the discrete cosine transform but also has excellent coding performance.

A Method to Construct a Large-Size Simple Integer Cosine Transform for High-Resolution Image and Video Coding

A matrix method is considered to construct simple order-32 integer cosine step transform. A one-norm simple order-32 integer transform is proposed and its fast algorithms are developed whose computational complexity is 4.3 times smaller than that of well-known algorithms and 19 times smaller than that of the H.265 standard.

Integer Cosine Transforms for High-Efficiency Image and Video Coding

Matrix methods for constructing one-norm order-8 and -16 integer cosine transforms are considered. One-norm order-8 and -16 integer transforms are proposed and fast algorithms are developed that implement these transforms with a low computational complexity that is less by a factor of 3---5 than the complexity of well-known algorithms and is less by a factor of 10 than that in the H.265 standard.

Designing Garbage-Free Reversible Implementations of the Integer Cosine Transform

Discrete linear transformations are important tools in information processing. Many such transforms are injective and therefore prime candidates for a physically reversible implementation into hardware. We present here reversible integer cosine transformations on n input integers. The resulting reversible circuit is able to perform both the forward transform and the inverse transform. The detailed structure of such a reversible design strongly depends on the odd prime factors of the determinant of the transform: whether those are of the form 2 k ± 1 or of the form 2 k ± 2 l ± 1 or neither of these forms.

Integer Cosine Transforms: Methods to Construct new Order 8, 16 Fast Transforms and Their Application

Matrix methods to construct simple fast integer order 16 type I, II cosine transforms of low complexity are considered. A new approach and a generalized method are proposed to construct integer order 8 cosine transforms and their fast algorithms without multiplication. A new integer step transform with fast algorithm is introduced. Two transforms are proposed, whose speed is 1.7 to 2.9 times greater and which provide a higher quality of video coding than standard H.265 does.

Image Steganography Using HBC and RDH Technique

There are algorithms in existence for hiding data within an image. The proposed scheme treats the image as a whole. Here Integer Cosine Transform (ICT) and Integer Wavelet Transform (IWT) is combined for converting signal to frequency. Hide Behind Corner (HBC) algorithm is used to place a key at corners of the image. All the corner keys are encrypted by generating Pseudo Random Numbers. The Secret keys are used for corner parts. Then the hidden image is transmitted. The receiver should be aware of the keys that are used at the corners while encrypting the image. Reverse Data Hiding (RDH) is used to get the original image and it proceeds once when all the corners are unlocked with proper secret keys. With these methods the performance of the stegnographic technique is improved in terms of PSNR value.

LLM Integer Cosine Transform and its Fast Algorithm

Existing video coding standards use only 4 × 4 and 8 × 8 transforms for energy compaction. Recent research has found that the use of larger transforms, such as 16 × 16, together with the existing transforms can improve coding performance especially in high-definition (HD) videos which are becoming more and more common. This raises the interest of seeking high-performance higher-order transforms with low computation requirement. In this paper, a method to derive orthogonal integer cosine transforms is proposed. The order-2N transform is defined using the order-N transform. A family of these integer transforms, Loeffler, Ligtenberg, and Moschytz (LLM) integer cosine transform, is derived using this method. Its fast algorithm structure is the same as LLM fast discrete cosine transform (DCT) algorithm but requires integer operations only. This new family of transforms is not only very close to the DCT but also has excellent coding performance.

Comments on "2-D Order-16 Integer Transforms for HD Video Coding

In a recent paper, Dong proposed a set of order-16 nonorthogonal integer cosine transforms (NICTs). They proved that the reconstruction error caused by the nonorthogonality is negligible as compared to the error caused by the quantization. However, we would like to point out three problems found in derivations and also give two comments. Nevertheless, the problems are defects only, hence do not affect the overall justifications to the proposed NICT. This letter is to enhance and clarify the proof of Dong 's work.

2-D Order-16 Integer Transforms for HD Video Coding

In this paper, the spatial properties of high-definition (HD) videos are investigated based on a large set of HD video sequences. Compared with lower resolution videos, the prediction errors of HD videos have higher correlation. Hence, we propose using 2-D order-16 transforms for HD video coding, which are expected to be more efficient to exploit this spatial property, and specifically propose two types of 2-D order-16 integer transforms, nonorthogonal integer cosine transform (ICT) and modified ICT. The former resembles the discrete cosine transform (DCT) and is approximately orthogonal, of which the transform error introduced by the nonorthogonality is proven to be negligible. The latter modifies the structure of the DCT matrix and is inherently orthogonal, no matter what the values of the matrix elements are. Both types allow selecting matrix elements more freely by releasing the orthogonality constraint and can provide comparable performance with that of the DCT. Each type is integrated into the audio and video coding standard (AVS) Enhanced Profile (EP) and the H.264 high profile (HP), respectively, and used adaptively as an alternative to the 2-D order-8 transform according to local activities. At the same time, many efforts have been devoted to further reducing the complexity of the 2-D order-16 transforms and specially for the modified ICT, a fast algorithm is developed and extended to a universal approach. Experimental results show that 2-D order-16 transforms provide significant performance improvement for both AVS enhanced profile and H.264 high profile, which means they can be efficient coding tools especially for HD video coding.

Rate-distortion optimized adaptive transform coding

We propose a rate-distortion optimized transform coding method that adaptively employs either integer cosine transform that is an integer-approximated version of discrete cosine transform (DCT) or integer sine transform (IST) in a rate-distortion sense. The DCT that has been adopted in most video-coding standards is known as a suboptimal substitute for the Karhunen-Loève transform. However, according to the correlation of a signal, an alternative transform can achieve higher coding efficiency. We introduce a discrete sine transform (DST) that achieves the high-energy compactness in a correlation coefficient range of −0.5 to 0.5 and is applied to the current design of H.264/AVC (advanced video coding). Moreover, to avoid the encoder and decoder mismatch and make the implementation simple, an IST that is an integer-approximated version of the DST is developed. The experimental results show that the proposed method achieves a Bjøntegaard Delta-RATE gain up to 5.49% compared to Joint model 11.0.

Improved Conversion From DCT Blocks to Integer Cosine Transform Blocks in H.264/AVC

As adoption of the newly standardized H.264 becomes increasingly more widespread, efforts must be made to transcode video from earlier standards, such as MPEG-2, to the H.264 format. One aspect of transcoding is the conversion from the discrete cosine transform (DCT) used in MPEG-2 to the integer-based DCT of H.264, the integer cosine transform. By investigating the structure of the transform kernels, two efficient schemes are introduced to convert an 8 times 8 DCT block into its corresponding four 4times4 integer cosine transform block8 times 8 DCT block into its corresponding four 4times4 integer cosine transform blockss. An analysis of computational complexity shows a reduction of up to 42% in multiplications over existing conversion schemes, while simulations of the conversion system with pre- and post-quantization show that the proposed methods yield high fidelity in terms of peak signal-to-noise ratio. Further approximation of matrix coefficients in the second proposed method yields additional conversion schemes which require no multiplications. These also provide comparable quality with fewer operations than existing schemes. Thus, the proposed transform conversion methods can potentially contribute to efficient transcoding systems.

The Technique of Prescaled Integer Transform: Concept, Design and Applications

Integer cosine transform (ICT) is adopted by H.264/AVC for its bit-exact implementation and significant complexity reduction compared to the discrete cosine transform (DCT) with an impact in peak signal-to-noise ratio (PSNR) of less than 0.02 dB. In this paper, a new technique, named prescaled integer transform (PIT), is proposed. With PIT, while all the merits of ICT are kept, the implementation complexity of decoder is further reduced compared to corresponding conventional ICT, which is especially important and beneficial for implementation on low-end processors. Since not all PIT kernels are good in respect of coding efficiency, design rules that lead to good PIT kernels are considered in this paper. Different types of PIT and their target applications are examined. Both fixed block-size transform and adaptive block-size transform (ABT) schemes of PIT are also studied. Experimental results show that no penalty in performance is observed with PIT when the PIT kernels employed are derived from the design rules. Up to 0.2 dB of improvement in PSNR for all intra frame coding compared to H.264/AVC can be achieved and the subjective quality is also slightly improved when PIT scheme is carefully designed. Using the same concept, a variation of PIT, post-scaled integer transform, can also be potentially designed to simplify the encoder in some special applications. PIT has been adopted in audio video coding standard (AVS), Chinese National Coding standard.

Transform-Domain Fast Sum of the Squared Difference Computation for H.264/AVC Rate-Distortion Optimization

In H.264/AVC, the rate-distortion optimization for mode decision plays a significant role to achieve its outstanding performance in terms of both compression efficiency and video quality. However, this mode decision process also introduces extremely high complexity in the encoding process especially the computation of the sum of squared differences (SSD) between the original and reconstructed image blocks. In this paper, fast SSD (FSSD) algorithms are proposed to reduce the complexity of the rate-distortion cost function implementation. The proposed FSSD algorithm is based on the theoretical equivalent of the SSDs in spatial and transform domains and determines the distortion in integer cosine transform domain using an iterative table-lookup quantization process. This approach could avoid the inverse quantization/transform and pixel reconstructions processes with nearly no rate-distortion performance degradation. In addition, the FSSD can also be used with efficient bit rate estimation algorithms to further reduce the cost function complexity. Experimental results show that the new FSSD can save up to 15% of total encoding time with less than 0.1% coding performance degradation and it can save up to 30% with ignorable performance degradation when combining with conventional bit rate estimation algorithm

Parallel-pipeline 8/spl times/8 forward 2-D ICT processor chip for image coding

The Integer Cosine Transform (ICT) presents a performance close to Discrete Cosine Transform (DCT) with a reduced computational complexity. The ICT kernel is integer-based, so computation only requires adding and shifting operations. This work presents a parallel-pipelined architecture of an 8/spl times/8 forward two-dimensional (2-D) ICT(10,9,6,2,3,1) processor for image encoding. A fully pipelined row-column decomposition method based on two one-dimensional (1-D) ICTs and a transpose buffer based on D-type flip-flops is used. The main characteristics of 1-D ICT architecture are high throughput, parallel processing, reduced internal storage, and 100% efficiency in computational elements. The arithmetic units are distributed and are made up of adders/subtractors operating at half the frequency of the input data rate. In this transform, the truncation and rounding errors are only introduced at the final normalization stage. The normalization coefficient word length of 18-bit (13-bit effective) has been established using the requirements of IEEE standard 1180-1990 as a reference. The processor has been implemented using standard cell design methodology in 0.35-/spl mu/m CMOS technology, measures 9.3 mm/sup 2/, and contains 12.4 k gates. The maximum frequency is 300 MHz with a latency of 214 cycles (260 cycles with normalization).