Transform-based Compression Techniques Research Articles

Improved differential pulse code modulation-block truncation coding method adopting two-level mean squared error near-optimal quantizers

The conventional hybrid method of block truncation coding (BTC) and differential pulse code modulation (DPCM), namely the DPCM-BTC method, offers better rate-distortion performance than the standard BTC. However, the quantization error in the hybrid method is easily increased for large block sizes due to the use of two representative levels in BTC. In this paper, we first derive a bivariate quadratic function representing the mean squared error (MSE) between the original block and the block reconstructed in the DPCM framework. The near-optimal representatives obtained by quantizing the minimum of the derived function can prevent the rapid increase of the quantization error. Experimental results show that the proposed method improves peak signal-to-noise ratio performance by up to 2dB at 1.5 bit/pixel (bpp) and by 1.2dB even at a low bit rate of 1.1 bpp as compared with the DPCM-BTC method without optimization. Even with the additional computation for the quantizer optimization, the computational complexity of the proposed method is still much lower than those of transform-based compression techniques.

ECG Signal Compression Based on Burrows-Wheeler Transformation and Inversion Ranks of Linear Prediction

Many transform-based compression techniques, such as Fourier, Walsh, Karhunen-Loeve (KL), wavelet, and discrete cosine transform (DCT), have been investigated and devised for electrocardiogram (ECG) signal compression. However, the recently introduced Burrows-Wheeler Transformation has not been completely investigated. In this paper, we investigate the lossless compression of ECG signals. We show that when compressing ECG signals, utilization of linear prediction, Burrows-Wheeler Transformation, and inversion ranks yield better compression gain in terms of weighted average bit per sample than recently proposed ECG-specific coders. Not only does our proposed technique yield better compression than ECG-specific compressors, it also has a major advantage: with a small modification, the proposed technique may be used as a universal coder.

Perceptual Coding of Audio Signals Using Adaptive Time-Frequency Transform

Wide band digital audio signals have a very high data-rate associated with them due to their complex nature and demand for high-quality reproduction. Although recent technological advancements have significantly reduced the cost of bandwidth and miniaturized storage facilities, the rapid increase in the volume of digital audio content constantly compels the need for better compression algorithms. Over the years various perceptually lossless compression techniques have been introduced, and transform-based compression techniques have made a significant impact in recent years. In this paper, we propose one such transform-based compression technique, where the joint time-frequency (TF) properties of the nonstationary nature of the audio signals were exploited in creating a compact energy representation of the signal in fewer coefficients. The decomposition coefficients were processed and perceptually filtered to retain only the relevant coefficients. Perceptual filtering (psychoacoustics) was applied in a novel way by analyzing and performing TF specific psychoacoustics experiments. An added advantage of the proposed technique is that, due to its signal adaptive nature, it does not need predetermined segmentation of audio signals for processing. Eight stereo audio signal samples of different varieties were used in the study. Subjective (mean opinion score--MOS) listening tests were performed and the subjective difference grades (SDG) were used to compare the performance of the proposed coder with MP3, AAC, and HE-AAC encoders. Compression ratios in the range of 8 to 40 were achieved by the proposed technique with subjective difference grades (SDG) ranging from ---0.53 to ---2.27.

Wavelet compression of medical imagery.

Wavelet compression is a transform-based compression technique recently shown to provide diagnostic-quality images at compression ratios as great as 30:1. Based on a recently developed field of applied mathematics, wavelet compression has found success in compression applications from digital fingerprints to seismic data. The underlying strength of the method is attributable in large part to the efficient representation of image data by the wavelet transform. This efficient or sparse representation forms the basis for high-quality image compression by providing subsequent steps of the compression scheme with data likely to result in long runs of zero. These long runs of zero in turn compress very efficiently, allowing wavelet compression to deliver substantially better performance than existing Fourier-based methods. Although the lack of standardization has historically been an impediment to widespread adoption of wavelet compression, this situation may begin to change as the operational benefits of the technology become better known.