Lower Bounds on the Redundancy of Huffman Codes with Known and Unknown Probabilities

In this paper we provide a method to obtain tight lower bounds on the minimum redundancy achievable by a Huffman code when the probability distribution underlying an alphabet is only partially known. In particular, we address the case where the occurrence probabilities are unknown for some of the symbols in an alphabet. Bounds can be obtained for alphabets of a given size, for alphabets of up to a given size, and for alphabets of arbitrary size. The method operates on a Computer Algebra System, yielding closed-form numbers for all results. Finally, we show the potential of the proposed method to shed some light on the structure of the minimum redundancy achievable by the Huffman code

Multilevel split regression wavelet analysis for lossless compression of remote sensing data

Spectral redundancy is a key element to be exploited in compression of remote sensing data. Combined with an entropy encoder, it can achieve competitive lossless coding performance. One of the latest techniques to decorrelate the spectral signal is the regression wavelet analysis (RWA). RWA applies a wavelet transform in the spectral domain and estimates the detail coeffi- cients through the approximation coefficients using linear regres- sion. RWA was originally coupled with JPEG 2000. This letter introduces a novel coding approach, where RWA is coupled with the predictor of CCSDS-123.0-B-1 standard and a lightweight contextual arithmetic coder. In addition, we also propose a smart strategy to select the number of RWA decomposition levels that maximize the coding performance. Experimental results indicate that, on average, the obtained coding gains vary between 0.1 and 1.35 bits-per-pixel-per-component compared with the other state- of-the-art coding technique

DPCM-based edge prediction for lossless screen content coding in HEVC

Screen content sequences are ubiquitous type of video data in numerous multimedia applications like video conferencing, remote education, and cloud gaming. These sequences are characterized for depicting a mix of computer generated graphics, text, and camera-captured material. Such a mix poses several challenges, as the content usually depicts multiple strong discontinuities, which are hard to encode using current techniques. Differential pulse code modulation (DPCM)-based intra-prediction has shown to improve coding efficiency for these sequences. In this paper we propose sample-based edge and angular prediction (SEAP), a collection of DPCM-based intra-prediction modes to improve lossless coding of screen content. SEAP is aimed at accurately predicting regions depicting not only camera-captured material, but also those depicting strong edges. It incorporates modes that allow selecting the best predictor for each pixel individually based on the characteristics of the causal neighborhood of the target pixel. We incorporate SEAP into HEVC intra-prediction. Evaluation results on various screen content sequences show the advantages of SEAP over other DPCM-based approaches, with bit-rate reductions of up to 19.56% compared to standardized RDPCM. When used in conjunction with the coding tools of the screen content coding extensions, SEAP provides bit-rate reductions of up to 8.63% compared to RDPCM

Piecewise mapping in HEVC lossless intra-prediction coding

The lossless intra-prediction coding modality of the High Efficiency Video Coding (HEVC) standard provides high coding performance while following frame-by-frame basis access to the coded data. This is of interest in many professional applications such as medical imaging, automotive vision and digital preservation in libraries and archives. Various improvements to lossless intra-prediction coding have been proposed recently, most of them based on sample-wise prediction using Differential Pulse Code Modulation (DPCM). Other recent proposals aim at further reducing the energy of intra-predicted residual blocks. However, the energy reduction achieved is frequently minimal due to the difficulty of correctly predicting the sign and magnitude of residual values. In this paper, we pursue a novel approach to this energy-reduction problem using piecewise mapping (pwm) functions. Specifically, we analyze the range of values in residual blocks and apply accordingly a pwm function to map specific residual values to unique lower values. We encode appropriate parameters associated with the pwm functions at the encoder, so that the corresponding inverse pwm functions at the decoder can map values back to the same residual values. These residual values are then used to reconstruct the original signal. This mapping is, therefore, reversible and introduces no losses. We evaluate the pwm functions on 4×4 residual blocks computed after DPCM-based prediction for lossless coding of a variety of camera-captured and screen content sequences. Evaluation results show that the pwm functions can attain maximum bit-rate reductions of 5.54% and 28.33% for screen content material compared to DPCM-based and block-wise intra-prediction, respectively. Compared to IntraBlock Copy, piecewise mapping can attain maximum bit-rate reductions of 11.48% for camera-captured material

Diffusion-based inpainting for coding remote-sensing data

Inpainting techniques based on partial differential equations (PDEs) such as diffusion processes are gaining growing importance as a novel family of image compression methods. Nevertheless, the application of inpainting in the field of hyperspectral imagery has been mainly focused on filling in missing information or dead pixels due to sensor failures. In this paper we propose a novel PDE-based inpainting algorithm to compress hyperspectral images. The method inpaints separately the known data in the spatial and in the spectral dimensions. Then it applies a prediction model to the final inpainting solution to obtain a representation much closer to the original image. Experimental results over a set of hyperspectral images indicate that the proposed algorithm can perform better than a recent proposed extension to prediction-based standard CCSDS-123.0 at low bitrate, better than JPEG 2000 Part 2 with the DWT 9/7 as a spectral transform at all bit-rates, and competitive to JPEG 2000 with principal component analysis (PCA), the optimal spectral decorrelation transform for Gaussian sources

Competitive Segmentation Performance on Near-lossless and Lossy Compressed Remote Sensing Images

Image segmentation lies at the heart of multiple image processing chains, and achieving accurate segmentation is of utmost importance as it impacts later processing. Image segmentation has recently gained interest in the field of remote sensing, mostly due to the widespread availability of remote sensing data. This increased availability poses the problem of transmitting and storing large volumes of data. Compression is a common strategy to alleviate this problem. However, lossy or near-lossless compression prevents a perfect reconstruction of the recovered data. This letter investigates the image segmentation performance in data reconstructed after a near-lossless or a lossy compression. Two image segmentation algorithms and two compression standards are evaluated on data from sev- eral instruments. Experimental results reveal that segmentation performance over previously near-lossless and lossy compressed images is not markedly reduced at low and moderate compression ratios. In some scenarios, accurate segmentation performance can be achieved even for high compression ratios

Hyperspectral IASI L1C data compression

The Infrared Atmospheric Sounding Interferometer (IASI), implemented on the MetOp satellite series, represents a significant step forward in atmospheric forecast and weather understanding. The instrument provides infrared soundings of unprecedented accuracy and spectral resolution to derive humidity and atmospheric temperature profiles, as well as some of the chemical components playing a key role in climate monitoring. IASI collects rich spectral information, which results in large amounts of data (about 16 Gigabytes per day). Efficient compression techniques are requested for both transmission and storage of such huge data. This study reviews the performance of several state of the art coding standards and techniques for IASI L1C data compression. Discussion embraces lossless, near-lossless and lossy compression. Several spectral transforms, essential to achieve improved coding performance due to the high spectral redundancy inherent to IASI products, are also discussed. Illustrative results are reported for a set of 96 IASI L1C orbits acquired over a full year (4 orbits per month for each IASI-A and IASI-B from July 2013 to June 2014) . Further, this survey provides organized data and facts to assist future research and the atmospheric scientific community

JPEG2000 ROI coding with fine-grain accuracy through rate-distortion optimization techniques

Region of interest (ROI) coding is a feature of prominent image coding systems that enables the specification of different coding priorities to certain regions of the image. JPEG2000 provides ROI coding through two mechanisms: either modifying wavelet coefficients or using rate-distortion optimization techniques. Although ROI coding methods based on the modification of wavelet coefficients provide an excellent accuracy to delimit the ROI area (referred to as fine-grain accuracy), they significantly penalize the coding efficiency. On the other hand, methods based on rate-distortion optimization improve the coding efficiency but, so far, have not been able to achieve the intended fine-grain accuracy. This letter introduces two ROI coding methods that, using rate-distortion optimization techniques, achieve a fine-grain accuracy, comparable to the one obtained when wavelet coefficients are modified, and are competitive in terms of coding efficiency

JPEG2000 ROI coding through component priority for digital mammography

Region Of Interest (ROI) coding is a prominent feature of some image coding systems aimed to prioritize specific areas of the image through the construction of a codestream that, decoded at increasing bit-rates, recovers the ROI first and with higher quality than the rest of the image. JPEG2000 is a wavelet-based coding system that is supported in the Digital Imaging and Communications in Medicine (DICOM) standard. Among other features, JPEG2000 provides lossy-to-lossless compression and ROI coding, which are especially relevant to the medical community. But, due to JPEG2000 supported ROI coding methods that guarantee lossless coding are not designed to achieve a high degree of accuracy to prioritize ROIs, they have not been incorporated in the medical community. - This paper introduces a ROI coding method that is able to prioritize multiple ROIs at different priorities, guaranteeing lossy-to-lossless coding. The proposed ROI Coding Through Component Prioritization (ROITCOP) method uses techniques of rate-distortion optimization combined with a simple yet effective strategy of ROI allocation that employs the multi-component support of JPEG2000 codestream. The main insight in ROITCOP is the allocation of each ROI to an component. Experimental results indicate that this ROI allocation strategy does not penalize coding performance whilst achieving an unprecedented degree of accuracy to delimit ROIs. - The proposed ROITCOP method maintains JPEG2000 compliance, thus easing its use in medical centers to share images. This paper analyzes in detail the use of ROITCOP to mammographies, where the ROIs are identified by computer-aided diagnosis. Extensive experimental tests using various ROI coding methods suggest that ROITCOP achieves enhanced coding performanc