Wavelet Encoding Research Articles

AWED: Asymmetric Wavelet Encoder–Decoder Framework for Simultaneous Gas Distribution Mapping and Gas Source Localization

AWED: Asymmetric Wavelet Encoder–Decoder Framework for Simultaneous Gas Distribution Mapping and Gas Source Localization

Wavelet Encoding Network for Inertial Signal Enhancement via Feature Supervision

Wavelet Encoding Network for Inertial Signal Enhancement via Feature Supervision

A General Model for the Design of Efficient Sign-Coding Tools for Wavelet-Based Encoders

Traditionally, it has been assumed that the compression of the sign of wavelet coefficients is not worth the effort because they form a zero-mean process. However, several image encoders such as JPEG 2000 include sign-coding capabilities. In this paper, we analyze the convenience of including sign-coding techniques into wavelet-based image encoders and propose a methodology that allows the design of sign-prediction tools for whatever kind of wavelet-based encoder. The proposed methodology is based on the use of metaheuristic algorithms to find the best sign prediction with the most appropriate context distribution that maximizes the resulting sign-compression rate of a particular wavelet encoder. Following our proposal, we have designed and implemented a sign-coding module for the LTW wavelet encoder, to evaluate the benefits of the sign-coding tool provided by our proposed methodology. The experimental results show that sign compression can save up to 18.91% of bit-rate when enabling sign-coding capabilities. Also, we have observed two general behaviors when coding the sign of wavelet coefficients: (a) the best results are provided from moderate to high compression rates; and (b) the sign redundancy may be better exploited when working with high-textured images.

A SAR image compression algorithm based on Mallat tower-type wavelet decomposition

Image compression algorithms based on wavelet transform can achieve ideal effect on optical image, while cannot do well in SAR image compression. The paper introduces wavelet encoding in optical image compression into SAR image processing and designs an improved SAR compression algorithm based on Mallat tower-type wavelet decomposition according to characteristics of SAR image. The algorithm firstly conducts noise reduction in wavelet domain on image and then performs differential pulse lossless coding on low-frequency sub-band after removing speckle noise. The high-frequency is scanned for important coefficients using spatial direction tree similar to SPIHT algorithm and processed with universal trellis coded quantization. The Euclidean distance among important coefficient can be expanded to improving quantification gain. It can be seen from simulation results analysis on algorithm compression performance that the proposed improved algorithm is more suitable for SAR image compression compared with SPIHT algorithm and JPEG2000 standard.

Wavelet Encoding Spectroscopic Imaging in Small FOV Regime: Comparison to Chemical Shift Imaging at 3 Tesla

We have recently proposed a new magnetic resonance spectroscopic imaging (MRSI) technique called wavelet encoding spectroscopic imaging (WE-SI), and described its implementation on a clinical 1.5 T scanner. This technique is proposed as an alternative to chemical shift imaging (CSI), to decrease acquisition time, and voxel contamination. The proposed method is implemented here on a clinical 3 T scanner. Phantom and in vivo studies are chosen to validate the technique at higher field, as well as to fully explore the usefulness of this technique, and find its niche of application in the chain of existing MRSI techniques. In wavelet encoding, a set of dilated and translated wavelets are used to span a localized space by dividing it into a set of sub-spaces with pre-determined sizes and locations. Due to their simple shapes, Haar wavelets are chosen. They are represented in the modified PRESS sequence by the selective excitation and refocusing radio-frequency (RF) pulses. The wavelets dilation and translation are achieved by changing the strength of the localization gradients and frequency shift of the RF pulses, respectively. Data acquisition time is reduced using the minimum recovery time when successive MR signals from adjacent sub-spaces are collected. The results obtained at 3 T confirm those obtained at 1.5 T, and demonstrate that despite the low signal-to-noise ratio, the proposed WE-SI provides accurate results and reduces both voxel contamination and acquisition time as compared to CSI. This applies especially in the small field-of-view regime where only a small number of voxels is required.

An Improved WSQ Algorithm Based on Lifting Wavelet and Adaptive Run-length Encoding

FBI’s WSQ (Wavelet Scalar Quantization) algorithm is well and widely used as the specific standard in the field of fingerprint image compressions currently. In this paper, based on the WSQ, first we decompose the captured fingerprint image by applying the lifting wavelet transform, and then use an efficient second adaptive run-length encoding in the high-frequency part of the Huffman stream to improve the encoding efficiency. Our experiment results show that the performance of proposed method is better than WSQ at the same bit rate.

3-D medical image compression using 3-D wavelet coders

This paper presents compression of 3-D medical images using 3-D wavelet encoders. Four wavelet transforms, namely, Daubechies 4, Daubechies 6, Cohen-Daubechies-Feauveau 9/7 and Cohen-Daubechies-Feauveau 5/3 are used in the first stage with encoders such as 3-D SPIHT, 3-D SPECK and 3-D BISK used in the second stage for the compression and the optimal wavelet-encoder combination is identified. Two versions of wavelet transform, symmetric and decoupled wavelet transform are considered. Experiments are performed using medical test images such as magnetic resonance images (MRI) and X-ray angiograms (XA). The performances of the proposed scheme are evaluated in terms of peak signal-to-noise ratio and bit rate. Further mean structural similarity (MSSIM) index is introduced to evaluate the structural similarity between the original and the reconstructed images. It is found from the test results that the 3-D Cohen-Daubechies-Feauveau 9/7 symmetric wavelet along with the 3-D SPIHT encoder yields the best compression result.

Still Image Compression using Embedded Zerotree Wavelet Encoding

This paper proposes a Embedded Zerotree Wavelet Encoding (EZW) for image compression. Shapiros Embedded Zerotree Wavelet encoder or EZW encoder for short (Sha93). An EZW encoder is an encoder specially designed to use with wavelet transforms, which explains why it has the word wavelet in its name. The EZW encoder was originally designed to operate on images (2D-signals) but it can also be used on other dimensional signals. The EZW encoder is based on progressive encoding to compress an image into a bit stream with increasing accuracy. This means that when more bits are added to the stream, the decoded image will contain more detail, a property similar to JPEG encoded images. It is also similar to the representation of a number like P. Every digit we add increases the accuracy of the number, but we can stop at any accuracy we like. Progressive encoding is also known as embedded encoding. Coding an image using the EZW scheme, together with some optimizations results in a remarkably effective image compressor with the property that the compressed data stream can have any bit rate desired. Any bit rate is only possible if there is information loss somewhere so that the compressor is lossy. However, lossless compression is also possible with an EZW encoder, but of course with less spectacular results.

Small field of view imaging using wavelet encoding with 2 dimensional RF pulses and gradient echo: phantom results

The objective of this work is to propose an imaging sequence based upon the wavelet encoding approach to provide MRI images free from folding artifacts, in the small field of view (FOV) regime, such as dynamic magnetic resonance imaging (MRI) studies. The method consists of using a 2D spatially selective RF excitation pulse inserted into a gradient- echo pulse sequence to excite spins within a determined plane where wavelet encoding is achieved in one direction and slice selection is performed in the second direction. Wavelet encoding allows for spatially localized excitation and consequently restricts the spins excited within a reduced FOV. It consists of varying, according to a predetermined scheme, the width and position of the profile of the so-called fast RF pulse of the 2D RF excitation pulse, to obey wavelet encoding translation and dilation conditions. This sequence is implemented on a 3 Tesla whole body Siemens scanner. Compared to Fourier encoding, the proposed technique tested on phantoms with different shapes and structures, is able to provide gradient-echo reduced FOV images free from aliased signals. Wavelet encoding is suitable for small FOV imaging in dynamic MRI studies.

A novel method of lossless compression for 2-D astronomical spectra images

A novel method of lossless compression for astronomical spectra images is proposed in this paper. Firstly, Integer Wavelet Transform is adopted to perform decorrelation of the data. Afterwards, Embedded Zero-tree Wavelet encoder is employed to describe the zero-tree structure of wavelet coefficients, and then the resulting stream put through Embedded Zero-tree Wavelet encoder can be transformed to character string including only five characters that is easily compressed by entropy coding. Finally, Arithmetic encoder is chosen as the entropy coder here. Groups of simulation data based on LAMOST and observation data from SDSS are used in the experiment to demonstrate the new method, and the experimental results are much better than those of GZIP and JPEG2000.

Implementation of three‐dimensional wavelet encoding spectroscopic imaging: In vivo application and method comparison

We have recently proposed a two-dimensional Wavelet Encoding-Spectroscopic Imaging (WE-SI) technique as an alternative to Chemical Shift Imaging (CSI), to reduce acquisition time and crossvoxel contamination in magnetic resonance spectroscopic imaging (MRSI). In this article we describe the extension of the WE-SI technique to three dimensions and its implementation on a clinical 1.5 T General Electric (GE) scanner. Phantom and in vivo studies are carried out to demonstrate the usefulness of this technique for further acquisition time reduction with low voxel contamination. In wavelet encoding, a set of dilated and translated prototype functions called wavelets are used to span a localized space by dividing it into a set of subspaces with predetermined sizes and locations. In spectroscopic imaging, this process is achieved using radiofrequency (RF) pulses with profiles resembling the wavelet shapes. Slice selective excitation and refocusing RF pulses, with single-band and dual-band profiles similar to Haar wavelets, are used in a modified PRESS sequence to acquire 3D WE-SI data. Wavelet dilation and translation are achieved by changing the strength of the localization gradients and frequency shift of the RF pulses, respectively. The desired spatial resolution in each direction sets the corresponding number of dilations (increases in the localization gradients), and consequently, the number of translations (frequency shift) of the Haar wavelets (RF pulses), which are used to collect magnetic resonance (MR) signals from the corresponding subspaces. Data acquisition time is reduced by using the minimum recovery time (TR(min)), also called effective time, when successive MR signals from adjacent subspaces are collected. Inverse wavelet transform is performed on the acquired data to produce metabolite maps. The proposed WE-SI method is compared in terms of acquisition time, pixel bleed, and signal-to-noise ratio to the CSI technique. The study outcome shows that 3D WE-SI provides accurate results while reducing both acquisition time and voxel contamination.

Still Image Processing on Coarse-Grained Reconfigurable Array Architectures

Due to the increasing demands on efficiency, performance and flexibility reconfigurable computational architectures are very promising candidates in embedded systems design. Recently coarse-grained reconfigurable array architectures (CGRAs), such as the ADRES CGRA and its corresponding DRESC compiler are gaining more popularity due to several technological breakthroughs in this area. We investigate the mapping of two image processing algorithms, Wavelet encoding and decoding, and TIFF compression on this novel type of array architectures in a systematic way. The results of our experiments show that CGRAs based on ADRES and its DRESC compiler technology deliver improved performance levels for these two benchmark applications when compared to results obtained on a state-of-the-art commercial DSP platform, the c64x DSP from Texas Instruments. ADRES/DRESC can beat its performance by at least 50% in cycle count and the power consumption even drops to 10% of the published numbers of the c64x DSP.

Multiple description wavelet coding with dual decomposition and cross packetization

In this paper, a novel wavelet-based multiple description coding (MDC) is proposed with dual decomposition (DD) and cross packetization (CP). Through dual decomposition, each description has two parts, the primary and the complementary. The former contains the structural information, including the positions and signs of significant coefficients, whereas the latter contains the residual data, which are the absolute values of the significant coefficients’ magnitude. The primary part is most crucial for source reconstruction; hence, their codes generated by the x-tree wavelet encoder are duplicated in both descriptions for heavy protection. On the other hand, the residual data are processed by the multiple description scalar quantizer to generate two indices for their respective descriptions as the complementary part. The proposed DD–MDC method effectively enhances error-resilience capability for robust transmission. For the packet-switching networks, the proposed CP, which produces the row packets and column packets for the two descriptions, respectively, is incorporated into the DD–MDC framework, leading to the DDCP–MDC scheme. Extensive simulation results have clearly shown that the proposed wavelet-based DD–MDC and DDCP–MDC methods are highly error resilient and consistently yield high coding gain; particularly, when only one description is available, the reconstructed image quality is superior to that obtained with other existing methods.

Low-Complexity Multiresolution Image Compression Using Wavelet Lower Trees

In this paper, a new image compression algorithm is proposed based on the efficient construction of wavelet coefficient lower trees. The main contribution of the proposed lower-tree wavelet (LTW) encoder is the utilization of coefficient trees, not only as an efficient method of grouping coefficients, but also as a fast way of coding them. Thus, it presents state-of-the-art compression performance, whereas its complexity is lower than the one presented in other wavelet coders, like SPIHT and JPEG 2000. Fast execution is achieved by means of a simple two-pass coding and one-pass decoding algorithm. Moreover, its computation does not require additional lists or complex data structures, so there is no memory overhead. A formal description of the algorithm is provided, while reference software is also given. Numerical results show that our codec works faster than SPIHT and JPEG 2000 (up to three times faster than SPIHT and fifteen times faster than JPEG 2000), with similar coding efficiency

Acquisition time reduction in magnetic resonance spectroscopic imaging using discrete wavelet encoding

This paper describes a new magnetic resonance spectroscopic imaging (MRSI) technique based upon the discrete wavelet transform to reduce acquisition time and cross voxel contamination. Prototype functions called wavelets are used in wavelet encoding to localize defined regions in localized space by dilations and translations. Wavelet encoding in MRSI is achieved by matching the slice selective RF pulse profiles to a set of dilated and translated wavelets. Single and dual band slice selective excitation and refocusing pulses, with profiles resembling Haar wavelets, are used in a spin–echo sequence to acquire 2D-MRSI wavelet encoding data. The 2D space region is spanned up to the desired resolution by a proportional number of dilations (increases in the localization gradients) and translations (frequency shift) of the Haar wavelets (RF pulses). Acquisition time is reduced by acquiring successive MR signals from regions of space with variable size and different locations with no requirement for a TR waiting time between acquisitions. An inverse wavelet transform is performed on the data to produce the correct spatial MR signal distribution.

An embedded wavelet image coder with parallel encoding and sequential decoding of bit-planes

Wavelet-based coders are widely used in image compression. Many popular embedded wavelet coders are based on a data structure known as zerotree. However, there exists another category of embedded wavelet coders that are fast and efficient without employing zerotree. These coders are based on three key concepts: (1) wavelet coefficient reordering, (2) bit-plane partitioning, and (3) encoding of bit-planes with certain efficient variants of run-length coding. In this paper, we propose a novel method to construct a bit-plane encoder that can be used in this category of non-zerotree coders. Instead of encoding the bit-planes progressively, the bit-plane encoding process can be finished in one pass when multiple bit-plane encoders are activated concurrently. With this proposed method, traditional partitioned-block based parallel processing strategy is enhanced with another dimension (depth of bit-planes) of processing flexibility. This bit-plane encoder inherently targets parallel processing architecture. The final output bitstream can be compatible with that of the original sequential coder if compatibility is preferred over speed and memory efficiency.

Design of Ring Convolutional Trellis Codes for MAP Decoding of MPEG-4 Images

We propose a trellis-coded modulation system using continuous-phase frequency-shift keying (CPFSK) and ring convolutional codes for transmitting the bits generated by an embedded zerotree wavelet encoder. Improved performance is achieved by using maximum a posteriori decoding of the zerotree symbols, and ring convolutional trellis codes are determined for this decoding method. The CPFSK transmitter is decomposed into a memoryless modulator and a continuous phase encoder over the ring of integers modulo 4; the latter is combined with a polynomial convolutional encoder over the same ring. In the code design process, a search is made of the combined trellis, where the branch metrics are modified to include the source transition matrix. Simulation results of image transmission are provided using the optimized system, including mismatched channel cases.

Feature preserving image compression

Image details appear as wavelet coefficients with large magnitude in the wavelet transform domain. Image compression methods such as the embedded zerotree wavelet encoding and the set partitioning in hierarchical trees select wavelet coefficients in the order of their significance (magnitude) and encode them generating an embedded bit stream. In existing wavelet based image compression techniques, the significance of a wavelet coefficient is solely defined by its magnitude.In this paper, we describe a flexible scheme to prioritize wavelet coefficients based on the features they exhibit. The proposed scheme combines tree based wavelet coefficient representation with the implicit transmission of data about image features that need to be emphasized. The experimental results presented in this paper demonstrate that it is possible to enhance the image features in the reconstructed images by embedding locally adaptive image processing techniques in the compression algorithm. The main advantage of the proposed technique over the existing methods is that it exploits the embedded zerotree data structure to eliminate the need to send side (additional) information to the decoder regarding the feature selection process.

Broad-source holographic reconstruction by use of wavelet encoding.

Reconstructing a hologram with spatially incoherent illumination smears the obtained image. We propose a wavelet based holographic recording process which uses the smearing to obtain a reconstruction with improved spatial resolution when incoherent illumination is applied.

Four-dimensional wavelet compression of arbitrarily sized echocardiographic data.

Wavelet-based methods have become most popular for the compression of two-dimensional medical images and sequences. The standard implementations consider data sizes that are powers of two. There is also a large body of literature treating issues such as the choice of the "optimal" wavelets and the performance comparison of competing algorithms. With the advent of telemedicine, there is a strong incentive to extend these techniques to higher dimensional data such as dynamic three-dimensional (3-D) echocardiography [four-dimensional (4-D) datasets]. One of the practical difficulties is that the size of this data is often not a multiple of a power of two, which can lead to increased computational complexity and impaired compression power. Our contribution in this paper is to present a genuine 4-D extension of the well-known zerotree algorithm for arbitrarily sized data. The key component of our method is a one-dimensional wavelet algorithm that can handle arbitrarily sized input signals. The method uses a pair of symmetric/antisymmetric wavelets (10/6) together with some appropriate midpoint symmetry boundary conditions that reduce border artifacts. The zerotree structure is also adapted so that it can accommodate noneven data splitting. We have applied our method to the compression of real 3-D dynamic sequences from clinical cardiac ultrasound examinations. Our new algorithm compares very favorably with other more ad hoc adaptations (image extension and tiling) of the standard powers-of-two methods, in terms of both compression performance and computational cost. It is vastly superior to slice-by-slice wavelet encoding. This was seen not only in numerical image quality parameters but also in expert ratings, where significant improvement using the new approach could be documented. Our validation experiments show that one can safely compress 4-D data sets at ratios of 128:1 without compromising the diagnostic value of the images. We also display some more extreme compression results at ratios of 2000:1 where some key diagnostically relevant key features are preserved.