Rade Kutil

A single-loop approach to SIMD parallelization of 2D wavelet lifting

Widespread use of wavelet transforms as in JPEG2000 demands efficient implementations on general purpose computers as well as dedicated hardware. The increasing availability of SIMD technologies is a great challenge since efficient SIMD parallelizations are not trivial. This work presents a parallelized 2D wavelet transform following a single-loop approach, i.e. a loop fusion of the lifting steps of horizontal filtering, and interleaving horizontal and vertical filtering for optimal temporal locality. In this way, each input value is read only once and each output value is written once without subsequent updates. Such an approach turns out to be a necessary basis for an efficient SIMD parallelization. Results are obtained on a general purpose processor with a 4-fold single-precision SIMD extension. Speedups of about 3.7 due to the use of SIMD, 2.55 due to the single-loop approach and up to 6 due to cache effects for pathologic data sizes are obtained, giving total speedups of up to 56.

Hardware and Software Aspects for 3-D Wavelet Decomposition on Shared Memory MIMD Computers

In this work we discuss hardware and software aspects of parallel 3-D wavelet/subband decomposition on shared memory MIMD computers. Experimental results are conducted on a SGI POWERChallenge GR.

Significance map-based adaptive wavelet zerotree codec (SMAWZ)

This paper presents a wavelet based codec (SMAWZ) that uses the most important features of the SPIHT algorithm (zero-trees) while eliminating all concepts that are incompatible with a reduced hardware environment. This is done by replacing dynamic list structures with static maps (significance maps) which leads to a simpler and spacially oriented coefficient scan order. Additionally, extensions such as wavelet packet support and object based coding are included.

Approaches to zerotree image and video coding on MIMD architectures

The wavelet transform is more and more widely used in image and video compression. One of the best known algorithms in image compression is the set partitioning in hierarchical trees algorithm which involves the wavelet transform. As today the parallelisation of the wavelet transform is sufficiently investigated, this work deals with the parallelisation of the compression algorithm itself as a next step. Two competitive approaches are presented: one is a direct parallelisation and the other uses an altered algorithm which suits better to the parallel architecture.

Parallelization of IIR filters using SIMD extensions

The SIMD parallelization of HR or recursive filters is more difficult than that of FIR filters due to additional data dependencies. While other methods concentrate on appropriate scheduling to enable SIMD parallel execution, this paper proposes a new method where data dependencies are resolved by fusing the recursive application of filter taps into single coefficients. In this way the overhead over perfect parallelity can be reduced to one vector multiply-accumulate operation. Speedups from 1.5 to 4.5 can be obtained with the 4-way SIMD Intel SSE extension, depending on the number of filter taps.

A symbolic transform attack on lightweight encryption based on wavelet filter parameterization

We present a family of attacks on lightweight encryption schemes for visual data that rely on wavelet filter parameterizations to provide security. All of the attacks construct a symbolic representation of the inverse wavelet transform. We show that this representation can be used in ciphertext-only attacks, known-plaintext attacks and in attacks in which some information on the plaintext is available. We investigate the success and feasibility of each of these attacks, and conclude that the presented type of attacks poses a principal problem for lightweight encryption schemes that rely on the parameterization of a (linear) transform.

Biased and unbiased estimation of the circular mean resultant length and its variance

The mean resultant length (MRL) is the length of the average of random vectors on the unit circle. It is used to measure the concentration of unimodal circular distributions. The sample MRL, as an estimator for the population MRL, has not been investigated thoroughly yet. This work examines the bias, variance and mean- squared error (MSE) of the MRL. Unbiased or near unbiased estimators are developed wherever possible for the squared and non-squared MRL, as well as their variances and MSE. All estimators are tested numerically on four representative circular distributions.

Anisotropic 3-D wavelet packet bases for video coding

Video coding algorithms based on 3-D wavelet transforms exist which have a competitive rate-distortion performance and are very fast because motion compensation is not needed. The compression efficiency of these algorithms can be increased by the use of more general wavelet packet transforms. Anisotropic wavelet packets are an even more generalized type of wavelet transform, where multidimensional wavelets do not necessarily have equal dilations in each dimension. This property is advantageous especially for 3-D video coding because video data has different characteristics in the time and spatial dimensions. This paper develops methods to adapt the SMAWZ codec to anisotropic 3-D wavelet packet bases and investigates algorithm complexity and the resulting rate-distortion performance. It can be shown that there exists a fixed anisotropic wavelet packet basis that is able to outperform MPEG-4 by up to 4dB especially for video sequences with low motion.

A generalization of quad-trees applied to image coding

Quad-trees are restricted to combined horizontal and vertical decomposition of tiles. If this restriction is dropped, anisotropic rectangular tiles result which can be arranged in a previously developed graph structure called “bush”. A new tiling algorithm is able to reduce the number of tiles by a factor of about two. Together with an existing efficient coding scheme for this graph, a lossless coding algorithm for bi-level and indexed color images is developed. It is compared to JBIG2 and PNG, and turns out to be efficient for situations with large uniform regions and high color payload.

Wavelet image and video coding on parallel architectures

We discuss parallel algorithms for wavelet-based image and video coding. After reviewing fundamentals of the parallel discrete wavelet transform, we cover the parallelization of two state-of-the-art compression schemes: a C++ 3D SPIHT video codec and a Java JPEG-2000 implementation.