Discrete wavelet transform of finite-length signals must necessarily handle the signal boundaries. The state-of-the-art approaches treat such boundaries in a complicated and inflexible way, using special prolog or epilog phases. This holds true in particular for images decomposed into a number of scales, exemplary in JPEG 2000 coding system. In this paper, the state-of-the-art approaches are extended to perform the treatment using a compact streaming core, possibly in multi-scale fashion. We present the core focused on CDF 5 3 wavelet and the symmetric border extension method, both employed in the JPEG 2000. As a result of our work, every input sample is visited only once, while the results are produced immediately, i.e. without buffering.
Originally, the problem of efficient implementation of the 1-D lifting scheme was addressed in @cite_24 by Ch. Chrysafis and A. Ortega. Their general approach transforms the input data in a single loop. Nonetheless, this is essentially the same method as the on-line or pipelined method mentioned in other papers (although not necessarily using lifting scheme nor 1-D transform). The key idea is to make the lifting scheme causal, so that it may be evaluated as a running scheme without buffering of the whole signal. However, due to borders of the finite signals, some buffering is necessary at least at the beginning and end of the single-loop processing. For 2-D signals, the same idea was also discovered in another papers under various names, e.g. in @cite_25 @cite_7 @cite_21 @cite_8 @cite_14 @cite_23 . The most sophisticated techniques, that we are aware of, were investigated by R. Kutil in @cite_3 . The author emphasizes that the main issue are the arduous prolog and epilog phases. Many authors @cite_6 @cite_19 @cite_4 @cite_11 also discovered a similar technique with a slightly different goal (a better utilization of cache lines). This technique is referred to as the aggregation, strip-mine, or loop tiling.
@cite_14 @cite_4 @cite_7 @cite_8 @cite_21 @cite_3 @cite_6 @cite_24 @cite_19 @cite_23 @cite_25 @cite_11
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A new transform is proposed that derives the overcomplete discrete wavelet transform (ODWT) subbands from the critically sampled DWT subbands (complete representation). This complete-to-overcomplete DWT (CODWT) has certain advantages in comparison to the conventional approach that performs the inverse DWT to reconstruct the input signal, followed by the a spl grave -trous or the lowband shift algorithm. Specifically, the computation of the input signal is not required. As a result, the minimum number of downsampling operations is performed and the use of upsampling is avoided. The proposed CODWT computes the ODWT subbands by using a set of prediction-filter matrices and filtering-and-downsampling operators applied to the DWT. This formulation demonstrates a clear separation between the single-rate and multirate components of the transform. This can be especially significant when the CODWT is used in resource-constrained environments, such as resolution-scalable image and video codecs. To illustrate the applicability of the proposed transform in these emerging applications, a new scheme for the transform-calculation is proposed, and existing coding techniques that benefit from its usage are surveyed. The analysis of the proposed CODWT in terms of arithmetic complexity and delay reveals significant gains as compared with the conventional approach. With the start of the widespread use of discrete wavelet transform in image processing, the need for its efficient implementation is becoming increasingly more important. This work presents several novel SIMD-vectorized algorithms of 2-D discrete wavelet transform, using a lifting scheme. At the beginning, a stand-alone core of an already known single-loop approach is extracted. This core is further simplified by an appropriate reorganization of operations. Furthermore, the influence of the CPU cache on a 2-D processing order is examined. Finally, SIMD-vectorizations and parallelizations of the proposed approaches are evaluated. The best of the proposed algorithms scale almost linearly with the number of threads. For all of the platforms used in the tests, these algorithms are significantly faster than other known methods, as shown in the experimental sections of the paper. This paper addresses the implementation of a 2-D Discrete Wavelet Transform on general-purpose microprocessors, focusing on both memory hierarchy and SIMD parallelization issues. Both topics are somewhat related, since SIMD extensions are only useful if the memory hierarchy is efficiently exploited. In this work, locality has been significantly improved by means of a novel approach called pipelined computation, which complements previous techniques based on loop tiling and non-linear layouts. As experimental platforms we have employed a Pentium-III (P-III) and a Pentium-4 (P-4) microprocessor. However, our SIMD-oriented tuning has been exclusively performed at source code level. Basically, we have reordered some loops and introduced some modifications that allow automatic vectorization. Taking into account the abstraction level at which the optimizations are carried out, the speedups obtained on the investigated platforms are quite satisfactory, even though further improvement can be obtained by dropping the level of abstraction (compiler intrinsics or assembly code). A novel approach to 2-D single-loop wavelet lifting with compatibility to JPEG 2000 is presented in this paper. A newly developed 2-D core of CDF 5 3 wavelet filter is presented that, using a new sequence of operations, simplify the design. Moreover, the proposed approach, that uses one pass for 2-D transform, directly produces final output and reduces significantly the need for storing intermediate results into memory. All the proposed structures can be efficiently pipelined in hardware. This paper describes the proposed approach, its implementation in FPGA, cost of such implementation, and brings an experimental evaluation as well as discussion of the features of the approach.