An Architectural Framework for VLSI Time-Recursive Computation with Applications

The time-recursive computation model has been proven as a particularly useful tool in audio, video, radar and sonar real- time data processing architectures. Unlike the FFT based architectures, the time-recursive ones require only local communication, they imply linear implementation cost and they operate in a single-input multiple-output (SIMO) manner. This is appropriate for the above applications since the data are supplied serially. Also, the time-recursive architectures are modular and regular and they allow high degree of parallelism; thus they are very appropriate for VLSI implementation.In this dissertation, we establish an architectural framework for parallel time-recursive computation. We consider a class of linear operators (or signal transformers) that are characterized by discrete time, time invariant, compactly supported, but otherwise arbitrary kernel functions. We specify the properties of linear operators that can be implemented efficiently in a time-recursive way. Based on these properties, we develop a systematic routine that produces a time-recursive architectural implementation for a given operator. We demonstrate the use and effectiveness of this routine by means of specific examples, namely the Discrete Cosine Transform (DCT), the Discrete Fourier Transform (DFT) and the Discrete Wavelet Transform (DWT).By using this architectural framework we obtain novel architectures for the uniform-DFT QMF bank, the cosine modulated QMF bank, the 1-D and 2-D Modulated Lapped Transform (MLT), as well as an Extended Lapped Transform (ELT). Furthermore, the architectural implementation of the Cepstral Transform and a Short Time Fourier Transform are considered based on the time-recursive architecture of the DFT. All of the above designs are modular, regular, with local communication and linear cost in operator counts. In particular, the 1-D MLT requires 1N + 3 adders and N - 1 rotation circuits, where N denotes the data block size. The 2-D MLT requires 3 1-D MLT circuits and no matrix transposition. The ELT has basis length equal to 4N and it requires 3N + 4 multipliers, 4N + 4 adders and N + 2 rotation circuits. These results are expected to have a significant impact on real-time audio and video data compression, in frequency domain adaptive filtering and in spectrum analysis

Parallel Construction of Wavelet Trees on Multicore Architectures

The wavelet tree has become a very useful data structure to efficiently represent and query large volumes of data in many different domains, from bioinformatics to geographic information systems. One problem with wavelet trees is their construction time. In this paper, we introduce two algorithms that reduce the time complexity of a wavelet tree's construction by taking advantage of nowadays ubiquitous multicore machines. Our first algorithm constructs all the levels of the wavelet in parallel in $O(n)$ time and $O(n\lg\sigma + \sigma\lg n)$ bits of working space, where $n$ is the size of the input sequence and $\sigma$ is the size of the alphabet. Our second algorithm constructs the wavelet tree in a domain-decomposition fashion, using our first algorithm in each segment, reaching $O(\lg n)$ time and $O(n\lg\sigma + p\sigma\lg n/\lg\sigma)$ bits of extra space, where $p$ is the number of available cores. Both algorithms are practical and report good speedup for large real datasets.Comment: This research has received funding from the European Union's Horizon 2020 research and innovation programme under the Marie Sk{\l}odowska-Curie Actions H2020-MSCA-RISE-2015 BIRDS GA No. 69094

Task-based adaptive multiresolution for time-space multi-scale reaction-diffusion systems on multi-core architectures

A new solver featuring time-space adaptation and error control has been recently introduced to tackle the numerical solution of stiff reaction-diffusion systems. Based on operator splitting, finite volume adaptive multiresolution and high order time integrators with specific stability properties for each operator, this strategy yields high computational efficiency for large multidimensional computations on standard architectures such as powerful workstations. However, the data structure of the original implementation, based on trees of pointers, provides limited opportunities for efficiency enhancements, while posing serious challenges in terms of parallel programming and load balancing. The present contribution proposes a new implementation of the whole set of numerical methods including Radau5 and ROCK4, relying on a fully different data structure together with the use of a specific library, TBB, for shared-memory, task-based parallelism with work-stealing. The performance of our implementation is assessed in a series of test-cases of increasing difficulty in two and three dimensions on multi-core and many-core architectures, demonstrating high scalability

A Deep Representation for Invariance And Music Classification

Representations in the auditory cortex might be based on mechanisms similar to the visual ventral stream; modules for building invariance to transformations and multiple layers for compositionality and selectivity. In this paper we propose the use of such computational modules for extracting invariant and discriminative audio representations. Building on a theory of invariance in hierarchical architectures, we propose a novel, mid-level representation for acoustical signals, using the empirical distributions of projections on a set of templates and their transformations. Under the assumption that, by construction, this dictionary of templates is composed from similar classes, and samples the orbit of variance-inducing signal transformations (such as shift and scale), the resulting signature is theoretically guaranteed to be unique, invariant to transformations and stable to deformations. Modules of projection and pooling can then constitute layers of deep networks, for learning composite representations. We present the main theoretical and computational aspects of a framework for unsupervised learning of invariant audio representations, empirically evaluated on music genre classification.Comment: 5 pages, CBMM Memo No. 002, (to appear) IEEE 2014 International Conference on Acoustics, Speech, and Signal Processing (ICASSP 2014

Wavelet/shearlet hybridized neural networks for biomedical image restoration

Recently, new programming paradigms have emerged that combine parallelism and numerical computations with algorithmic differentiation. This approach allows for the hybridization of neural network techniques for inverse imaging problems with more traditional methods such as wavelet-based sparsity modelling techniques. The benefits are twofold: on the one hand traditional methods with well-known properties can be integrated in neural networks, either as separate layers or tightly integrated in the network, on the other hand, parameters in traditional methods can be trained end-to-end from datasets in a neural network "fashion" (e.g., using Adagrad or Adam optimizers). In this paper, we explore these hybrid neural networks in the context of shearlet-based regularization for the purpose of biomedical image restoration. Due to the reduced number of parameters, this approach seems a promising strategy especially when dealing with small training data sets

The Cascading Haar Wavelet algorithm for computing the Walsh-Hadamard Transform

We propose a novel algorithm for computing the Walsh-Hadamard Transform (WHT) which consists entirely of Haar wavelet transforms. We prove that the algorithm, which we call the Cascading Haar Wavelet (CHW) algorithm, shares precisely the same serial complexity as the popular divide-and-conquer algorithm for the WHT. We also propose a natural way of parallelizing the algorithm which has a number of attractive features