Felix Friedrich

Multiscale wedgelet denoising algorithms

We present a heuristic algorithm for the choice of the wedgelet regularization parameter for the purpose of denoising in the case where the noise variance σ2 is not known. Numerical experiments comparing wavelet thresholding with wedgelet denoising, and with the related schemes quadtree approximation and platelet approximation, allow to assess the respective strengths of the different approaches. For small values of σ2, wavelets are clearly superior to wedgelets, and they are better at restoring textured regions. For large σ2, or for images of a predominantly geometric nature, wedgelets yield consistently better results. Moreover, the tests reveal that the heuristic algorithm is quite effective in choosing the regularization parameter.

Efficient Moment Computation over Polygonal Domains with an Application to Rapid Wedgelet Approximation

Many algorithms in image processing rely on the computation of sums of pixel values over a large variety of subsets of the image domain. This includes the computation of image moments for pattern recognition purposes, or adaptive smoothing and regression methods, such as wedgelets. In the first part of the paper, we present a general method which allows the fast computation of sums over a large class of polygonal domains. The approach relies on the idea of considering polygonal domains with a fixed angular resolution, combined with an efficient implementation of a discrete version of Green’s theorem. The second part deals with the application of the new methodology to a particular computational problem, namely wedgelet approximation. Our technique results in a speedup of

Array-Structured object types for mathematical programming

O(10^3)

Active Cells: A Computing Model for Rapid Construction of On-Chip Multi-core Systems

by comparison to preexisting implementations. A further attractive feature of our implementation is the instantaneous access to the full scale of wedgelet minimizers. We introduce a new scheme that replaces the locally constant regression underlying wedgelets by basically arbitrary local regression models. Due to the speedup obtained by the techniques explained in the first part, this scheme is computationally efficient and at the same time much more flexible than previously suggested methods such as wedgelets or platelets. In the final section we present numerical experiments showing the increase in speed and flexibility.

Complexity L0-Penalized M-Estimation: Consistency in More Dimensions

In this paper a concept for structured mathematical programming within an object-oriented language is presented. It leads to better readable, more natural and more compact code in typical linear algebra applications and provides options for optimized implementation. We also discuss the realization of this concept as an extension of the programming language Active Oberon. We define new built-in array types that provide a slight modification of classical arrays in Oberon. By introducing range-valued indices as array designators, we permit the use of regular sub-domains of arrays as parameters of operators and procedures. The built-in types are complemented by custom array structured object types. The latter can be specified by the programmer and are designed to be syntactically compatible with the former. They provide the needed flexibility for the language.

A low power configurable SoC for simulating delay-based audio effects

We present a novel computing model that allows to conveniently construct multi-core systems with different computer architectures, ranging from homogeneous many-core architectures to networks of heterogeneous general purpose processor cores or signal processing engines. A hardware library implemented on Field Programmable Gate Arrays (FPGAs) and a compiler provide a platform for prototyping and constructing distributed systems on a chip. A number of case studies have been carried out to prove the concept conveyed by the computing model.

On the Design and Implementation of an Efficient Lock-Free Scheduler

We study the asymptotics in L2 for complexity penalized least squares regression for the discrete approximation of finite-dimensional signals on continuous domains—e.g., images—by piecewise smooth functions. We introduce a fairly general setting, which comprises most of the presently popular partitions of signal or image domains, like interval, wedgelet or related partitions, as well as Delaunay triangulations. Then, we prove consistency and derive convergence rates. Finally, we illustrate by way of relevant examples that the abstract results are useful for many applications.

An Elementary Rigorous Introduction to Exact Sampling

The rapid growth in the capability of modern FPGA devices allows developers to build a complete system on a single chip. These types of FPGA-based SoC (System-On-a-Chip) can normally achieve reduced system power, cost and size, and at the same time offer users a great deal of flexibility. The development of such SoCs normally starts from using a hardware/software co-design methodology in order to partition system tasks into computation-intensive and flexibility-demanding parts. Then, dedicated hardware and software will be implemented to realize these two parts. This paper presents an example which demonstrates the result of applying the hardware/software co-design methodology, a power efficient and performance reliable system architecture for realizing audio delay effects. Compared to similar implementations, our system architecture can save 40% of dynamic power consumption while offering the same data throughput and user flexibility.

Beyond wavelets: New image representation paradigms

Schedulers for symmetric multiprocessing (SMP) machines use sophisticated algorithms to schedule processes onto the available processor cores. Hardware-dependent code and the use of locks to protect shared data structures from simultaneous access lead to poor portability, the difficulty to prove correctness, and a myriad of problems associated with locking such as limiting the available parallelism, deadlocks, starvation, interrupt handling, and so on. In this work we explore what can be achieved in terms of portability and simplicity in an SMP scheduler that achieves similar performance to state-of-the-art schedulers. By strictly limiting ourselves to only lock-free data structures in the scheduler, the problems associated with locking vanish altogether. We show that by employing implicit cooperative scheduling, additional guarantees can be made that allow novel and very efficient implementations of memory-efficient unbounded lock-free queues. Cooperative multitasking has the additional benefit that it provides an extensive hardware independence. It even allows the scheduler to be used as a runtime library for applications running on top of standard operating systems. In a comparison against Windows Server and Linux running on up to 64 cores we analyze the performance of the lock-free scheduler and show that it matches or even outperforms the performance of these two state-of-the-art schedulers in a variety of benchmarks.

A Tribute to J. Bertin's Graphical Data Analysis

We introduce coupling from the past, a recently developed method for exact sampling from a given distribution. Focus is on rigour and thorough proofs. We stay on an elementary level which requires little or no prior knowledge from probability theory. This should fill an obvious gap between innumerable intuitive and incomplete reviews, and few precise derivations on an abstract level.