Preliminary Study on the Feasibility of Performing Quantitative Precipitation Estimation Using X-band Radar

IRCTR has built an experimental X-band Doppler po-larimetric weather radar system aimed at obtaining high temporal and spatial resolution measurements of precipitation, with particular interest in light rain and drizzle. In this paper a first analysis of the feasibility of obtaining accurate quantitative precipitation estimation from the radar data performed using a high density network of rain gauges is presented

Matching Pursuit through Genetic Algorithms

Matching Pursuit is a greedy algorithmthat decomposes any signal into a linear expansion of waveforms taken from a redundant dictionary. Computing the projection of the signal on every element of the basis has a high computational cost. To reduce this computational cost, optimized computational error minimization methods have to be found. Genetic Algorithms have shown to be a good tool to this approach

R-D Analysis of Adaptive Edge Representations

This paper presents a Rate-Distortion analysis for a simple horizon edge image model. A quadtree with anisotropy and rotation is performed on this kind of image, giving a toy model for a non-linear adaptive coding technique, and its Rate-Distortion behavior is studied. The effect of refining the quadtree decomposition is also analyzed

Evolutionary Multiresolution Matching Pursuit and its Relations with the Human Visual System

This paper proposes a multiresolution Matching Pursuit decomposition of natural images. Matching Pursuit is a greedy algorithm that decomposes any signal into a linear expansion of waveforms taken from a redundant dictionary, by iteratively picking the waveform that best matches the input signal. Since the computational cost rapidly grows with the size of the signal, we propose a multiresolution strategy that, together with an efficient dictionary, significantly reduces the encoding complexity while still providing an efficient representation. Such a decomposition is perceptually very effective at low bit rate coding, thanks to similiarities with the Human Visual System information processing

High flexibility scalable image coding

This paper presents a new, highly flexible, scalable image coder based on a Matching Pursuit expansion. The dictionary of atoms is built by translation, rotation and anisotropic refinement of gaussian functions, in order to efficiently capture edges in natural images. In the same time, the dictionary is invariant under isotropic scaling, which interestingly leads to very simple spatial resizing operations. It is shown that the proposed scheme compares to state-of-the-art coders when the compressed image is transcoded to a lower (octave-based) spatial resolution. In contrary to common compression formats, our bit-stream can moreover easily and efficiently be decoded at any spatial resolution, even with irrational re-scaling factors. In the same time, the Matching Pursuit algorithm provides an intrinsically progressive stream. This worthy feature allows for easy rate filtering operations, where the least important atoms are simply discarded to fit restrictive bandwidth constraints. Our scheme is finally shown to favorably compare to state-of-the-art progressive coders for moderate to quite important rate reductions

A generalized Rate-Distortion limit for edge representation

This paper presents a rate-distortion analysis for a simple horizon edge image model. A quadtree with anisotropy and rotation is performed in this kind of image, giving a toy model for a non-linear adaptive coding technique, and its rate-distortion behavior is studied. The effect of refining the quadtree decomposition in the Rate-Distortion decay is also studied

An improved decoding scheme for Matching Pursuit Streams

This work presents an improved coefficient decoding method for Matching Pursuit streams. It builds on the adaptive a posteriori quantization of coefficients, and implements an interpolation scheme that enhances the inverse quantization performance at the decoder. A class of interpolation functions is introduced, that capture the behavior of coefficients after conditional scalar quantization. The accuracy of the interpolation scheme is verified experimentally, and the novel decoding algorithm is further evaluated in image coding applications. It can be seen that the proposed method improves the rate-distortion performance by up to 0.5 dB, only by changing the reconstruction strategy at the decoder

A Matching Pursuit Full Search Algorithm for Image Approximations

There is a growing interest on adapted signal expansions for efficient sparse approximations. For this purpose, signal expansions on over-complete bases are of high interest. Several strategies exist in order to get sparse approximations of a signal as a superposition of functions from a redundant dictionary. One of these strategies is the well known Matching Pursuit (MP). MP is an algorithm where complexity depends on the accuracy of the desired approximation. This is due to its greedy iterative nature. For very large dictionaries, however, complexity depends in great manner on the size of this, i.e. at each iteration the whole dictionary has to be browsed. Sometimes, heuristic procedures need to be adopted due to the overwhelming complexity that this may represent. However, these reduce the search space and, consequently, a poorer signal approximation is retrieved. In this work, we propose a feasible approach for Full Search Matching Pursuit (FSMP) for the particular case of natural image approximations with an-isotropically refined oriented atoms (which have the purpose of exploiting image geometry). Thanks to the structure of the dictionary and its spatio-temporal localisation, several enhancements are possible to speed-up the calculation of the most critical step: the scalar product of the signal with all the functions from the dictionary

Color Image Scalable Coding with Matching Pursuit

This paper presents a new scalable and highly flexible color image coder based on a Matching Pursuit expansion. The Matching Pursuit algorithm provides an intrinsically progressive stream and the proposed coder allows us to reconstruct color information from the first bit received. In order to efficiently capture edges in natural images, the dictionary of atoms is built by translation, rotation and anisotropic refinement of a wavelet-like mother function. This dictionary is moreover invariant under shifts and isotropic scaling, thus leading to very simple spatial resizing operations. This flexibility and adaptivity of the MP coder makes it appropriate for asymmetric applications with heterogeneous end user terminals

A Posteriori Quantization of Progressive Matching Pursuit Streams

This paper proposes a rate-distortion optimal a posteriori quantization scheme for Matching Pursuit coefficients. The a posteriori quantization applies to a Matching Pursuit expansion that has been generated off-line, and cannot benefit of any feedback loop to the encoder in order to compensate for the quantization noise. The redundancy of the Matching Pursuit dictionary provides an indicator of the relative importance of coefficients and atom indices, and subsequently on the quantization error. It is used to define a universal upper-bound on the decay of the coefficients, sorted in decreasing order of magnitude. A new quantization scheme is then derived, where this bound is used as an Oracle for the design of an optimal a posteriori quantizer. The latter turns the exponentially distributed coefficient entropy-constrained quantization problem into a simple uniform quantization problem. Using simulations with random dictionaries, we show that the proposed exponentially upper-bounded quantization (EUQ) clearly outperforms classical schemes. Stepping on the ideal Oracle-based approach, a sub-optimal adaptive scheme is then designed that approximates the EUQ but still outperforms competing quantization methods in terms of rate-distortion characteristics. Finally, the proposed quantization method is studied in the context of image coding. It performs similarly to state-of-the-art coding methods (and even better at low rates), while interestingly providing a progressive stream, very easy to transcode and adapt to changing rate constraints