Grayscale and colour image Codec based on matching pursuit in the spatio-frequency domain

This report presents and evaluates a novel idea for scalable lossy colour image coding with Matching Pursuit (MP) performed in a transform domain. The benefits of the idea of MP performed in the transform domain are analysed in detail. The main contribution of this work is extending MP with wavelets to colour coding and proposing a coding method. We exploit correlations between image subbands after wavelet transformation in RGB colour space. Then, a new and simple quantisation and coding scheme of colour MP decomposition based on Run Length Encoding (RLE), inspired by the idea of coding indexes in relational databases, is applied. As a final coding step arithmetic coding is used assuming uniform distributions of MP atom parameters. The target application is compression at low and medium bit-rates. Coding performance is compared to JPEG 2000 showing the potential to outperform the latter with more sophisticated than uniform data models for arithmetic coder. The results are presented for grayscale and colour coding of 12 standard test images

Generalization of the K-SVD algorithm for minimization of ß-divergence

[EN] In this paper, we propose, describe, and test a modification of the K-SVD algorithm. Given a set of training data, the proposed algorithm computes an overcomplete dictionary by minimizing the ß-divergence () between the data and its representation as linear combinations of atoms of the dictionary, under strict sparsity restrictions. For the special case , the proposed algorithm minimizes the Frobenius norm and, therefore, for the proposed algorithm is equivalent to the original K-SVD algorithm. We describe the modifications needed and discuss the possible shortcomings of the new algorithm. The algorithm is tested with random matrices and with an example based on speech separation.This work has been partially supported by the EU together with the Spanish Government through TEC2015-67387-C4-1-R (MINECO/FEDER) and by Programa de FPU del Ministerio de Educacion, Cultura y Deporte FPU13/03828 (Spain).García Mollá, VM.; San Juan-Sebastian, P.; Virtanen, T.; Vidal Maciá, AM.; Alonso-Jordá, P. (2019). Generalization of the K-SVD algorithm for minimization of ß-divergence. Digital Signal Processing. 92:47-53. https://doi.org/10.1016/j.dsp.2019.05.001S47539

Sharp Convergence Rates for Matching Pursuit

We study the fundamental limits of matching pursuit, or the pure greedy algorithm, for approximating a target function by a sparse linear combination of elements from a dictionary. When the target function is contained in the variation space corresponding to the dictionary, many impressive works over the past few decades have obtained upper and lower bounds on the error of matching pursuit, but they do not match. The main contribution of this paper is to close this gap and obtain a sharp characterization of the decay rate of matching pursuit. Specifically, we construct a worst case dictionary which shows that the existing best upper bound cannot be significantly improved. It turns out that, unlike other greedy algorithm variants, the converge rate is suboptimal and is determined by the solution to a certain non-linear equation. This enables us to conclude that any amount of shrinkage improves matching pursuit in the worst case

Rotation and scale invariant shape representation and recognition using Matching Pursuit

Using a low-level representation of images, like matching pursuit, we introduce a new way of describing objects through a general description using a translation, rotation, and isotropic scale invariant dictionary of basis functions. We then use this description as a predefined dictionary of the object to conduct a shape recognition task. We show some promising results for the detection with simple shapes

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

Affine invariant Matching Pursuit-based shape representation and recognition using scale-space

In this paper, we propose an analytical low-level representation of images, obtained by a decomposition process, here the matching pursuit (MP) algorithm, as a new way of describing objects through a general continuous description using an affine invariant dictionary of basis functions. This description is used to recognize objects in images. In the learning phase, a template object is decomposed, and the extracted subset of basis functions, called meta-atom, gives the description of our object. We then extend naturally this description into the linear scale-space using the definition of our basis functions, and thus bringing a more general representation of our object. We use this enhanced description as a predefined dictionary of the object to conduct an MP-based shape recognition (MPSR) task into the linear scale-space. The introduction of the scale-space approach improves the robustness of our method, and permits to avoid local minima problems encountered when minimizing a non-convex energy function. We show results for the detection of complex synthetic shapes, as well as natural (aerial and medical) images

Modern Statistical/Machine Learning Techniques for Bio/Neuro-imaging Applications

Developments in modern bio-imaging techniques have allowed the routine collection of a vast amount of data from various techniques. The challenges lie in how to build accurate and efficient models to draw conclusions from the data and facilitate scientific discoveries. Fortunately, recent advances in statistics, machine learning, and deep learning provide valuable tools. This thesis describes some of our efforts to build scalable Bayesian models for four bio-imaging applications: (1) Stochastic Optical Reconstruction Microscopy (STORM) Imaging, (2) particle tracking, (3) voltage smoothing, (4) detect color-labeled neurons in c elegans and assign identity to the detections