Amina Chebira

Life Beyond Bases: The Advent of Frames (Part II)

While the first part of this article presented most of the basic theoretical developments of frames, this part is more user friendly. It covers a large number of known frame families (harmonic tight frames, equiangular frames, unit-norm tight frame, Gabor frames, cosine-modulated frames, double-density frames, multidimensional frames, filter bank frame) as well as those applications where frames made a difference.

An Introduction to Frames

This survey gives an introduction to redundant signal representations called frames. These representations have recently emerged as yet another powerful tool in the signal processing toolbox and have become popular through use in numerous applications. Our aim is to familiarize a general audience with the area, while at the same time giving a snapshot of the current state-of-the-art.

A multiresolution approach to automated classification of protein subcellular location images

BackgroundFluorescence microscopy is widely used to determine the subcellular location of proteins. Efforts to determine location on a proteome-wide basis create a need for automated methods to analyze the resulting images. Over the past ten years, the feasibility of using machine learning methods to recognize all major subcellular location patterns has been convincingly demonstrated, using diverse feature sets and classifiers. On a well-studied data set of 2D HeLa single-cell images, the best performance to date, 91.5%, was obtained by including a set of multiresolution features. This demonstrates the value of multiresolution approaches to this important problem.ResultsWe report here a novel approach for the classification of subcellular location patterns by classifying in multiresolution subspaces. Our system is able to work with any feature set and any classifier. It consists of multiresolution (MR) decomposition, followed by feature computation and classification in each MR subspace, yielding local decisions that are then combined into a global decision. With 26 texture features alone and a neural network classifier, we obtained an increase in accuracy on the 2D HeLa data set to 95.3%.ConclusionWe demonstrate that the space-frequency localized information in the multiresolution subspaces adds significantly to the discriminative power of the system. Moreover, we show that a vastly reduced set of features is sufficient, consisting of our novel modified Haralick texture features. Our proposed system is general, allowing for any combinations of sets of features and any combination of classifiers.Fluorescence microscopy is widely used to determine the subcellular location of proteins. Efforts to determine location on a proteome-wide basis create a need for automated methods to analyze the resulting images. Over the past ten years, the feasibility of using machine learning methods to recognize all major subcellular location patterns has been convincingly demonstrated, using diverse feature sets and classifiers. On a well-studied data set of 2D HeLa single-cell images, the best performance to date, 91.5%, was obtained by including a set of multiresolution features. This demonstrates the value of multiresolution approaches to this important problem. We report here a novel approach for the classification of subcellular location patterns by classifying in multiresolution subspaces. Our system is able to work with any feature set and any classifier. It consists of multiresolution (MR) decomposition, followed by feature computation and classification in each MR subspace, yielding local decisions that are then combined into a global decision. With 26 texture features alone and a neural network classifier, we obtained an increase in accuracy on the 2D HeLa data set to 95.3%. We demonstrate that the space-frequency localized information in the multiresolution subspaces adds significantly to the discriminative power of the system. Moreover, we show that a vastly reduced set of features is sufficient, consisting of our novel modified Haralick texture features. Our proposed system is general, allowing for any combinations of sets of features and any combination of classifiers.

Near-Optimal Sensor Placement for Linear Inverse Problems

A classic problem is the estimation of a set of parameters from measurements collected by only a few sensors. The number of sensors is often limited by physical or economical constraints and their placement is of fundamental importance to obtain accurate estimates. Unfortunately, the selection of the optimal sensor locations is intrinsically combinatorial and the available approximation algorithms are not guaranteed to generate good solutions in all cases of interest. We propose FrameSense, a greedy algorithm for the selection of optimal sensor locations. The core cost function of the algorithm is the frame potential, a scalar property of matrices that measures the orthogonality of its rows. Notably, FrameSense is the first algorithm that is near-optimal in terms of mean square error, meaning that its solution is always guaranteed to be close to the optimal one. Moreover, we show with an extensive set of numerical experiments that FrameSense achieves state-of-the-art performance while having the lowest computational cost, when compared to other greedy methods.

Sampling and reconstructing diffusion fields with localized sources

We study the spatiotemporal sampling of a diffusion field generated by K point sources, aiming to fully reconstruct the unknown initial field distribution from the sample measurements. The sampling operator in our problem can be described by a matrix derived from the diffusion model. We analyze the important properties of the sampling matrices, leading to precise bounds on the spatial and temporal sampling densities under which perfect field reconstruction is feasible. Moreover, our analysis indicates that it is possible to compensate linearly for insufficient spatial sampling densities by oversampling in time. Numerical simulations on initial field reconstruction under different spatiotemporal sampling densities confirm our theoretical results.

EigenMaps: algorithms for optimal thermal maps extraction and sensor placement on multicore processors

Chip designers place on-chip sensors to measure local temperatures, thus preventing thermal runaway situations in multicore processing architectures. However, thermal characterization is directly dependent on the number of placed sensors, which should be minimized, while guaranteeing full detection of all hot-spots and worst case temperature gradient. In this paper, we present EigenMaps: a new set of algorithms to recover precisely the overall thermal map from a minimal number of sensors and a near-optimal sensor allocation algorithm. The proposed methods are stable with respect to possible temperature sensor calibration inaccuracies, and achieve significant improvements compared to the state-of-the-art. In particular, we estimate an entire thermal map for an industrial 8-core industrial design within 1°C of accuracy with just four sensors. Moreover, when the measurements are corrupted by noise (SNR of 15 dB), we can achieve the same precision only with 16 sensors.

Topology preserving STACS segmentation of protein subcellular location images

We present an algorithm for the segmentation of multicell fluorescence microscopy images. Such images abound and a segmentation algorithm robust to different experimental conditions as well as cell types is becoming a necessity. In cellular imaging, among the most often used segmentation algorithms is seeded watershed. One of its features is that it tends to oversegment, splitting the cells, as well as create segmented regions much larger than a true cell. This can be an advantage (the entire cell is within the region) as well as a disadvantage (a large amount of background noise is included). We present an algorithm which segments with tight contours by building upon an active contour algorithm - STACS, by Pluempitiwiriyawej et al. We adapt the algorithm to suit the needs of our data and use another technique, topology preservation by Han et al., to build our topology preserving STACS (TPSTACS). Our algorithm significantly outperforms the seeded watershed both visually as well as by standard measures of segmentation quality: recall/precision, area similarity and area overlap

Filter Bank Fusion Frames

In this paper we characterize and construct novel oversampled filter banks implementing fusion frames. A fusion frame is a sequence of orthogonal projection operators whose sum can be inverted in a numerically stable way. When properly designed, fusion frames can provide redundant encodings of signals which are optimally robust against certain types of noise and erasures. However, up to this point, few implementable constructions of such frames were known; we show how to construct them using oversampled filter banks. In this work, we first provide polyphase domain characterizations of filter bank fusion frames. We then use these characterizations to construct filter bank fusion frame versions of discrete wavelet and Gabor transforms, emphasizing those specific finite impulse response filters whose frequency responses are well-behaved.

TOWARDS AN IMAGE ANALYSIS TOOLBOX FOR HIGH-THROUGHPUT DROSOPHILA EMBRYO RNAI SCREENS

We build an image analysis toolbox for high-throughput Drosophila embryo RNAi screens. The goal is to tag the embryo as normal, developmentally delayed or abnormal based on the ventral furrow formation. We break the problem into two parts: in the first, we detect the developmental stage based on the progress of the ventral furrow formation, and in the second, we tag the embryo as normal/developmentally delayed/abnormal based on the stage detected and the elapsed time. The crux of the algorithm is the multiresolution classifier, and we show that, by classifying in multiresolution spaces, we obtain better results than by classifying the embryo image alone. The final 2D accuracy obtained was 93.17%, while by using 3D information, it increased to 98.35%

Sensor networks for diffusion fields: Detection of sources in space and time

We consider the problem of reconstructing a diffusion field, such as temperature, from samples collected by a sensor network. Motivated by the fast decay of the eigenvalues of the diffusion equation, we approximate the field by a truncated series. We show that the approximation error decays rapidly with time. On the other hand, the information content in the field also decays with time, suggesting the need for a proper choice of the sampling strategy. We propose two algorithms for sampling and reconstruction of the field. The first one reconstructs the distribution of point sources appearing at known times using the finite rate of innovation (FRI) framework. The second algorithm addresses a more difficult problem of estimating the unknown times at which the point sources appear, in addition to their locations and magnitudes. It relies on the assumption that the sources appear at distinct times. We verify that the algorithms are capable of reconstructing the field accurately through a set of numerical experiments. Specifically, we show that the second algorithm successfully recovers an arbitrary number of sources with unknown release times, satisfying the assumption. For simplicity, we develop the 1-D theory, noting the possibility of extending the framework to more general domains.