Toward single particle reconstruction without particle picking: Breaking the detection limit

Single-particle cryo-electron microscopy (cryo-EM) has recently joined X-ray crystallography and NMR spectroscopy as a high-resolution structural method for biological macromolecules. In a cryo-EM experiment, the microscope produces images called micrographs. Projections of the molecule of interest are embedded in the micrographs at unknown locations, and under unknown viewing directions. Standard imaging techniques first locate these projections (detection) and then reconstruct the 3-D structure from them. Unfortunately, high noise levels hinder detection. When reliable detection is rendered impossible, the standard techniques fail. This is a problem especially for small molecules, which can be particularly hard to detect. In this paper, we propose a radically different approach: we contend that the structure could, in principle, be reconstructed directly from the micrographs, without intermediate detection. As a result, even small molecules should be within reach for cryo-EM. To support this claim, we setup a simplified mathematical model and demonstrate how our autocorrelation analysis technique allows to go directly from the micrographs to the sought signals. This involves only one pass over the micrographs, which is desirable for large experiments. We show numerical results and discuss challenges that lay ahead to turn this proof-of-concept into a competitive alternative to state-of-the-art algorithms

A Panorama on Multiscale Geometric Representations, Intertwining Spatial, Directional and Frequency Selectivity

The richness of natural images makes the quest for optimal representations in image processing and computer vision challenging. The latter observation has not prevented the design of image representations, which trade off between efficiency and complexity, while achieving accurate rendering of smooth regions as well as reproducing faithful contours and textures. The most recent ones, proposed in the past decade, share an hybrid heritage highlighting the multiscale and oriented nature of edges and patterns in images. This paper presents a panorama of the aforementioned literature on decompositions in multiscale, multi-orientation bases or dictionaries. They typically exhibit redundancy to improve sparsity in the transformed domain and sometimes its invariance with respect to simple geometric deformations (translation, rotation). Oriented multiscale dictionaries extend traditional wavelet processing and may offer rotation invariance. Highly redundant dictionaries require specific algorithms to simplify the search for an efficient (sparse) representation. We also discuss the extension of multiscale geometric decompositions to non-Euclidean domains such as the sphere or arbitrary meshed surfaces. The etymology of panorama suggests an overview, based on a choice of partially overlapping "pictures". We hope that this paper will contribute to the appreciation and apprehension of a stream of current research directions in image understanding.Comment: 65 pages, 33 figures, 303 reference

Calibration Challenges for Future Radio Telescopes

Instruments for radio astronomical observations have come a long way. While the first telescopes were based on very large dishes and 2-antenna interferometers, current instruments consist of dozens of steerable dishes, whereas future instruments will be even larger distributed sensor arrays with a hierarchy of phased array elements. For such arrays to provide meaningful output (images), accurate calibration is of critical importance. Calibration must solve for the unknown antenna gains and phases, as well as the unknown atmospheric and ionospheric disturbances. Future telescopes will have a large number of elements and a large field of view. In this case the parameters are strongly direction dependent, resulting in a large number of unknown parameters even if appropriately constrained physical or phenomenological descriptions are used. This makes calibration a daunting parameter estimation task, that is reviewed from a signal processing perspective in this article.Comment: 12 pages, 7 figures, 20 subfigures The title quoted in the meta-data is the title after release / final editing

Biologically inspired feature extraction for rotation and scale tolerant pattern analysis

Biologically motivated information processing has been an important area of scientific research for decades. The central topic addressed in this dissertation is utilization of lateral inhibition and more generally, linear networks with recurrent connectivity along with complex-log conformal mapping in machine based implementations of information encoding, feature extraction and pattern recognition. The reasoning behind and method for spatially uniform implementation of inhibitory/excitatory network model in the framework of non-uniform log-polar transform is presented. For the space invariant connectivity model characterized by Topelitz-Block-Toeplitz matrix, the overall network response is obtained without matrix inverse operations providing the connection matrix generating function is bound by unity. It was shown that for the network with the inter-neuron connection function expandable in a Fourier series in polar angle, the overall network response is steerable. The decorrelating/whitening characteristics of networks with lateral inhibition are used in order to develop space invariant pre-whitening kernels specialized for specific category of input signals. These filters have extremely small memory footprint and are successfully utilized in order to improve performance of adaptive neural whitening algorithms. Finally, the method for feature extraction based on localized Independent Component Analysis (ICA) transform in log-polar domain and aided by previously developed pre-whitening filters is implemented. Since output codes produced by ICA are very sparse, a small number of non-zero coefficients was sufficient to encode input data and obtain reliable pattern recognition performance