Efficient Inter-Geodesic Distance Computation and Fast Classical Scaling.

Multidimensional scaling (MDS) is a dimensionality reduction tool used for information analysis, data visualization and manifold learning. Most MDS procedures embed data points in low-dimensional euclidean (flat) domains, such that distances between the points are as close as possible to given inter-point dissimilarities. We present an efficient solver for classical scaling, a specific MDS model, by extrapolating the information provided by distances measured from a subset of the points to the remainder. The computational and space complexities of the new MDS methods are thereby reduced from quadratic to quasi-linear in the number of data points. Incorporating both local and global information about the data allows us to construct a low-rank approximation of the inter-geodesic distances between the data points. As a by-product, the proposed method allows for efficient computation of geodesic distances.

Assessment of Coded Excitation Implementation for Estimating Heat-Induced Speed of Sound Changes.

Speed of sound (SoS) is an acoustic property that is highly sensitive to changes in tissues. SoS can be mapped non-invasively using ultrasonic through transmission wave tomography. This however, practically limits its clinical use to the breast. A pulse-echo-based method that has broader clinical use and that can reliably measure treatment-induced changes in SoS even under poor signal-to-noise ratio (SNR) is highly desirable. The aim of this study was to evaluate the implementation of coded excitations (CoEs) to improve pulse-echo monitoring of heat-induced changes in the SoS. In this study, a binary phase modulated Barker sequence and a linear frequency-modulated chirp were compared with a common Gaussian pulse transmission. The comparison was conducted using computer simulations, as well as transmissions in both agar-gelatin phantoms and ex vivo bovine liver. SoS changes were experimentally induced by heating the specimens with a therapeutic ultrasound system. The performance of each transmission signal was evaluated by correlating the relative echo shifts to the normalized SoS measured by through transmission. The computer simulations indicated that CoEs are beneficial at very low SNR. The Barker code performed better than both the chirp and Gaussian pulses, particularly at SNRs <10 dB (R2 = 0.81 ± 0.06, 0.68 ± 0.07 and 0.55 ± 0.08, respectively, at 0 dB). At high SNRs, the CoEs performed statistically on par with the Gaussian pulse. The experimental findings indicated that both Barker and chirp codes performed better than the Gaussian pulse on ex vivo liver (R2 = 0.80 ± 0.15, 0.79 ± 0.15 and 0.54 ± 0.17, respectively) and comparably on agar-gelatin phantoms. In conclusion, CoEs can be beneficial for assessing temperature-induced changes in the SoS using the pulse-echo method under poor SNR.

Spatially-Adaptive Reconstruction in Computed Tomography Using Neural Networks.

We propose a supervised machine learning approach for boosting existing signal and image recovery methods and demonstrate its efficacy on example of image reconstruction in computed tomography. Our technique is based on a local nonlinear fusion of several image estimates, all obtained by applying a chosen reconstruction algorithm with different values of its control parameters. Usually such output images have different bias/variance trade-off. The fusion of the images is performed by feed-forward neural network trained on a set of known examples. Numerical experiments show an improvement in reconstruction quality relatively to existing direct and iterative reconstruction methods.

Learned shrinkage approach for low-dose reconstruction in computed tomography.

We propose a direct nonlinear reconstruction algorithm for Computed Tomography (CT), designed to handle low-dose measurements. It involves the filtered back-projection and adaptive nonlinear filtering in both the projection and the image domains. The filter is an extension of the learned shrinkage method by Hel-Or and Shaked to the case of indirect observations. The shrinkage functions are learned using a training set of reference CT images. The optimization is performed with respect to an error functional in the image domain that combines the mean square error with a gradient-based penalty, promoting image sharpness. Our numerical simulations indicate that the proposed algorithm can manage well with noisy measurements, allowing a dose reduction by a factor of 4, while reducing noise and streak artifacts in the FBP reconstruction, comparable to the performance of a statistically based iterative algorithm.

Approximate Fourier phase information in the phase retrieval problem: what it gives and how to use it.

This work evaluates the importance of approximate Fourier phase information in the phase retrieval problem. The main discovery is that a rough phase estimate (up to π/2 rad) allows development of very efficient algorithms whose reconstruction time is an order of magnitude faster than that of the current method of choice--the hybrid input-output (HIO) algorithm. Moreover, a heuristic explanation is provided of why continuous optimization methods like gradient descent or Newton-type algorithms fail when applied to the phase retrieval problem and how the approximate phase information can remedy this situation. Numerical simulations are presented to demonstrate the validity of our analysis and success of our reconstruction method even in cases where the HIO algorithm fails, namely, complex-valued signals without tight support information.

Blind decomposition of transmission light microscopic hyperspectral cube using sparse representation.

In this paper, we address the problem of fully automated decomposition of hyperspectral images for transmission light microscopy. The hyperspectral images are decomposed into spectrally homogeneous compounds. The resulting compounds are described by their spectral characteristics and optical density. We present the multiplicative physical model of image formation in transmission light microscopy, justify reduction of a hyperspectral image decomposition problem to a blind source separation problem, and provide method for hyperspectral restoration of separated compounds. In our approach, dimensionality reduction using principal component analysis (PCA) is followed by a blind source separation (BSS) algorithm. The BSS method is based on sparsifying transformation of observed images and relative Newton optimization procedure. The presented method was verified on hyperspectral images of biological tissues. The method was compared to the existing approach based on nonnegative matrix factorization. Experiments showed that the presented method is faster and better separates the biological compounds from imaging artifacts. The results obtained in this work may be used for improving automatic microscope hardware calibration and computer-aided diagnostics.

Learning subject-specific spatial and temporal filters for single-trial EEG classification.

There are a wide variety of electroencephalography (EEG) analysis methods. Most of them are based on averaging over multiple trials in order to increase signal-to-noise ratio. The method introduced in this article is a single trial method. Our approach is based on the assumption that the "response of interest" to each task is smooth, and is contained in several sensor channels. We propose a two-stage preprocessing method. In the first stage, we apply spatial filtering by taking weighted linear combinations of the sensor measurements. In the second stage, we perform time-domain filtering. In both steps, we derive filters that maximize a class dissimilarity measure subject to regularizing constraints on the total variation of the average estimated signal (or, alternatively, on the signal's strength in time intervals where it is known to be absent). No other spatial or spectral assumptions with regard to the anatomy or sources were made.

Blind deconvolution of images using optimal sparse representations.

The relative Newton algorithm, previously proposed for quasi-maximum likelihood blind source separation and blind deconvolution of one-dimensional signals is generalized for blind deconvolution of images. Smooth approximation of the absolute value is used as the nonlinear term for sparse sources. In addition, we propose a method of sparsification, which allows blind deconvolution of arbitrary sources, and show how to find optimal sparsifying transformations by supervised learning.

Reconstruction in diffraction ultrasound tomography using nonuniform FFT.

We show an iterative reconstruction framework for diffraction ultrasound tomography. The use of broad-band illumination allows significant reduction of the number of projections compared to straight ray tomography. The proposed algorithm makes use of forward nonuniform fast Fourier transform (NUFFT) for iterative Fourier inversion. Incorporation of total variation regularization allows the reduction of noise and Gibbs phenomena while preserving the edges. The complexity of the NUFFT-based reconstruction is comparable to the frequency-domain interpolation (gridding) algorithm, whereas the reconstruction accuracy (in sense of the L2 and the L(infinity) norm) is better.