Inner Bound on the GDOF of the K-User MIMO Gaussian Symmetric Interference Channel

The K-user multiple input multiple output (MIMO) Gaussian symmetric interference channel where each transmitter has M antennas and each receiver has N antennas is studied from a generalized degrees of freedom (GDOF) perspective. An inner bound on the GDOF is derived using a combination of techniques such as treating interference as noise, zero forcing (ZF) at the receivers, interference alignment (IA), and extending the Han-Kobayashi (HK) scheme to K users, as a function of the number of antennas and the log INR/log SNR level. Several interesting conclusions are drawn from the derived bounds. It is shown that when K > N/M + 1, a combination of the HK and IA schemes performs the best among the schemes considered. When N/M < K <= N/M + 1, the HK-scheme outperforms other schemes and is found to be GDOF optimal in many cases. In addition, when the SNR and INR are at the same level, ZF-receiving and the HK-scheme have the same GDOF performance.

Outer Bounds on the Sum Rate of the K-User MIMO Gaussian Interference Channel

This paper derives outer bounds on the sum rate of the K-user MIMO Gaussian interference channel (GIC). Three outer bounds are derived, under different assumptions of cooperation and providing side information to receivers. The novelty in the derivation lies in the careful selection of side information, which results in the cancellation of the negative differential entropy terms containing signal components, leading to a tractable outer bound. The overall outer bound is obtained by taking the minimum of the three outer bounds. The derived bounds are simplified for the MIMO Gaussian symmetric IC to obtain outer bounds on the generalized degrees of freedom (GDOF). The relative performance of the bounds yields insight into the performance limits of multiuser MIMO GICs and the relative merits of different schemes for interference management. These insights are confirmed by establishing the optimality of the bounds in specific cases using an inner bound on the GDOF derived by the authors in a previous work. It is also shown that many of the existing results on the GDOF of the GIC can be obtained as special cases of the bounds, e. g., by setting K = 2 or the number of antennas at each user to 1.

Study of Wrist Pulse Signals Using a Bi-Modal Gaussian Model

Wrist pulse signals contain important information about the health of a person and hence diagnosis based on pulse signals has assumed great importance. In this paper we demonstrate the efficacy of a two term Gaussian model to extract information from pulse signals. Results have been obtained by conducting experiments on several subjects to record wrist pulse signals for the cases of before exercise and after exercise. Parameters have been extracted from the recorded signals using the model and a paired t-test is performed, which shows that the parameters are significantly different between the two groups. Further, a recursive cluster elimination based support vector machine is used to perform classification between the groups. An average classification accuracy of 99.46% is obtained, along with top classifiers. It is thus shown that the parameters of the Gaussian model show changes across groups and hence the model is effective in distinguishing the changes taking place due to the two different recording conditions. The study has potential applications in healthcare.

Directional bilateral filters for smoothing fluorescence microscopy images

Images obtained through fluorescence microscopy at low numerical aperture (NA) are noisy and have poor resolution. Images of specimens such as F-actin filaments obtained using confocal or widefield fluorescence microscopes contain directional information and it is important that an image smoothing or filtering technique preserve the directionality. F-actin filaments are widely studied in pathology because the abnormalities in actin dynamics play a key role in diagnosis of cancer, cardiac diseases, vascular diseases, myofibrillar myopathies, neurological disorders, etc. We develop the directional bilateral filter as a means of filtering out the noise in the image without significantly altering the directionality of the F-actin filaments. The bilateral filter is anisotropic to start with, but we add an additional degree of anisotropy by employing an oriented domain kernel for smoothing. The orientation is locally adapted using a structure tensor and the parameters of the bilateral filter are optimized for within the framework of statistical risk minimization. We show that the directional bilateral filter has better denoising performance than the traditional Gaussian bilateral filter and other denoising techniques such as SURE-LET, non-local means, and guided image filtering at various noise levels in terms of peak signal-to-noise ratio (PSNR). We also show quantitative improvements in low NA images of F-actin filaments. (C) 2015 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution 3.0 Unported License.

Fluctuation theory of Rashba Fermi gases: Gaussian and beyond

Fermi gases with generalized Rashba spin-orbit coupling induced by a synthetic gauge field have the potential of realizing many interesting states, such as rashbon condensates and topological phases. Here, we address the key open problem of the fluctuation theory of such systems and demonstrate that beyond-Gaussian effects are essential to capture the finite temperature physics of such systems. We obtain their phase diagram by constructing an approximate non-Gaussian theory. We conclusively establish that spin-orbit coupling can enhance the exponentially small transition temperature (T-c) of a weakly attracting superfluid to the order of the Fermi temperature, paving a pathway towards high T-c superfluids.

Patch-based and multiresolution optimum bilateral filters for denoising images corrupted by Gaussian noise

We propose optimal bilateral filtering techniques for Gaussian noise suppression in images. To achieve maximum denoising performance via optimal filter parameter selection, we adopt Stein's unbiased risk estimate (SURE)-an unbiased estimate of the mean-squared error (MSE). Unlike MSE, SURE is independent of the ground truth and can be used in practical scenarios where the ground truth is unavailable. In our recent work, we derived SURE expressions in the context of the bilateral filter and proposed SURE-optimal bilateral filter (SOBF). We selected the optimal parameters of SOBF using the SURE criterion. To further improve the denoising performance of SOBF, we propose variants of SOBF, namely, SURE-optimal multiresolution bilateral filter (SMBF), which involves optimal bilateral filtering in a wavelet framework, and SURE-optimal patch-based bilateral filter (SPBF), where the bilateral filter parameters are optimized on small image patches. Using SURE guarantees automated parameter selection. The multiresolution and localized denoising in SMBF and SPBF, respectively, yield superior denoising performance when compared with the globally optimal SOBF. Experimental validations and comparisons show that the proposed denoisers perform on par with some state-of-the-art denoising techniques. (C) 2015 SPIE and IS&T

Hybrid Working Set Algorithm for SVM Learning With a Kernel Coprocessor on FPGA

Support vector machines (SVM) are a popular class of supervised models in machine learning. The associated compute intensive learning algorithm limits their use in real-time applications. This paper presents a fully scalable architecture of a coprocessor, which can compute multiple rows of the kernel matrix in parallel. Further, we propose an extended variant of the popular decomposition technique, sequential minimal optimization, which we call hybrid working set (HWS) algorithm, to effectively utilize the benefits of cached kernel columns and the parallel computational power of the coprocessor. The coprocessor is implemented on Xilinx Virtex 7 field-programmable gate array-based VC707 board and achieves a speedup of upto 25x for kernel computation over single threaded computation on Intel Core i5. An application speedup of upto 15x over software implementation of LIBSVM and speedup of upto 23x over SVMLight is achieved using the HWS algorithm in unison with the coprocessor. The reduction in the number of iterations and sensitivity of the optimization time to variation in cache size using the HWS algorithm are also shown.

MULTI-INSTRUMENT DETECTION IN POLYPHONIC MUSIC USING GAUSSIAN MIXTURE BASED FACTORIAL HMM

We formulate the problem of detecting the constituent instruments in a polyphonic music piece as a joint decoding problem. From monophonic data, parametric Gaussian Mixture Hidden Markov Models (GM-HMM) are obtained for each instrument. We propose a method to use the above models in a factorial framework, termed as Factorial GM-HMM (F-GM-HMM). The states are jointly inferred to explain the evolution of each instrument in the mixture observation sequence. The dependencies are decoupled using variational inference technique. We show that the joint time evolution of all instruments' states can be captured using F-GM-HMM. We compare performance of proposed method with that of Student's-t mixture model (tMM) and GM-HMM in an existing latent variable framework. Experiments on two to five polyphony with 8 instrument models trained on the RWC dataset, tested on RWC and TRIOS datasets show that F-GM-HMM gives an advantage over the other considered models in segments containing co-occurring instruments.

On the Gaussian Many-to-One X Channel

In this paper, the Gaussian many-to-one X channel (XC), which is a special case of general multiuser XC, is studied. In the Gaussian many-to-one XC, communication links exist between all transmitters and one of the receivers, along with a communication link between each transmitter and its corresponding receiver. As per the XC assumption, transmission of messages is allowed on all the links of the channel. This communication model is different from the corresponding manyto- one interference channel (IC). Transmission strategies, which involve using Gaussian codebooks and treating interference from a subset of transmitters as noise, are formulated for the above channel. Sum-rate is used as the criterion of optimality for evaluating the strategies. Initially, a 3 x 3 many-to-one XC is considered and three transmission strategies are analyzed. The first two strategies are shown to achieve sum-rate capacity under certain channel conditions. For the third strategy, a sum-rate outer bound is derived and the gap between the outer bound and the achieved rate is characterized. These results are later extended to the K x K case. Next, a region in which the many-to-one XC can be operated as a many-to-one IC without the loss of sum-rate is identified. Furthermore, in the above region, it is shown that using Gaussian codebooks and treating interference as noise achieve a rate point that is within K/2 -1 bits from the sum-rate capacity. Subsequently, some implications of the above results to the Gaussian many-to-one IC are discussed. Transmission strategies for the many-to-one IC are formulated, and channel conditions under which the strategies achieve sum-rate capacity are obtained. A region where the sum-rate capacity can be characterized to within K/2 -1 bits is also identified. Finally, the regions where the derived channel conditions are satisfied for each strategy are illustrated for a 3 x 3 many-to-one XC and the corresponding many-to-one IC.

Counting zero kernel pairs over a finite field

Helmke et al. have recently given a formula for the number of reachable pairs of matrices over a finite field. We give a new and elementary proof of the same formula by solving the equivalent problem of determining the number of so called zero kernel pairs over a finite field. We show that the problem is, equivalent to certain other enumeration problems and outline a connection with some recent results of Guo and Yang on the natural density of rectangular unimodular matrices over F-qx]. We also propose a new conjecture on the density of unimodular matrix polynomials. (C) 2016 Elsevier Inc. All rights reserved.

On Fast Bilateral Filtering Using Fourier Kernels

It was demonstrated in earlier work that, by approximating its range kernel using shiftable functions, the nonlinear bilateral filter can be computed using a series of fast convolutions. Previous approaches based on shiftable approximation have, however, been restricted to Gaussian range kernels. In this work, we propose a novel approximation that can be applied to any range kernel, provided it has a pointwise-convergent Fourier series. More specifically, we propose to approximate the Gaussian range kernel of the bilateral filter using a Fourier basis, where the coefficients of the basis are obtained by solving a series of least-squares problems. The coefficients can be efficiently computed using a recursive form of the QR decomposition. By controlling the cardinality of the Fourier basis, we can obtain a good tradeoff between the run-time and the filtering accuracy. In particular, we are able to guarantee subpixel accuracy for the overall filtering, which is not provided by the most existing methods for fast bilateral filtering. We present simulation results to demonstrate the speed and accuracy of the proposed algorithm.

FAST AND ACCURATE BILATERAL FILTERING USING GAUSS-POLYNOMIAL DECOMPOSITION

The bilateral filter is a versatile non-linear filter that has found diverse applications in image processing, computer vision, computer graphics, and computational photography. A common form of the filter is the Gaussian bilateral filter in which both the spatial and range kernels are Gaussian. A direct implementation of this filter requires O(sigma(2)) operations per pixel, where sigma is the standard deviation of the spatial Gaussian. In this paper, we propose an accurate approximation algorithm that can cut down the computational complexity to O(1) per pixel for any arbitrary sigma (constant-time implementation). This is based on the observation that the range kernel operates via the translations of a fixed Gaussian over the range space, and that these translated Gaussians can be accurately approximated using the so-called Gauss-polynomials. The overall algorithm emerging from this approximation involves a series of spatial Gaussian filtering, which can be efficiently implemented (in parallel) using separability and recursion. We present some preliminary results to demonstrate that the proposed algorithm compares favorably with some of the existing fast algorithms in terms of speed and accuracy.

Nonparametric Bayesian Density Modeling with Gaussian Processes

We present the Gaussian process density sampler (GPDS), an exchangeable generative model for use in nonparametric Bayesian density estimation. Samples drawn from the GPDS are consistent with exact, independent samples from a distribution defined by a density that is a transformation of a function drawn from a Gaussian process prior. Our formulation allows us to infer an unknown density from data using Markov chain Monte Carlo, which gives samples from the posterior distribution over density functions and from the predictive distribution on data space. We describe two such MCMC methods. Both methods also allow inference of the hyperparameters of the Gaussian process.