Learning effective feature descriptors that bridge the semantic gap between low-level visual features directly extracted from image pixels and the corresponding high-level semantics perceived by humans is a challenging task in image retrieval. This paper proposes a hybrid deep learning architecture (HDLA) that generates sparse latent topic-based representation with the objective of minimizing the semantic gap problem in image retrieval. In fact, HDLA has a deep network structure with a constrained replicated Softmax Model in the lower layer and constrained restricted Boltzmann machines in the upper layers. The advantage of HDLA is that there exist nonnegativity restrictions on the model weights together with $$\ell _1$$ -sparsity enforced over the activations of the hidden layer nodes of the network. This, in turn, enhances the modeling power of the network and leads to sparse, parts-based latent topic representation of images. Experimental results on various benchmark datasets show that the proposed model exhibits better generalization ability and the resulting high-level abstraction yields better retrieval performance as compared to state-of-the-art latent topic-based image representation schemes.

Resolution analysis for the problem of signal recovery from finitely many linear samples is the subject of the paper. The classical Rayleigh limit serves only as a lower bound on resolution since it does not assume any recovery strategy and is based only on observed data. The authors show that details finer than the Rayleigh limit can be recovered by simple linear processing that incorporates prior information. They first define a measure of resolution based on allowable levels of error that is more appropriate for current signal recovery strategies than the Rayleigh definition. In the practical situation in which only finitely many noisy observations are available, one must restrict the class of signals in order to make the resolution measure meaningful. They consider the set of bandlimited and essentially time-limited signals since it describes most signals encountered in practice. For this set they show how to precompute resolution limits from knowledge of measurement functionals, signal-to-noise ratio, passband, energy concentration regions, energy concentration factor, and a prescribed level of error tolerance. In the process they also derive an algorithm for high resolution signal recovery. They illustrate the results with an example.

The problem of tomographic reconstruction from a few discrete projections is addressed. When the projection data are discrete and few in number, the image formed by the convolution back-projection algorithm may not be consistent with the observed projections and is known to exhibit artifacts. Hence, the problem formulated here is one of finding an image that is closest to a nominal and is consistent with the projection data and other convex constraints such as positivity. The measure of closeness used is a Hilbert space norm, typically a weighted sum/integral of squares, with weights used to reflect expected deviation from the nominal in different regions. In the absence of constraints, this approach leads to a direct, noniterative algorithm (based on a simple matrix-vector computation) for construction of the image. When additional convex constraints such as positivity and upper-bounds need to be enforced on the reconstructed image to improve resolution, a quadratically convergent Newton algorithm is suggested.>

Parameter estimation for superimposed chirp signals is a difficult signal processing problem that shows up in many applications. Cramer-Rao lower bounds are derived here for the error variance in the parameter estimates. The approach reported uses global Hankel rank reduction to estimate instantaneous frequencies followed by total least squares fitting to obtain initial estimates of the parameters. These estimates are used to initialize a search for the maximum likelihood estimates. Results on synthetic data are compared with the Cramer-Rao lower bounds.>

This paper is a tutorial on linear, state space, model-based methods for certain nonlinear estimation problems commonly encountered in signal and data analysis. A prototypical problem that is studied is that of estimating the frequencies of multiple, superimposed sinusoids from a short record of noise-corrupted data. The approach expounded however, is applicable to a vast range of nonlinear signal analysis problems and applications in direction finding and damped sinusoid retrieval are dealt with in some detail. The benefits that result from using a state space description of the signal are highlighted in this paper. It is shown that state space models provide an elegant tool for exposing the structure present in the problem. The approach also allows for robust parameterization of the model with respect to finite precision errors. The robustness of the parameter set is complemented by the availability of numerically robust tools to estimate the parameters. The resulting algorithms are compatible with multiprocessor implementations.>

The problem of partitioning the vertex set of an edge-weighted undirected graph into two parts of specified sizes so that the cost of the partition defined as the sum of the weights on edges joining vertices in different parts is minimized is addressed. This problem is NP-hard and has several important applications in VLSI layout, where the graph size is typically large and the brute-force approach of listing all feasible partitions and comparing costs is computationally prohibitive. It is shown that if the n*n connection matrix of the graph has rank p, then the search can be confined to a smaller set of n/sup p(p+1)/2/ partitions. Procedures are developed for constructing all such partitions in O(n/sup p(p+3)/2/) time. For matrices with large rank, a principal components approximation of the connection matrix is suggested. The algorithms provide a bound on the proximity of the cost of the constructed partition to the optimal cost based on the eigenvalues left out in the rank reduction process.>

A rational model is proposed for reconstruction of bandlimited signals from successive observations, bandlimits, and knowledge of signal peak location. The singular values of a matrix constructed from this information, display the error in modeling this data with rational models of different candidate orders. The parameters of the approximate model may be estimated from the singular vectors. The proposed approach has good spectral resolution ability and a certain degree of robustness to errors in data.>

The problem of tracking the frequencies of slowly time-varying superimposed sinusoids in the presence of noise is addressed. An algorithm based on singular value decomposition (SVD) of the data matrix is developed for the problem, and its performance is evaluated by numerical experiments on computer-synthesized data. The algorithm is based on the discovery that even when the frequencies are changing with time, as long as they change slowly locally, a Hankel matrix constructed directly from the noise-free signal is close to a matrix of rank equal to twice the number of real-valued sinusoids superimposed in the signal. Thus, in the presence of additive noise, instead of using the SVD of many small matrices constructed from local blocks of data, all the available data can be included in one large matrix, which can then be approximated by its principal singular vectors and singular values, to achieve greater noise suppression. The number of sinusoidal components and the instantaneous frequency tracks are directly estimated from the principal singular vectors of the large Hankel matrix.>

The authors suggest a modification of the Toeplitz approximation method for estimating frequencies of multiple sinusoids from covariance measurements. The method constructs a state-feedback matrix following a low-rank approximation of the Toeplitz covariance matrix via singular-value decomposition. Ideally, the eigenvalues of this state-feedback matrix will be on the unit circle in the complex plane, and the angles that they make with the real axis will be equal to the unknown sinusoid frequencies. The modification proposed here exploits this prior knowledge of the modulus of the eigenvalues and guarantees that even in the presence of noise the eigenvalues of the estimated state-feedback matrix will lie on the unit circle.>

Presented in this paper are three design methods that use singular value decomposition and principal components analysis to construct IIR filters that approximate a desired filter response. The desired response may be specified in either the time domain or the frequency domain. The singular values of certain Hankel matrices constructed from the filter specifications, display the error in approximating the desired response by filters of different orders. The designer chooses the filter order based on the error that can be tolerated. An advantage common to these methods is that the user does not have to prespecify the filter order. Two of the new design methods have an additional advantage: They can be used when only the desired amplitude-response of the filter is specified, and the filter's phase response is unimportant. (Finally, in comparison to some extant design methods, the methods investigated here, seem to produce high-quality filters using lower orders.)

This paper presents a new algorithm for the extrapolation of multidimensional bandlimited sequences. The new algorithm is capable of incorporating prior knowledge of the concentration of signal energy on a finite region and imposes no restriction on either the location of observations from the multidimensional signal to be extrapolated or the shape of its passband.

Two point sets {pi} and {p'i}; i = 1, 2,..., N are related by p'i = Rpi + T + Ni, where R is a rotation matrix, T a translation vector, and Ni a noise vector. Given {pi} and {p'i}, we present an algorithm for finding the least-squares solution of R and T, which is based on the singular value decomposition (SVD) of a 3 × 3 matrix. This new algorithm is compared to two earlier algorithms with respect to computer time requirements.

This paper describes the development of a wavefront-based language and architecture for a programmable special-purpose multiprocessor array. Based on the notion of computational wavefront, the hardware of the processor array is designed to provide a computing medium that preserves the key properties of the wavefront. In conjunction, a wavefront language (MDFL) is introduced that drastically reduces the complexity of the description of parallel algorithms and simulates the wavefront propagation across the computing network. Together, the hardware and the language lead to a programmable wavefront array processor (WAP). The WAP blends the advantages of the dedicated systolic array and the general-purpose data-flow machine, and provides a powerful tool for the high-speed execution of a large class of matrix operations and related algorithms which have widespread applications.