Joint modeling of language and vision has been drawing increasing interest. A multimodal data representation allowing for bidirectional retrieval of images by sentences and vice versa is a key aspect of this modeling. In this paper we show that a cross-view mapping of the search space to the query space achieves state of the art performance in bidirectional retrieval using off the shelf feature...

Markowitz’s portfolio selection problem chooses weights for stocks in a portfolio based on a covariance matrix of stock returns. Our study proposes to reduce noise in the estimated covariance matrix using a Tikhonov filter function. In addition, we propose a new strategy to resolve the rank deficiency of the covariance matrix, and a method to choose a Tikhonov parameter which determines a filte...

This paper proposes an iterative computation of sparse representations of functions defined on Rd , which exploits a formulation of the sparsification problem equivalent to Support Vector Machine and based on Tikhonov regularization. Through this equivalent formulation, the sparsification reduces to an approximation problem with a Tikhonov regularizer, which selects the null coefficients of the...

Kalman filter is one of the most common ways to deal with dynamic data and has been widely used in project fields. However, the accuracy of Kalman filter for discrete dynamic system is poor when the observation matrix is ill-conditioned. Therefore, the method for overcoming the harmful effect caused by ill-conditioned observation matrix in discrete dynamic system is studied in this paper. First...

Motivated from the theoretical and practical results in compressed sensing, efforts have been undertaken by the inverse problems community to derive analogous results, for instance linear convergence rates, for Tikhonov regularization with `1-penalty term for the solution of ill-posed equations. Conceptually, the main difference between these two fields is that regularization in general is an u...

We present an image reconstruction method for diffuse optical tomography (DOT) by using the sparsity regularization and expectation-maximization (EM) algorithm. Typical image reconstruction approaches in DOT employ Tikhonov-type regularization, which imposes restrictions on the L(2) norm of the optical properties (absorption/scattering coefficients). It tends to cause a blurring effect in the r...

In this paper we prove some new converse and saturation results for Tikhonov regularization of linear ill-posed problems Tx = y, where T is a linear operator between two Hilbert spaces.

We investigate the Tikhonov regularization of control constrained optimal control problems. We use a specialized source condition in combination with a condition on the active sets. In the case of high convergence rates, these conditions are necessary and sufficient.