In this paper, we first propose a variational model for the limited-angle computed tomography (CT) image reconstruction and then convert the model into an end-to-end deep network. We use the penalty method to solve th...
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Classifier chain (CC) is a multi-label learning approach that constructs a sequence of binary classifiers according to a label order. Each classifier in the sequence is responsible for predicting the relevance of one ...
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In many applications, it is necessary to retrieve the sub-signal building blocks of a multicomponent signal, which is usually non-stationary in real-world and real-life applications. Empirical mode decomposition (EMD)...
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In nature and engineering world, the measured signals are usually affected by multiple complicated factors and they appear as multicomponent non-stationary modes. In many situations we need to separate these signals t...
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In nature and engineering world, the measured signals are usually affected by multiple complicated factors and they appear as multicomponent non-stationary modes. In many situations we need to separate these signals to a finite number of mono-components to represent the intrinsic modes and underlying dynamics implicated in the source signals. Recently the synchrosqueezing transform (SST) was developed as an empirical mode decomposition (EMD)-like tool to enhance the time-frequency resolution and energy concentration of a multicomponent non-stationary signal and provides more accurate component recovery. To recover individual components, the SST method consists of two steps. First the instantaneous frequency (IF) of a component is estimated from the SST plane. Secondly, after IF is recovered, the associated component is computed by a definite integral along the estimated IF curve on the SST plane. The reconstruction accuracy for a component depends heavily on the accuracy of the IFs estimation carried out in the first step. More recently, a direct method of the time-frequency approach, called signal separation operation (SSO), was introduced for multicomponent signal separation. While both SST and SSO are mathematically rigorous on IF estimation, SSO avoids the second step of the two-step SST method in component recovery (mode retrieval). The SSO method is based the short-time Fourier transform. In this paper we propose a direct method of signal separation based on the adaptive continuous wavelet transform (CWT). We introduce two models of the adaptive CWT-based approach for signal separation: the sinusoidal signal-based model and the linear chirp-based model, which are derived respectively from sinusoidal signal approximation and the linear chirp approximation at any local time. A more accurate component recovery formula is derived from linear chirp local approximation. We present the theoretical analysis of our approach. For each model, we establish the error bound
The synchrosqueezing transform (SST) has been developed as a powerful EMD-like tool for instantaneous frequency (IF) estimation and component separation of non-stationary multicomponent signals. Recently, a direct met...
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Exploiting label correlations is important to multi-label classification. Previous methods capture the high-order label correlations mainly by transforming the label matrix to a latent label space with low-rank matrix...
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In this paper we consider a class of -minimization and wavelet frame-based models for image deblurring and denoising. Mathematically, they can be formulated as minimizing the sum of a data fidelity term and the l0-...
In this paper we consider a class of -minimization and wavelet frame-based models for image deblurring and denoising. Mathematically, they can be formulated as minimizing the sum of a data fidelity term and the l0-'norm' of the framelet coefficients of the underlying image, and we are particularly interested in three different types of data fidelity forms for image restoration problems. We first study the first-order optimality conditions for these models. We then propose a penalty decomposition (PD) method for solving these problems in which a sequence of penalty subproblems are solved by a block coordinate descent (BCD) method. Under some suitable assumptions, we establish that any accumulation point of the sequence generated by the PD method satisfies the first-order optimality conditions of these problems. Moreover, for the problems in which the data fidelity term is convex, we show that such an accumulation point is a local minimizer of the problems. In addition, we show that any accumulation point of the sequence generated by the BCD method is a block coordinate minimizer of the penalty subproblem. Furthermore, under some convexity assumptions on the data fidelity term, we prove that such an accumulation point is a local minimizer of the penalty subproblem. Numerical simulations show that the proposed -minimization methods enjoy great potential for image deblurring and denoising in terms of solution quality and/or speed.
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