Linear Prediction (LP) analysis is commonly used in speech processing. LP is based on Auto-Regressive (AR) model and it estimates the AR model parameter from signals with l2-norm optimization. Recently, sparse estimation is paid attention since it can extract significant features from big data. The sparse estimation is realized by l1 or l0-norm optimization or regularization. Sparse LP analysis methods based on l1-norm optimization have been proposed. Since excitation of speech is not white Gaussian, a sparse LP estimation can estimate more accurate parameter than the conventional l2-norm based LP. These are time-invariant and real-valued analysis. We have been studied Time-Varying Complex AR (TV-CAR) analysis for an analytic signal and have evaluated the performance on speech processing. The TV-CAR methods are l2-norm methods. In this paper, we propose the sparse TV-CAR analysis based on adaptive LASSO (Least absolute shrinkage and selection operator) that is l1-norm regularization and evaluate the performance on F0 estimation of speech using IRAPT (Instantaneous RAPT). The experimental results show that the sparse TV-CAR methods perform better for a high level of additive Pink noise.

Sparse representation has been successfully applied to visual tracking. Recent progresses in sparse tracking are mainly made within the particle filter framework. However, most sparse trackers need to extract complex feature representations for each particle in the limited sample space, leading to expensive computation cost and yielding inferior tracking performance. To deal with the above issues, we propose a novel sparse tracking method based on the circulant reverse lasso model. Benefiting from the properties of circulant matrices, densely sampled target candidates are implicitly generated by cyclically shifting the base feature descriptors, and then embedded into a reverse sparse reconstruction model as a dictionary to encode a robust appearance template. The alternating direction method of multipliers is employed for solving the reverse sparse model and the optimization process can be efficiently solved in the frequency domain, which enables the proposed tracker to run in real-time. The calculated sparse coefficient map represents the similarity scores between the template and circular shifted samples. Thus the target location can be directly predicted according to the coordinates of the peak coefficient. A scale-aware template updating strategy is combined with the correlation filter template learning to take into account both appearance deformations and scale variations. Both quantitative and qualitative evaluations on two challenging tracking benchmarks demonstrate that the proposed algorithm performs favorably against several state-of-the-art sparse representation based tracking methods.

Lasso regression based on the L1 regularization is one of the most popular sparse estimation methods. It is often required to set appropriately in advance the regularization parameter that determines the degree of regularization. Although the empirical Bayes approach provides an effective method to estimate the regularization parameter, its solution has yet to be fully investigated in the lasso regression model. In this study, we analyze the empirical Bayes estimator of the one-parameter model of lasso regression and show its uniqueness and its properties. Furthermore, we compare this estimator with that of the variational approximation, and its accuracy is evaluated.

We propose a novel algorithm for the recovery of non-sparse, but compressible signals from linear undersampled measurements. The algorithm proposed in this paper consists of two steps. The first step recovers the signal by the l1-norm minimization. Then, the second step decomposes the l1 reconstruction into major and minor components. By using the major components, measurements for the minor components of the target signal are estimated. The minor components are further estimated using the estimated measurements exploiting a maximum a posterior (MAP) estimation, which leads to a ridge regression with the regularization parameter determined using the error bound for the estimated measurements. After a slight modification to the major components, the final estimate is obtained by combining the two estimates. Computational cost of the proposed algorithm is mostly the same as the l1-nom minimization. Simulation results for one-dimensional computer generated signals show that the proposed algorithm gives 11.8% better results on average than the l1-norm minimization and the lasso estimator. Simulations using standard images also show that the proposed algorithm outperforms those conventional methods.

This paper presents a novel liver segmentation algorithm that achieves higher performance than conventional algorithms in the segmentation of cases with unusual liver shapes and/or large liver lesions. An L1 norm was introduced to the mean squared difference to find the most relevant cases with an input case from a training dataset. A patient-specific probabilistic atlas was generated from the retrieved cases to compensate for livers with unusual shapes, which accounts for liver shape more specifically than a conventional probabilistic atlas that is averaged over a number of training cases. To make the above process robust against large pathological lesions, we incorporated a novel term based on a set of “lesion bases” proposed in this study that account for the differences from normal liver parenchyma. Subsequently, the patient-specific probabilistic atlas was forwarded to a graph-cuts-based fine segmentation step, in which a penalty function was computed from the probabilistic atlas. A leave-one-out test using clinical abdominal CT volumes was conducted to validate the performance, and proved that the proposed segmentation algorithm with the proposed patient-specific atlas reinforced by the lesion bases outperformed the conventional algorithm with a statistically significant difference.

This paper describes a new method for lossy audio signal compression via compressive sensing (CS). In this method, a structured shrinkage operator is employed to decompose the audio signal into three layers, with two sparse layers, tonal and transient, and additive noise, and then, both the tonal and transient layers are compressed using CS. Since the shrinkage operator is able to take into account the structure information of the coefficients in the transform domain, it is able to achieve a better sparse approximation of the audio signal than traditional methods do. In addition, we propose a sparsity allocation algorithm, which adjusts the sparsity between the two layers, thus improving the performance of CS. Experimental results demonstrated that the new method provided a better compression performance than conventional methods did.