Lorentzian Iterative Hard Thresholding: Robust Compressed Sensing with Prior Information

Commonly employed reconstruction algorithms in compressed sensing (CS) use the $L_2$ norm as the metric for the residual error. However, it is well-known that least squares (LS) based estimators are highly sensitive to outliers present in the measurement vector leading to a poor performance when the noise no longer follows the Gaussian assumption but, instead, is better characterized by heavier-than-Gaussian tailed distributions. In this paper, we propose a robust iterative hard Thresholding (IHT) algorithm for reconstructing sparse signals in the presence of impulsive noise. To address this problem, we use a Lorentzian cost function instead of the $L_2$ cost function employed by the traditional IHT algorithm. We also modify the algorithm to incorporate prior signal information in the recovery process. Specifically, we study the case of CS with partially known support. The proposed algorithm is a fast method with computational load comparable to the LS based IHT, whilst having the advantage of robustness against heavy-tailed impulsive noise. Sufficient conditions for stability are studied and a reconstruction error bound is derived. We also derive sufficient conditions for stable sparse signal recovery with partially known support. Theoretical analysis shows that including prior support information relaxes the conditions for successful reconstruction. Simulation results demonstrate that the Lorentzian-based IHT algorithm significantly outperform commonly employed sparse reconstruction techniques in impulsive environments, while providing comparable performance in less demanding, light-tailed environments. Numerical results also demonstrate that the partially known support inclusion improves the performance of the proposed algorithm, thereby requiring fewer samples to yield an approximate reconstruction.Comment: 28 pages, 9 figures, accepted in IEEE Transactions on Signal Processin

Smile detection in the wild based on transfer learning

Smile detection from unconstrained facial images is a specialized and challenging problem. As one of the most informative expressions, smiles convey basic underlying emotions, such as happiness and satisfaction, which lead to multiple applications, e.g., human behavior analysis and interactive controlling. Compared to the size of databases for face recognition, far less labeled data is available for training smile detection systems. To leverage the large amount of labeled data from face recognition datasets and to alleviate overfitting on smile detection, an efficient transfer learning-based smile detection approach is proposed in this paper. Unlike previous works which use either hand-engineered features or train deep convolutional networks from scratch, a well-trained deep face recognition model is explored and fine-tuned for smile detection in the wild. Three different models are built as a result of fine-tuning the face recognition model with different inputs, including aligned, unaligned and grayscale images generated from the GENKI-4K dataset. Experiments show that the proposed approach achieves improved state-of-the-art performance. Robustness of the model to noise and blur artifacts is also evaluated in this paper

Exploiting Prior Knowledge in Compressed Sensing Wireless ECG Systems

Recent results in telecardiology show that compressed sensing (CS) is a promising tool to lower energy consumption in wireless body area networks for electrocardiogram (ECG) monitoring. However, the performance of current CS-based algorithms, in terms of compression rate and reconstruction quality of the ECG, still falls short of the performance attained by state-of-the-art wavelet based algorithms. In this paper, we propose to exploit the structure of the wavelet representation of the ECG signal to boost the performance of CS-based methods for compression and reconstruction of ECG signals. More precisely, we incorporate prior information about the wavelet dependencies across scales into the reconstruction algorithms and exploit the high fraction of common support of the wavelet coefficients of consecutive ECG segments. Experimental results utilizing the MIT-BIH Arrhythmia Database show that significant performance gains, in terms of compression rate and reconstruction quality, can be obtained by the proposed algorithms compared to current CS-based methods.Comment: Accepted for publication at IEEE Journal of Biomedical and Health Informatic

Rank Conditioned Rank Selection Filters for Signal Restoration

A class of nonlinear filters called rank conditioned rank selection (RCRS) filters is developed and analyzed in this paper. The RCRS filters are developed within the general framework of rank selection(RS) filters, which are filters constrained to output an order statistic from the observation set. Many previously proposed rank order based filters can be formulated as RS filters. The only difference between such filters is in the information used in deciding which order statistic to output. The information used by RCRS filters is the ranks of selected input samples, hence the name rank conditioned rank selection filters. The number of input sample ranks used is referred to as the order of the RCRS filter. The order can range from zero to the number of samples in the observation window, giving the filters valuable flexibility. Low-order filters can give good performance and are relatively simple to optimize and implement. If improved performance is demanded, the order can be increased but at the expense of filter simplicity. In this paper, many statistical and deterministic properties of the RCRS filters are presented. A procedure for optimizing over the class of RCRS filters is also presented. Finally, extensive computer simulation results that illustrate the performance of RCRS filters in comparison with other techniques in image restoration applications are presented

Partition-based Interpolation for Color Filter Array Demosaicking and Super-Resolution Reconstruction

A class of partition-based interpolators that addresses a variety of image interpolation applications are proposed. The proposed interpolators first partition an image into a finite set of partitions that capture local image structures. Missing high resolution pixels are then obtained through linear operations on neighboring pixels that exploit the captured image structure. By exploiting the local image structure, the proposed algorithm produces excellent performance on both edge and uniform regions. The presented results demonstrate that partition-based interpolation yields results superior to traditional and advanced algorithms in the applications of color filter array (CFA) demosaicking and super-resolution reconstruction