To meet the growing demand of wireless and power efficient neural recordings systems, we demonstrate an unsupervised dictionary learning algorithm in Compressed Sensing (CS) framework which can be implemented in VLSI systems. Without prior label information of neural spikes, we extend our previous work to unsupervised learning and construct a dictionary with discriminative structures for spike sorting. To further improve the reconstruction and classification performance, we proposed a joint prediction to determine the class of neural spikes in dictionary learning. When the neural spikes is compressed 50 times, our approach can achieve an average gain of 2 dB and 15 percentage units over state-of-the-art of CS approaches in terms of the reconstruction quality and classification accuracy respectively.

Model-based compressive sensing (CS) exploits the structure inherent in sparse signals for the design of better signal recovery algorithms. This information about structure is often captured in the form of a prior on the sparse coefficients, with the Laplacian being the most common such choice (leading to l1 -norm minimization). Recent work has exploited the discriminative capability of sparse representations for image classification by employing class-specific dictionaries in the CS framework. Our contribution is a logical extension of these ideas into structured sparsity for classification. We introduce the notion of discriminative class-specific priors in conjunction with class specific dictionaries, specifically the spike-and-slab prior widely applied in Bayesian sparse regression. Significantly, the proposed framework takes the burden off the demand for abundant training image samples necessary for the success of sparsity-based classification schemes. We demonstrate this practical benefit of our approach in important applications, such as face recognition and object categorization.

Promising results have been achieved in image classification problems by exploiting the discriminative power of sparse representations for classification (SRC). Recently, it has been shown that the use of class-specific spike-and-slab priors in conjunction with the class-specific dictionaries from SRC is particularly effective in low training scenarios. As a logical extension, we build on this framework for multitask scenarios, wherein multiple representations of the same physical phenomena are available. We experimentally demonstrate the benefits of mining joint information from different camera views for multi-view face recognition.

Dictionary learning techniques have gained tremendous success in many classification problems. Inspired by the dirty model for multi-task regression problems, we proposed a novel method called group-structured dirty dictionary learning (GDDL) that incorporates the group structure (for each task) with the dirty model (across tasks) in the dictionary training process. Its benefits are two-fold: 1) the group structure enforces implicitly the label consistency needed between dictionary atoms and training data for classification; and 2) for each class, the dirty model separates the sparse coefficients into ones with shared support and unique support, with the first set being more discriminative. We use proximal operators and block coordinate decent to solve the optimization problem. GDDL has been shown to give state-of-art result on both synthetic simulation and two face recognition datasets.

In this paper, we propose a new video frame interpolation technique by a locally-adaptive robust principal component analysis (RPCA) with weight priors. The proposed algorithm relies on two main steps: 1. the pre-processing step initializes the new frame by a simplified motion-compensated frame interpolation and assigns each pixel a confident weight based on both the difference of motion estimation and local consistency; and 2. the refinement step updates the frame by a proposed weighted robust principal component analysis (WRPCA) algorithm. Experiments demonstrate that the proposed method outperforms the state-of-the-art algorithms, both in visual quality and PSNR performance.

Sparse modeling has demonstrated its superior performances in many applications. Compared to optimization based approaches, Bayesian sparse modeling generally provides a more sparse result with a knowledge of confidence. Using the Spike and Slab priors, we propose the hierarchical sparse models for the scenario of single task and multitask - Hi-BCS and CHi-BCS. We draw the connections of these two methods to their optimization based counterparts and use expectation propagation for inference. The experiment results using synthetic and real data demonstrate that the performance of Hi-BCS and Chi-BCS are comparable or better than their optimization based counterparts.

Model-based compressive sensing (CS) exploits the structure inherent in sparse signals for the design of better signal recovery algorithms. This information about structure is often captured in the form of a prior on the sparse coefficients, the Laplacian being the most common such choice (leading to l1-norm minimization). The recent seminal contribution by Wright et al. exploits the discriminative capability of sparse representations for image classification, specifically face recognition. Their approach employs the analytical framework of CS with class-specific dictionaries. Our contribution is a logical extension of these ideas into structured sparsity for classification. We use class-specific dictionaries in conjunction with discriminative class-specific priors, specifically the spike-and-slab prior widely applied in Bayesian regression. Significantly, the proposed framework takes the burden off the demand for abundant training image samples necessary for the success of sparsity-based classification schemes.

We demonstrate a method to build signal dependent sparse representation dictionary for neural action potentials using K-SVD algorithm and Discrete Wavelets Transform. We also show a method to utilize this dictionary to recover the neural signal in the Compressive Sensing (CS) framework. Comparing against the non-signal dependent CS recovery algorithms, this new recovery algorithm can achieve same reconstruction quality with 2.5 times less compressed sensing measurements. For the same compression ratio, the purposed approach can increase recovery signal's signal to noise and distortion ratio (SNDR) by around 6 dB compare to non-signal dependent recovery method. We also evaluated the recovered signal using spike sorting techniques. The results have shown that the spikes clusters still maintain clear separation even when the compression ratio is at 15-20% of the Nyquist rate. This work also implies that any hardware implementation of compressed sensing could be scaled down in term of power and chip area by the same order if this signal dependent framework is used to recover the signal.