Compressive sensing (CS) reconstruction of a spectrum-sparse signal from undersampled data is, in fact, an ill-posed problem. In this paper, we mathematically prove that, in certain cases, the exact CS reconstruction of a spectrum-sparse signal from undersampled data is impossible. Then we present the exact CS reconstruction condition of undersampled spectrum-sparse signals, which is valuable for digital signal compression.

Content-based image retrieval is nowadays one of the possible and promising solutions to manage image databases effectively. However, with the large number of images, there still exists a great discrepancy between the users’ expectations (accuracy and efficiency) and the real performance in image retrieval. In this work, new optimization strategies are proposed on vocabulary tree building, retrieval, and matching methods. More precisely, a new clustering strategy combining classification and conventional $K$-Means method is firstly redefined. Then a new matching technique is built to eliminate the error caused by large-scaled scale-invariant feature transform (SIFT). Additionally, a new unit mechanism is proposed to reduce the cost of indexing time. Finally, the numerical results show that excellent performances are obtained in both accuracy and efficiency based on the proposed improvements for image retrieval.

Human action recognition is an important area of human action recognition research. Focusing on the problem of self-occlusion in the field of human action recognition, a new adaptive occlusion state behavior recognition approach was presented based on Markov random field and probabilistic Latent Semantic Analysis (pLSA). Firstly, the Markov random field was used to represent the occlusion relationship between human body parts in terms an occlusion state variable by phase space obtained. Then, we proposed a hierarchical area variety model. Finally, we use the topic model of pLSA to recognize the human behavior. Experiments were performed on the KTH, Weizmann, and Humaneva dataset to test and evaluate the proposed method. The compared experiment results showed that what the proposed method can achieve was more effective than the compared methods.

Finding similar images to a given query image can be computed by different distance measures. One of the general distance measures is the Earth Mover’s Distance (EMD). Although EMD has proven its ability to retrieve similar images in an average precision of around 95%, high execution time is its major drawback. Embedding EMD into L₁ is a solution that solves this problem by sacrificing performance; however, it generates a heavily tailed image feature vector. We aimed to reduce the execution time of embedded EMD and increase its performance using three dimension reduction methods: sampling, sketching, and Dimension Reduction in Embedding by Adjustment in Tail (DREAT). Sampling is a method that randomly picks a small fraction of the image features. On the other hand, sketching is a distance estimation method that is based on specific summary statistics. The last method, DREAT, randomly selects an equally distributed fraction of the image features. We tested the methods on handwritten Persian digit images. Our first proposed method, sampling, reduces execution time by sacrificing the recognition performance. The sketching method outperforms sampling in the recognition, but it records higher execution time. The DREAT outperforms sampling and sketching in both the execution time and performance.