Sparse Recovery with Very Sparse Compressed Counting

Compressed sensing (sparse signal recovery) often encounters nonnegative data (e.g., images). Recently we developed the methodology of using (dense) Compressed Counting for recovering nonnegative K-sparse signals. In this paper, we adopt very sparse Compressed Counting for nonnegative signal recovery. Our design matrix is sampled from a maximally-skewed p-stable distribution (0<p<1), and we sparsify the design matrix so that on average (1-g)-fraction of the entries become zero. The idea is related to very sparse stable random projections (Li et al 2006 and Li 2007), the prior work for estimating summary statistics of the data. In our theoretical analysis, we show that, when p->0, it suffices to use M= K/(1-exp(-gK) log N measurements, so that all coordinates can be recovered in one scan of the coordinates. If g = 1 (i.e., dense design), then M = K log N. If g= 1/K or 2/K (i.e., very sparse design), then M = 1.58K log N or M = 1.16K log N. This means the design matrix can be indeed very sparse at only a minor inflation of the sample complexity. Interestingly, as p->1, the required number of measurements is essentially M = 2.7K log N, provided g= 1/K. It turns out that this result is a general worst-case bound

Intelligibility and comprehensibility of the Filipino English accent to Hong Kong English speakers

Intercultural communication between Hong Kong people and Filipinos is common and crucial in Hong Kong as Filipinos are the largest non-local ethnic group, and Filipino domestic helpers play a significant role in households and childcare. This study investigated the phonological patterns of Filipino English and explored the intelligibility and comprehensibility of the English spoken by Filipino domestic helpers to student teachers of English in Hong Kong. By analysing the speech produced by three Filipino English speakers, features of Filipino-accented English were identified. Moreover, by conducting listening-dictation tasks, it was found that the listeners considered 30% and 80.6% of the isolated words and keywords in a passage respectively to be intelligible, and 74.7% of the speech produced by Filipino English speakers was comprehensible. The major types of features of the Filipino English accent, which are also found to be factors which contribute to problems in intelligibility and comprehensibility such as consonant substitutions, deletion of consonants and consonant clusters, no distinction between long and short vowels, replacement of vowels, and shifting of word stress, are discussed in detail in this research paper along with the pedagogical and social implications