\u0388\u03bd\u03b1\u03c2 \u03c0\u03b5\u03c1\u03b9\u03bf\u03c1\u03b9\u03c3\u03bc\u03cc\u03c2 \u03c0\u03bf\u03c5 \u03b1\u03c0\u03b1\u03bd\u03c4\u03ac\u03c4\u03b1\u03b9 \u03c3\u03c5\u03c7\u03bd\u03ac \u03c3\u03c4\u03b1 \u03b1\u03c3\u03cd\u03c1\u03bc\u03b1\u03c4\u03b1 \u03b4\u03af\u03ba\u03c4\u03c5\u03b1 \u03b1\u03b9\u03c3\u03b8\u03b7\u03c4\u03ae\u03c1\u03c9\u03bd \u03b5\u03af\u03bd\u03b1\u03b9 \u03c4\u03b1 \u03c0\u03b5\u03c1\u03b9\u03bf\u03c1\u03b9\u03c3\u03bc\u03ad\u03bd\u03b1 \u03b1\u03c0\u03bf\u03b8\u03ad\u03bc\u03b1\u03c4\u03b1 \u03c4\u03b7\u03c2 \u03bc\u03c0\u03b1\u03c4\u03b1\u03c1\u03af\u03b1\u03c2. \u0397 \u03bc\u03b5\u03af\u03c9\u03c3\u03b7 \u03c4\u03bf\u03c5 \u03cc\u03b3\u03ba\u03bf\u03c5 \u03c4\u03c9\u03bd \u03b4\u03b5\u03b4\u03bf\u03bc\u03ad\u03bd\u03c9\u03bd \u03c0\u03bf\u03c5 \u03b1\u03c0\u03bf\u03c3\u03c4\u03ad\u03bb\u03bb\u03bf\u03bd\u03c4\u03b1\u03b9 \u03b1\u03c0\u03cc \u03c4\u03bf\u03c5\u03c2 \u03b1\u03b9\u03c3\u03b8\u03b7\u03c4\u03ae\u03c1\u03b5\u03c2 \u03ad\u03c7\u03b5\u03b9 \u03b4\u03b9\u03c0\u03bb\u03cc \u03c1\u03cc\u03bb\u03bf: \u03b1\u03c6\u03b5\u03bd\u03cc\u03c2 \u03b1\u03c5\u03be\u03ac\u03bd\u03b5\u03b9 \u03c4\u03b7\u03bd \u03b1\u03c5\u03c4\u03bf\u03bd\u03bf\u03bc\u03af\u03b1 \u03c4\u03bf\u03c5 \u03c3\u03c5\u03c3\u03c4\u03ae\u03bc\u03b1\u03c4\u03bf\u03c2 \u03ba\u03b1\u03b9 \u03b1\u03c6\u03b5\u03c4\u03ad\u03c1\u03bf\u03c5 \u03bc\u03b5\u03b9\u03ce\u03bd\u03b5\u03b9 \u03c4\u03bf \u03ba\u03cc\u03c3\u03c4\u03bf\u03c2 \u03c4\u03b7\u03bb\u03b5\u03bc\u03b5\u03c4\u03c1\u03af\u03b1\u03c2 \u03b5\u03be\u03b1\u03b9\u03c4\u03af\u03b1\u03c2 \u03c4\u03bf\u03c5 \u03c0\u03b5\u03c1\u03b9\u03bf\u03c1\u03b9\u03c3\u03bc\u03ad\u03bd\u03bf\u03c5 \u03cc\u03b3\u03ba\u03bf\u03c5 \u03b4\u03b5\u03b4\u03bf\u03bc\u03ad\u03bd\u03c9\u03bd \u03c0\u03bf\u03c5 \u03b1\u03c0\u03bf\u03c3\u03c4\u03ad\u03bb\u03bb\u03bf\u03bd\u03c4\u03b1\u03b9. \u03a3\u03b5 \u03ad\u03bd\u03b1 \u03c3\u03cd\u03c3\u03c4\u03b7\u03bc\u03b1 \u03b4\u03b9\u03b1\u03c7\u03b5\u03af\u03c1\u03b9\u03c3\u03b7\u03c2 \u03c5\u03b4\u03ac\u03c4\u03b9\u03bd\u03c9\u03bd \u03c0\u03cc\u03c1\u03c9\u03bd, \u03ba\u03c1\u03af\u03c3\u03b9\u03bc\u03bf \u03b6\u03ae\u03c4\u03b7\u03bc\u03b1 \u03b1\u03c0\u03bf\u03c4\u03b5\u03bb\u03b5\u03af \u03b5\u03c0\u03af\u03c3\u03b7\u03c2 \u03b7 \u03b5\u03bc\u03c0\u03b9\u03c3\u03c4\u03b5\u03c5\u03c4\u03b9\u03ba\u03cc\u03c4\u03b7\u03c4\u03b1 \u03c4\u03c9\u03bd \u03b4\u03b5\u03b4\u03bf\u03bc\u03ad\u03bd\u03c9\u03bd. \u038c\u03c4\u03b1\u03bd, \u03b3\u03b9\u03b1 \u03c0\u03b1\u03c1\u03ac\u03b4\u03b5\u03b9\u03b3\u03bc\u03b1, \u03c0\u03b5\u03c1\u03b9\u03bb\u03b1\u03bc\u03b2\u03ac\u03bd\u03bf\u03bd\u03c4\u03b1\u03b9 \u03b4\u03b5\u03b4\u03bf\u03bc\u03ad\u03bd\u03b1 \u03ba\u03b1\u03c4\u03b1\u03bd\u03ac\u03bb\u03c9\u03c3\u03b7\u03c2 \u03b1\u03c0\u03cc \u03bf\u03b9\u03ba\u03b9\u03b1\u03ba\u03bf\u03cd\u03c2 \u03bc\u03b5\u03c4\u03c1\u03b7\u03c4\u03ad\u03c2. \u039f\u03b9 \u03c0\u03b1\u03c1\u03b1\u03c0\u03ac\u03bd\u03c9 \u03c3\u03c4\u03cc\u03c7\u03bf\u03b9 \u03bc\u03c0\u03bf\u03c1\u03bf\u03cd\u03bd \u03bd\u03b1 \u03b5\u03c0\u03b9\u03c4\u03b5\u03c5\u03c7\u03b8\u03bf\u03cd\u03bd \u03bc\u03b5 \u03c7\u03c1\u03ae\u03c3\u03b7 \u03c4\u03b7\u03c2 \u03c4\u03b5\u03c7\u03bd\u03b9\u03ba\u03ae\u03c2 \u03c3\u03c5\u03bc\u03c0\u03b9\u03b5\u03c3\u03c4\u03b9\u03ba\u03ae\u03c2 \u03b4\u03b5\u03b9\u03b3\u03bc\u03b1\u03c4\u03bf\u03bb\u03b7\u03c8\u03af\u03b1\u03c2 \u03b7 \u03bf\u03c0\u03bf\u03af\u03b1 \u03b5\u03c0\u03b9\u03c4\u03c5\u03b3\u03c7\u03ac\u03bd\u03b5\u03b9 \u03c5\u03c8\u03b7\u03bb\u03ae \u03c3\u03c5\u03bc\u03c0\u03af\u03b5\u03c3\u03b7 \u03c4\u03c9\u03bd \u03b4\u03b5\u03b4\u03bf\u03bc\u03ad\u03bd\u03c9\u03bd \u03ba\u03b1\u03b8\u03ce\u03c2 \u03ba\u03b1\u03b9 \u03c4\u03b7\u03bd \u03c4\u03b1\u03c5\u03c4\u03cc\u03c7\u03c1\u03bf\u03bd\u03b7 \u03ba\u03c1\u03c5\u03c0\u03c4\u03bf\u03b3\u03c1\u03ac\u03c6\u03b7\u03c3\u03ae \u03c4\u03bf\u03c5\u03c2.<\/p>\n
\u0397 \u03c3\u03c5\u03bc\u03c0\u03b9\u03b5\u03c3\u03c4\u03b9\u03ba\u03ae \u03b4\u03b5\u03b9\u03b3\u03bc\u03b1\u03c4\u03bf\u03bb\u03b7\u03c8\u03af\u03b1 \u03c0\u03c1\u03b1\u03b3\u03bc\u03b1\u03c4\u03bf\u03c0\u03bf\u03b9\u03b5\u03af\u03c4\u03b1\u03b9 \u03c3\u03b5 \u03b4\u03c5\u03bf \u03b5\u03c0\u03af\u03c0\u03b5\u03b4\u03b1: \u03c3\u03c4\u03b1 \u03ac\u03ba\u03c1\u03b1 \u03c4\u03bf\u03c5 \u03b4\u03b9\u03ba\u03c4\u03cd\u03bf\u03c5 \u03ba\u03b1\u03b9 \u03c3\u03c4\u03bf \u03ba\u03ad\u03bd\u03c4\u03c1\u03bf \u03b5\u03bb\u03ad\u03b3\u03c7\u03bf\u03c5. \u0391\u03c1\u03c7\u03b9\u03ba\u03ac, \u03b5\u03c6\u03b1\u03c1\u03bc\u03cc\u03b6\u03b5\u03c4\u03b1\u03b9 \u03b7 \u03c3\u03c5\u03bc\u03c0\u03af\u03b5\u03c3\u03b7 \u03c4\u03c9\u03bd \u03b4\u03b5\u03b4\u03bf\u03bc\u03ad\u03bd\u03c9\u03bd \u03c3\u03c4\u03b1 \u03ac\u03ba\u03c1\u03b1 \u03c4\u03bf\u03c5 \u03b4\u03b9\u03ba\u03c4\u03cd\u03bf\u03c5. \u0388\u03c3\u03c4\u03c9 x \u03c4\u03bf \u03b1\u03c1\u03c7\u03b9\u03ba\u03cc \u03b4\u03b9\u03ac\u03bd\u03c5\u03c3\u03bc\u03b1 \u03b4\u03b5\u03b4\u03bf\u03bc\u03ad\u03bd\u03c9\u03bd \u03bc\u03ae\u03ba\u03bf\u03c5\u03c2 \u039d. \u03a4\u03bf \u03c3\u03c5\u03bc\u03c0\u03b9\u03b5\u03c3\u03bc\u03ad\u03bd\u03bf \u03b4\u03b9\u03ac\u03bd\u03c5\u03c3\u03bc\u03b1 y \u03bc\u03ae\u03ba\u03bf\u03c5\u03c2 \u039c \u03b4\u03af\u03bd\u03b5\u03c4\u03b1\u03b9 \u03b1\u03c0\u03cc \u03c4\u03b7 \u03c3\u03c7\u03ad\u03c3\u03b7 y = \u03a6\u00b7x. \u039f \u03c0\u03af\u03bd\u03b1\u03ba\u03b1\u03c2 \u03a6, \u03b4\u03b9\u03b1\u03c3\u03c4\u03ac\u03c3\u03b5\u03c9\u03bd MxN, \u03bc\u03bf\u03bd\u03c4\u03b5\u03bb\u03bf\u03c0\u03bf\u03b9\u03b5\u03af \u03c4\u03b7 \u03b4\u03b9\u03b1\u03b4\u03b9\u03ba\u03b1\u03c3\u03af\u03b1 \u03b3\u03c1\u03b1\u03bc\u03bc\u03b9\u03ba\u03ae\u03c2 \u03c5\u03c0\u03bf\u03b4\u03b5\u03b9\u03b3\u03bc\u03b1\u03c4\u03bf\u03bb\u03b7\u03c8\u03af\u03b1\u03c2. \u039c\u03b5\u03c1\u03b9\u03ba\u03ac \u03c0\u03b1\u03c1\u03b1\u03b4\u03b5\u03af\u03b3\u03bc\u03b1\u03c4\u03b1 \u03c0\u03b9\u03bd\u03ac\u03ba\u03c9\u03bd \u03c0\u03bf\u03c5 \u03b5\u03b3\u03b3\u03c5\u03ce\u03bd\u03c4\u03b1\u03b9 \u03c4\u03b7\u03bd \u03b1\u03ba\u03c1\u03b9\u03b2\u03ae \u03b1\u03bd\u03b1\u03ba\u03b1\u03c4\u03b1\u03c3\u03ba\u03b5\u03c5\u03ae \u03c4\u03bf\u03c5 \u03b1\u03c1\u03c7\u03b9\u03ba\u03bf\u03cd \u03b4\u03b9\u03b1\u03bd\u03cd\u03c3\u03bc\u03b1\u03c4\u03bf\u03c2 x \u03b1\u03c0\u03cc \u03c4\u03b9\u03c2 \u03c3\u03c5\u03bc\u03c0\u03b9\u03b5\u03c3\u03bc\u03ad\u03bd\u03b5\u03c2 \u03bc\u03b5\u03c4\u03c1\u03ae\u03c3\u03b5\u03b9\u03c2 y \u03b1\u03c0\u03bf\u03c4\u03b5\u03bb\u03bf\u03cd\u03bd \u03c0\u03af\u03bd\u03b1\u03ba\u03b5\u03c2 \u03c4\u03c9\u03bd \u03bf\u03c0\u03bf\u03af\u03c9\u03bd \u03c4\u03b1 \u03c3\u03c4\u03bf\u03b9\u03c7\u03b5\u03af\u03b1 \u03b5\u03c0\u03b9\u03bb\u03ad\u03b3\u03bf\u03bd\u03c4\u03b1\u03b9 \u03c4\u03c5\u03c7\u03b1\u03af\u03b1 \u03b1\u03c0\u03cc Gaussian, Bernoulli, \u03ba.\u03ac. \u03ba\u03b1\u03c4\u03b1\u03bd\u03bf\u03bc\u03ad\u03c2. \u03a3\u03c4\u03bf \u03ba\u03ad\u03bd\u03c4\u03c1\u03bf \u03b5\u03bb\u03ad\u03b3\u03c7\u03bf\u03c5 \u03c0\u03c1\u03b1\u03b3\u03bc\u03b1\u03c4\u03bf\u03c0\u03bf\u03b9\u03b5\u03af\u03c4\u03b1\u03b9 \u03b7 \u03b1\u03c0\u03bf\u03c3\u03c5\u03bc\u03c0\u03af\u03b5\u03c3\u03b7 \u03c4\u03c9\u03bd \u03b4\u03b5\u03b4\u03bf\u03bc\u03ad\u03bd\u03c9\u03bd \u03c0\u03c1\u03bf\u03ba\u03b5\u03b9\u03bc\u03ad\u03bd\u03bf\u03c5 \u03bd\u03b1 \u03b5\u03c0\u03b5\u03be\u03b5\u03c1\u03b3\u03b1\u03c3\u03c4\u03bf\u03cd\u03bd. \u0397 \u03b1\u03c0\u03bf\u03c3\u03c5\u03bc\u03c0\u03af\u03b5\u03c3\u03b7 \u03c4\u03c9\u03bd \u03b4\u03b5\u03b4\u03bf\u03bc\u03ad\u03bd\u03c9\u03bd \u03c0\u03c1\u03b1\u03b3\u03bc\u03b1\u03c4\u03bf\u03c0\u03bf\u03b9\u03b5\u03af\u03c4\u03b1\u03b9 \u03b5\u03c0\u03b9\u03bb\u03cd\u03bf\u03bd\u03c4\u03b1\u03c2 \u03ba\u03b1\u03c4\u03ac\u03bb\u03bb\u03b7\u03bb\u03b1 \u03c0\u03c1\u03bf\u03b2\u03bb\u03ae\u03bc\u03b1\u03c4\u03b1 (\u03ba\u03c5\u03c1\u03c4\u03ae\u03c2 \u03ae \u03bc\u03b7-\u03ba\u03c5\u03c1\u03c4\u03ae\u03c2) \u03b2\u03b5\u03bb\u03c4\u03b9\u03c3\u03c4\u03bf\u03c0\u03bf\u03af\u03b7\u03c3\u03b7\u03c2 \u03b4\u03bf\u03b8\u03ad\u03bd\u03c4\u03bf\u03c2 \u03c4\u03bf\u03c5 \u03c0\u03b5\u03c1\u03b9\u03bf\u03c1\u03b9\u03c3\u03bc\u03bf\u03cd y = \u03a6\u00b7\u03a8\u00b7v, \u03cc\u03c0\u03bf\u03c5 y \u03b5\u03af\u03bd\u03b1\u03b9 \u03c4\u03bf \u03b4\u03b9\u03ac\u03bd\u03c5\u03c3\u03bc\u03b1 \u03c4\u03c9\u03bd \u03c3\u03c5\u03bc\u03c0\u03b9\u03b5\u03c3\u03bc\u03ad\u03bd\u03c9\u03bd \u03bc\u03b5\u03c4\u03c1\u03ae\u03c3\u03b5\u03c9\u03bd, \u03a6 \u03bf \u03c0\u03af\u03bd\u03b1\u03ba\u03b1\u03c2 \u03b4\u03b5\u03b9\u03b3\u03bc\u03b1\u03c4\u03bf\u03bb\u03b7\u03c8\u03af\u03b1\u03c2, \u03ba\u03b1\u03b9 \u03a8 \u03ad\u03bd\u03b1\u03c2 \u03bc\u03b5\u03c4\u03b1\u03c3\u03c7\u03b7\u03bc\u03b1\u03c4\u03b9\u03c3\u03bc\u03cc\u03c2 \u03b1\u03c1\u03b1\u03b9\u03bf\u03c0\u03bf\u03af\u03b7\u03c3\u03b7\u03c2 \u03c4\u03bf\u03c5 \u03b1\u03c1\u03c7\u03b9\u03ba\u03bf\u03cd \u03b4\u03b9\u03b1\u03bd\u03cd\u03c3\u03bc\u03b1\u03c4\u03bf\u03c2 x \u03c3\u03b5 \u03bc\u03b9\u03b1 \u039a-\u03b1\u03c1\u03b1\u03b9\u03ae (\u03b1\u03c0\u03cc \u03c4\u03b1 \u039d \u03c3\u03c4\u03bf\u03b9\u03c7\u03b5\u03af\u03b1, \u03bc\u03cc\u03bd\u03bf \u03c4\u03b1 \u039a \u03b5\u03af\u03bd\u03b1\u03b9 \u03b4\u03b9\u03b1\u03c6\u03bf\u03c1\u03b5\u03c4\u03b9\u03ba\u03ac \u03c4\u03bf\u03c5 \u03bc\u03b7\u03b4\u03b5\u03bd\u03cc\u03c2) \u03b1\u03bd\u03b1\u03c0\u03b1\u03c1\u03ac\u03c3\u03c4\u03b1\u03c3\u03b7 v. \u03a3\u03c4\u03b7\u03bd \u03c5\u03bb\u03bf\u03c0\u03bf\u03af\u03b7\u03c3\u03ae \u03bc\u03b1\u03c2 \u03c3\u03c4\u03b1 \u03c0\u03bb\u03b1\u03af\u03c3\u03b9\u03b1 \u03c4\u03bf\u03c5 SmartWater2020, \u03c7\u03c1\u03b7\u03c3\u03b9\u03bc\u03bf\u03c0\u03bf\u03b9\u03b5\u03af\u03c4\u03b1\u03b9 \u03bf short-Time Fourrier Transform (SFTF) \u03c9\u03c2 \u03bc\u03b5\u03c4\u03b1\u03c3\u03c7\u03b7\u03bc\u03b1\u03c4\u03b9\u03c3\u03bc\u03cc\u03c2 \u03b1\u03c1\u03b1\u03b9\u03bf\u03c0\u03bf\u03af\u03b7\u03c3\u03b7\u03c2, \u03b5\u03bd\u03ce \u03b3\u03b9\u03b1 \u03c4\u03b7\u03bd \u03b1\u03bd\u03b1\u03ba\u03b1\u03c4\u03b1\u03c3\u03ba\u03b5\u03c5\u03ae \u03c4\u03bf\u03c5 \u03b1\u03c1\u03c7\u03b9\u03ba\u03bf\u03cd \u03b4\u03b9\u03b1\u03bd\u03cd\u03c3\u03bc\u03b1\u03c4\u03bf\u03c2 x \u03c7\u03c1\u03b7\u03c3\u03b9\u03bc\u03bf\u03c0\u03bf\u03b9\u03b5\u03af\u03c4\u03b1\u03b9 \u03bf \u03b1\u03bb\u03b3\u03cc\u03c1\u03b9\u03b8\u03bc\u03bf\u03c2 NESTA (https:\/\/statweb.stanford.edu\/~candes\/nesta\/).<\/p>\n
A limitation often encountered in wireless sensor networks is the limited battery capacity. Reducing the amount of data sent by the sensors has a dual role: on the one hand, it increases the autonomy of the system and, on the other hand, it reduces telemetry costs due to the limited volume of data to be transmitted. In a water management system, data confidentiality is also a critical issue. When, for instance, consumption data from home meters are included. The above objectives can be achieved exploiting the framework of compressive sensing, which achieves high data compression and simultaneous encryption.<\/p>\n
Compressive sensing is performed in two stages: at the edges of the network and at the control center. First, data compression is carried out at the edges of the network. Let x be the original data vector of length N. The compressed vector y of length M is given by the relation y = \u03a6\u00b7x. The matrix \u03a6, of dimension MxN, models the linear subsampling process. Examples of such matrices that guarantee an accurate reconstruction of the original vector x from the compressed measurements y include matrices whose elements are drawn from a Gaussian, Bernoulli, etc. distributions. At the control center, decompression\/reconstruction of the data takes place to be further processed. Data decompression is performed by solving appropriate (convex or non-convex) optimization problems given the constraint y = \u03a6\u00b7\u03a8\u00b7v, where y is the vector of compressed measurements, \u03a6 is the sampling matrix, and \u03a8 a sparsifying transformation of the original vector x into a K-sparse (only K out of the N samples are nonzero) representation v. In our implementation in the framework of SmartWater2020, the Short-Time Fourrier Transform (SFTF) is employed as the sparsifying transformation, whilst the NESTA algorithm is used for the reconstruction of the original vector x (https:\/\/statweb.stanford.edu\/~candes\/nesta\/).<\/p>\n
<\/p>\n","protected":false},"excerpt":{"rendered":"