S. A. Kassam. Signal Detection in Non-Gaussian Noise. SpringerVerlag, 1988.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....by the Gaussian s quadratic potential function, which tends to blur edges due to the high cost of abrupt transitions. The generalized Gaussian MRF (GGMRF) 12] uses a potential function similar to the log of the generalized Gaussian noise density found commonly in robust detection and estimation[13]. It renders edges accurately without prior knowledge of their size, and it results in a convex optimization problem with no local minima. A particular case of the GGMRF, with the absolute value of local inter pixel di#erences as the potential function, appears to produce superior ....

....the squared di#erence potential functions in (4) excessively penalizes abrupt changes in f . The blurring e#ect is particularly undesirable along the edges that often occur in real tomograms. In [12] we proposed a simple generalization of MRF s based on the concept of generalized Gaussian noise[13]. This model has the functional form # c, 5) where 1 2, and # is a parameter which is inversely proportional to the scale of f . We call the class of random fields with this distribution generalized Gaussian Markov random fields (GGMRF) since this model is contained ....

S.A. Kassam, Signal Detection in Non-Gaussian Noise, Springer-Verlag, New York, 1988.

....function of discrete quantum interactions between light and matter which cannot in principle be perfectly predicted. This uncertainty leads to the development of probabilistic models for the received signal observations and places signal detection in the general framework of statistical inference [63, 64, 65]. The goal of target detection is to decide, based on a set of received signal observations y, whether a target is present in the image sequence. The target detection problem can be viewed as a binary hypothesis testing problem with hypotheses : Target Present and : Target Absent. Given a ....

....ratio function to a decision threshold, 1; yj 2 H 1 ) yj 2 H 0 ) 0; 2:13) where ffi(y) is the probability of accepting hypothesis H 1 . In practice, the most common signal detection problem is the detection of a known signal in additive noise [63, 64]. This is a binary hypothesis testing problem where the observations y can be expressed as , 2:14) The signals s i for this problem may be deterministic and completely known, deterministic with unknown parameters (e.g. amplitude) or they may be non deterministic signals with known ....

[Article contains additional citation context not shown here]

Saleem A. Kassam. Signal Detection in Non-Gaussian Noise. Springer-Verlag, 1988.

....outputs of the parallel acquisition receiver for chip asynchronous DS SS systems. Using the ML criterion, an optimal decision rule is derived. Since the optimal decision rule is difficult to implement, a simpler suboptimal decision rule is derived based on the criterion of local detection power [3]. II. OPTIMAL AND SUBOPTIMAL DECISION RULES A. Distribution of Noncoherent Correlator Outputs In a DS SS system, the received signal can be expressed as (1) In (1) is the signal power; is the data sequence waveform; where is the th chip of a PN code sequence of period , and is the PN code ....

....we use the criterion of local detection power leading to locally optimum (LO) detectors in signal detection theory. The motivation of using this criterion is as follows. First, since an LO detector has the maximum slope of its power function when the signal to noise ratio (SNR) approaches zero [3], it is expected to have quite good performance when the SNR is low. Second, an LO detector can always be obtained and is usually much easier to implement than other detectors including uniformly most powerful and optimum detectors [4] 5] The LO decision rule is to choose such that (8) where ....

S. A. Kassam, Signal Detection in Non-Gaussian Noise. New York: Springer-Verlag, 1987.

....can now be expressed as the following parameter hypothesis testing problem, because the null hypothesis is the special case of the alternative hypothesis: 18) and (19) III. LOCALLY OPTIMUM RANK DETECTOR TEST STATISTIC Based upon the generalized version of the Neyman Pearson s fundamental lemma [11], 12] a locally optimum (LO) detector in general maximizes the slope of the power function as the signal to noise ratio (SNR) approaches zero. The LO detectors are specially useful when the strength of the desired signal is weak. The LOR detector is a nonparametric LO detector based on signs and ....

S. A. Kassam, Signal Detection in Non-Gaussian Noise. New York: Springer-Verlag, 1988.

....feature set of the claimed client identity. Thus, an authentication system is much faster than an identification system and moreover deals with the imposture problem. The problem of person authentication is a detection problem. Such a problem can be analyzed by means of a binary hypothesis test [7]. The first hypothesis H accepts a certain candidate claim for a client identity and the second hypothesis H0 rejects this claim. A hypothesis test can be seen as a partition of the sample space of the observations into disjoint subsets. These subsets are separated by a set of decision functions. ....

....us to chose crisp codebook vectors. Thus, 7) is not modified and the centers of the fuzzy vectors should be used for all arithmetic operations. F. Median Radial Basis Function Network An RBF network is a two layer neural network used for classification or functional approxi mation purposes [7]. The inputs of the RBF network consist of the results provided by various modalities employed. Each hidden unit implements a Gaussian function which models a cluster: bj (x) exp[ x yj)Ts (x yj) 15) where x is the entry vector, yj is the mean vector and Sj is the covariance matrix and j ....

S.A. Kassam, Signal detection in Non-Gaussian Noise. Springer-Verlag, 1988.

.... m plX v v v is a realization of , with l f g I the SNR chip. Note that 33 87 . Now, we derive a decision rule for the joint detection of the current and previous samples in the region using the LO test statistic. From the generalized Neyman Pearson lemma [5], the LO test statistic can be obtained as (4) is the order of the first nonzero derivative of at Glsu . By averaging over , it can be shown as in [4] that (4) yields n n p (5) t o x m t o x . Note that It o x m It o y x l t o x m t o ....

.... t o x m t o x . Note that It o x m It o y x l t o x m t o m t o yI x m o yI x can be considered as the sum of signal energy in the present and immediate previous cells. The class of energy detectors are frequently used for random signals in classical signal detection problems [5]. 2.3. System Description The structure of the combiner based on the decision rule obtained in the previous subsection is shown in Fig. 1. In the combiner, the outputs of the two matched filters are squared and summed to produce . Then, with one delay unit and an adder, we can obtain . If It ....

S.A. Kassam, Signal Detection in Non-Gaussian Noise, NY: Springer-Verlag, 1987.

....and effectiveness for detecting weak signals. A subclass of the LO detectors, the locally optimum rank (LOR) detector, has been investigated because an LOR detector requires only simple arithmetic operations, has lower sensitivity to small deviations of the noise pdf, and has nonparametric nature [6] [8] It has been commonly assumed that the additive noise samples are statistically independent. In practice, however, this assumption is often violated. Thus, investigations on signal detections in dependent noise are desirable. Among the typical investigations on signal detection problems ....

....the weakly dependent noise W i , i =1; 2; are the MA of i.i.d. random variables as W i = e i #e i,1 u i,2 ; 2) where e i , i =1; 2; are i.i.d. random variables with common pdf f e . The pdf f e is even symmetric with bounded continuous derivatives and satisfies the regularity conditions [6]. In (2) # is called the dependence parameter determining the correlation coefficient of W i ,andu i is the unit step sequence defined by u i =1when i 0 and u i =0when i#0. Let X , W , e,ands be the n tuple vectors representing #X 1 ;X 2 ; ###;X n #, #W 1 ;W 2 ; ###;W n #, #e 1 ;e 2 ; ....

S.A. Kassam, Signal Detection in Non-Gaussian Noise, New York: Springer-Verlag, 1987.

....# 1998 Elsevier Science B.V. All rights Keywords: Signal detection; Median shift sign; Sign detector; Nonparametric; Locally optimum 1. Introduction The problem of signal detection can be considered as a parameter testing problem of a null hypothesis against an alternative hypothesis [12,19,26]. As a consequence, the knowledge of a priori information on the parameter is required for establishing the hypothesis testing problem. Unfortunately, it is very di#cult, if not impossible, to exactly estimate the value of a parameter in practice. If we are not able to get a priori information on ....

....of the optimum MS value. Consider the generalized Gaussian (GG) generalized Cauchy (GC) and generalized logistic (GS) distributions, whose pdfs are given by (k)#(1 k) e###x##A###k## , 13) B(k,#) #1#[#x# A (k) k ### ##k (14) e#kx#### (1#e#x####)#k , 15) respectively [19], 8] where , 16) #, 17) 18) Fig. 2. Median shift value versus detection probability, when n 100, # 0.01, S 0.5 and # 1.0. B(k,#) k####k#(##1 k) k)#(#)#(1 k) 19) ####k#(##1 k) #(3 k) ### #(#) #(1 k) ### # (20) #2# 4k #. 21) Here k 0, # 0, # is the ....

S.A. Kassam, Signal Detection in Non-Gaussian Noise, Springer, New York, 1988.

....##(t)##(t ##) exp[j(w t###) ##(t) 4) where ##(t) is the fading process, ## is the random delay at the receiver, and ## ## w # ## is the random phase at the receiver. In general, impulsive noise can be modeled as a random variable whose pdf has a tail heavier than that of a Gaussian pdf [4]. In this paper, the impulsive noise #(t) is modeled as a Gaussian mixture noise with the # contaminated pdf [4] f (x) 1 #) f (x)## f (x) 5) where # is called the contamination ratio. In Eq. 5) we assume that the background noise pdf f and the tail noise pdf f are Gaussian with ....

....receiver, and ## ## w # ## is the random phase at the receiver. In general, impulsive noise can be modeled as a random variable whose pdf has a tail heavier than that of a Gaussian pdf [4] In this paper, the impulsive noise #(t) is modeled as a Gaussian mixture noise with the # contaminated pdf [4] f (x) 1 #) f (x)## f (x) 5) where # is called the contamination ratio. In Eq. 5) we assume that the background noise pdf f and the tail noise pdf f are Gaussian with equal mean and variances ## and ## M## , respectively: we use the notation #(x; #, m ) to denote ....

S.A. Kassam, Signal Detection in Non-Gaussian Noise, Springer, New York, 1987.

....will also use to denote the th smallest member of the set . We define , and in a similar manner. Let and be the discrete probability mass functions (pmfs) of , and jointly under and , respectively. Then (13) 14) Applying the generalized version of the Neyman Pearson s fundamental lemma [9], 10] we get the test statistic of the LOR detector as the ratio (15) where is the first nonzero derivative of at Using (13) 15) it can be shown that the test statistic of the LOR detector is (16) 17) 18) with and . The proof of the result (16) is given in Appendix B. For the Gaussian ....

S. A. Kassam, Signal Detection in Non-Gaussian Noise. New York: Springer-Verlag, 1988.

....problem in noisy observations has been considered in many previous studies. Among the various signal detection problems, weak signal detection has been of much interest in detection theory and applications. Among the typical investigations on locally optimum (LO) detectors are those considered in [1,4,5,11]. It has been commonly assumed that the additive noise samples are statistically independent. In practice, however, this assumption is often violated, and the optimum detectors designed under this assumption are no longer optimum in practice. Such a situation becomes more realistic as the ....

....noise i 1,2, 2 ,n, are the unilateral MA of i.i.d. random variables: e ##e u , 2) where e , i 1,2, 2 ,n, are the i.i.d. random variables with common p.d.f. f . The p.d.f. f is even symmetric with bounded continuous derivatives and satisfies the regularity condition [4]. This model is not only an analytically tractable model but also a good representation of practical dependent noise when the dependence is weak. Here, # is called the dependence parameter determining the correlation coe#cient of , and u is the unit step sequence, i.e. u 0 when i(0 and ....

[Article contains additional citation context not shown here]

S.A. Kassam, Signal Detection in Non-Gaussian Noise, Springer, New York, 1987.

....wI k njX t t t is a realization of , with j I the SNR chip. Note that . Now, we derive a decision rule for the joint detection of the current and previous samples in the region using the LO test statistic. From the generalized Neyman Pearson lemma [5], the LO test statistic can be obtained as (4) is the order of the first nonzero derivative of at Gjqs . By averaging over , it can be shown as in [4] that (4) yields l l zn (5) r m v k r m v . Note that Ir m v kIr m w v j r m v kz r m kz r ....

....zn (5) r m v k r m v . Note that Ir m v kIr m w v j r m v kz r m kz r m wI v kz m wI v can be considered as the sum of signal energy in the present and immediate previous cells. The class of energy detectors are frequently used for random signals in classical signal detection problems [5]. 2.3. System Description The structure of the combiner based on the decision rule obtained in the previous subsection is shown in Fig. 1. In the combiner, the outputs of the two matched filters are squared and summed to produce . Then, with one delay unit and an adder, we can obtain . If ....

S.A. Kassam, Signal Detection in Non-Gaussian Noise, NY: Springer-Verlag, 1987.

....problem as a hypothesis testing problem and then use the locally optimum (LO) test statistic for the problem. The motivation of using the LO test statistic is as follows: first, since the LO detector has the maximum slope of its power function when the signal to noise ratio (SNR) approaches zero [5], it is expected to have quite good performance when the SNR is low with a specified false alarm probability. Second, the LO detector can always be obtained and is usually easier to implement than other detectors including uniformly most powerful and optimum detectors [6] 7] In this paper, a ....

....and variance r D sK r a realization of . Note that Now, we derive a decision rule for the joint detection of the two region using the LO test statistic. From the generalized Neyman Pearson lemma [5], the LO test statistic can be obtained as s s s (4) is the order of the first nonzero derivative of at . By averaging over , it can be shown [10] that (4) yields F (5) ##u # . Note that ## u ....

[Article contains additional citation context not shown here]

S.A. Kassam, Signal Detection in Non-Gaussian Noise, NY: Springer-Verlag, 1987.

....therein. There are many aspects of this problem that we have not treated here. Issues such as robustness and nonGaussian noise have been touched upon very briefly; however, these are important issues in applications, and more detailed treatments of these issues can be found, for examples, in [1] [58], 60] and [74] We also mentioned briefly RKHS methods for the detection of non Gaussian signals, and for signal and noise models exhibiting fractal behavior. Further techniques for the detection of non Gaussian signals are reviewed in [30] and methods for exploiting self similarity are ....

S. A. Kassam, Signal Detection in Non-Gaussian Noise. New York: Springer-Verlag, 1988.

....i j b w(j) b F (j)p(j)j fi Gamma j b w(j) Gamma b F (j)p(j)j fi oe fi (i) fi (17) where oe fi (i) is constant for the given codeword bit c i . The nonlinear structure of the matched filter is similar to local optimum detector nonlinearity that limits the outliers of the sGG model [32]. This model was considered for the DCT domain watermarking by Hern andez et al. [26] where the sGG model presented the distribution of the DCT coefficients in 64 equivalent channels of JPEG compression. The authors considered this model assuming that all fading in the equivalent channel is only ....

....Additionally, if the attacker can discover some periodicity in the watermark structure, this could be effectively used for remodulation to reach the above goal. Since, the behavior of the correlator and sign correlator detectors that are mostly used in watermarking decoders is well studied in [32] we will not concentrate on this point here. We will rather present some practical aspects of remodulation. One method consists of changing the amplitude relationship among the pixels in a given neighborhood set. In the most general case, one has to solve a local optimization problem of watermark ....

S. Kassam. Signal Detection in Non-Gaussian Noise. Springer Verlag, 1998.

....(q is small) we are then interested in developing a locally optimum (LO) detector, which is most powerful for the q range of interest. Assuming a uniformly distributed p(f) and denoting the amplitude of the k th sample of the received vector R k , we can express the LO detection statistic as [2]: L LO (x) n k=1 n m=1 h # (R k )h # (Rm ) h(R k )h(R m )R k Rm r s (m,k)x k x # m n k=1 r s (k,k) # h ## (R k ) h(R k )R 2 k # h # (R k ) h(R k )R k # 2 # x k x # k where r s (m,k) denote elements of the correlation matrix R s . Using the notation #x,y# = k x k ....

.... #R s v(x) v(x)# , 9) where R q and R s are now correlation operators, # f , g# = R t f (t)g # (t)dt, and the functions y, z and v are the continuous forms of the vectors in (5) The second order approximation of the likelihood ratio for the problem (8) is related to the LO test statistic [2]: L(x) f x (x q) f x (x 0) # 1 q 2 2 L LO (x) 10) 4. Composite Hypotheses We now extend the continuous time detection problem to the case where the signal has been subjected to an unknown time frequency or time scale shift. The problem can be stated as a choice between the ....

S. Kassam. Signal Detection in Non-Gaussian Noise. Springer-Verlag, New York, 1988.

No context found.

S. A. Kassam. Signal Detection in Non-Gaussian Noise. SpringerVerlag, 1988.

No context found.

S. A. Kassam, Signal Detection in Non-Gaussian Noise, Springer-Verlang, Berlin, Germany, 1988.

No context found.

S.A. Kassam, Signal Detection in Non-Gaussian Noise,New York: Springer-Verlag, 1988.

No context found.

S.A. Kassam, Signal Detection in Non-Gaussian Noise. SpringerVerlag, 1988.

No context found.

S.A. Kassam, Signal Detection in Non-Gaussian Noise, Springer-Verlag, New York, 1987.

No context found.

S.A. Kassam, Signal Detection in Non-Gaussian Noise, Springer Verlag, 1987.

No context found.

S.A. Kassam, Signal Detection in Non-Gaussian Noise, Springer-Verlag, New York, 1988.

No context found.

S. A. Kassam, Signal detection in Non-Gaussian Noise, Springer-Verlag, 1988.

No context found.

S. Kassam, Signal Detection in Non-Gaussian Noise,SpringerVerlag, 1998.

First 50 documents  Next 50

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC