Signal detection in tensor data

Abstract

Signal detection in tensor data The present description relates to a method for detecting a useful signal, the method comprising:- acquiring a raw signal, by a sensor;- providing the raw signal, to a processing device, the signal being represented by a tensor of order greater than or equal to 3;- calculating an invariance value associated with the tensor, the invariance value being calculated on the basis of at least one trace invariant for order tensors; - comparing the invariance value associated with the tensor with a first reference value; - based on the comparison, providing, by the processing device, an estimate of the signal-to-noise ratio of the raw signal; and- if the estimated signal-to-noise ratio is different from 0, providing the tensor to a circuit configured to process the raw signal. Figure for abstract: Fig. 6

Description

Title of the invention: Signal detection in tensor data Technical field

[0001] The present description relates generally to signal detection during the acquisition of tensor data, and in particular during the acquisition of image representations. Prior art

[0002] Sensors, such as for example multi-sensors, configured to acquire data such as multi-channel images, videos, hyper-spectral images, etc. are subject to noise, of internal and / or external origin. The acquired data is then corrupted by noise, the quantity of which is defined by a signal-to-noise ratio.

[0003] Signal detection methods exist when the data are represented in the form of matrices, which is for example the case for grayscale images. However, the application of these methods for data in the form of tensors of order greater than or equal to 3 requires the reduction of the data in order to convert them into matrices or vectors. This data reduction therefore results in a loss of performance in signal detection.

[0004] It is desirable to improve signal detection methods for data represented as a tensor of order greater than or equal to 3. Summary of the invention

[0005] One embodiment provides a method of detecting a useful signal, the method comprising: - the acquisition of a raw signal, by a sensor; - providing the raw signal to a processing device, the raw signal being represented by a tensor of order d greater than or equal to 3; - the calculation, by the processing device, of an invariance value associated with the tensor, the invariance value being calculated on the basis of at least one trace invariant under the orthogonal group of degree d for tensors of order d; - the comparison, by the processing device, of the invariance value associated with the tensor with a first reference value; - on the basis of the comparison, the provision, by the processing device, of an estimate of the signal-to-noise ratio of the raw signal; and - if the estimated signal-to-noise ratio is different from 0, supplying the tensor to a circuit configured to process the raw signal.

[0006] According to one embodiment, the sensor is configured to acquire image representations and the circuit configured to process the raw signal is an image processing circuit.

[0007] According to one embodiment, the invariance value associated with the tensor is a linear combination of a plurality of trace invariants Ij for the orthogonal group for tensors of order d, the combination being of the form °where 'cs values ​​are weighting coefficients.

[0008] According to one embodiment, the linear combination comprises melonic trace invariants and / or tadpole type and / or tetrahedral and / or pillow type.

[0009] According to one embodiment, the weighting coefficient of a “pillow” type trace invariant is equal to the inverse of the variance of the invariant for a pure noise tensor.

[0010] According to one embodiment, the weighting coefficient of a melonic trace and / or “tadpole” and / or tetrahedral type invariant is equal to the symmetrization weight of the invariant.

[0011] According to one embodiment, the first reference value is a function of the expectation of the invariance value for a pure noise tensor.

[0012] According to one embodiment, the first reference value is equal to E[ I ] + 2^Var(I) ' °where E[I] and Var(I) are respectively the expectation and variance of the invariance value for a pure noise tensor.

[0013] According to one embodiment, if the invariance value is greater than the first reference value, the processing device is configured to determine that the raw signal acquired by the sensor comprises a useful signal.

[0014] According to one embodiment, the above method further comprises, when it is determined that the invariance value is greater than the first reference value: - comparing the invariance value with a second reference value depending on the expectation of the invariance value for a tensor associated with a signal-to-noise ratio of value [3.

[0015] One embodiment provides a device comprising: - a sensor configured to acquire a raw signal; - a processing device configured to execute instructions stored in a non-volatile memory of the device, the execution of the instructions making it possible to detect whether the raw signal comprises a useful signal, by doing: - shaping the raw signal in the form of a tensor of order greater than 3; - the calculation of an invariance value of the tensor; - comparison of the invariance value with a reference value; - based on the comparison, the estimation of the signal-to-noise ratio present in the raw signal; and - if it is determined that the signal-to-noise ratio is non-zero, providing the tensor to a circuit configured to perform raw signal processing operations.

[0016] According to one embodiment, the sensor is configured to acquire image representations and wherein the circuit configured to perform raw signal processing operations is an image processing circuit.

[0017] One embodiment provides a method for determining a combination of trace invariants, the combination being of the form ^.ctjlj, °where the Ij are trace invariants and the values ​​aj are weighting coefficients, adapted to a device, the method comprising: - providing indication of the device's memory resources to an external device; - providing the indication of a processing time to the external device; - providing an indication of dimensions of the order of tensors to the external device; - searching for a set of trace invariants, in association with a set of weights, forming the combination, among a plurality of trace invariants, each set of trace invariants being associated with a cost and each cost value being stored in a memory of the external device in association with an identifier of the associated set, the search for the set of invariants being carried out on the basis of the memory resources and / or the calculation time and / or the indication of the dimensions provided; - providing the set of trace invariants and weights to the device so that an invariance value is calculated, by the device, based on the determined combination of invariants.

[0018] According to one embodiment, the weights, associated with each trace invariant in each combination, are determined by performing a gradient descent on an objective function determining a distance between the distribution of the invariance value associated with the combination for a pure noise tensor and for a tensor having a non-zero signal-to-noise ratio.

[0019] According to one embodiment, each trace invariant is a melonic and / or tadpole-type and / or tetrahedral and / or pillow-type trace invariant. Brief description of the drawings

[0020] These characteristics and advantages, as well as others, will be explained in detail in the following description of particular embodiments given without limitation in relation to the attached figures among which:

[0021] [Fig.l] is a block diagram representing a processing device;

[0022] [Fig.2] is an example of a tensor and graphs representing trace invariants;

[0023] [Fig.3A] and [Fig.3B] illustrate graphs representing sets of trace invariants;

[0024] [Fig.4A] and [Fig.4B] illustrate analytical calculations of trace invariant moments associated with the distribution of pure noise tensors;

[0025] [Fig.5] is a graph illustrating distributions of trace invariants;

[0026] [Fig.6] is a flowchart illustrating steps of a method for detecting signal, according to an embodiment of the present description;

[0027] [Fig.7] is a flowchart illustrating steps of a signal detection method, according to another embodiment of the present description;

[0028] [Fig.8A] and [Fig.8B] illustrate the behavior of the numerator of an objective function for several invariants and several graphs;

[0029] [Fig.9A], [Fig.9B], [Fig.10A] and [Fig.10B] are graphs illustrating the distribution of weights provided by a symmetrization process;

[0030] [Fig. 11 A] and [Fig. 11 B] are graphs illustrating gradient descents associated with the objective function;

[0031] [Fig.l2A] and [Fig.l2B] are graphs illustrating the values ​​of the objective function for different graphs and as a function of the value of the signal-to-noise ratio;

[0032] [Fig. 13A], [Fig. 13B], [Fig. 13C] and [Fig. 13D] are graphs illustrating trace invariant distributions;

[0033] [Fig.l4A], [Fig.l4B] and [Fig.l4C] are graphs illustrating success rates in signal detection, according to one embodiment of the present disclosure;

[0034] [Fig. 15] is a graph illustrating weights obtained by gradient descent;

[0035] [Fig. 16] is a flowchart illustrating a method of selecting a set trace invariants, according to an embodiment of the present description; and

[0036] [Fig. 17] is a graph illustrating success rates in signal detection, according to an embodiment of the present description and according to a matrix method. Description of the embodiments

[0037] The same elements have been designated by the same references in the different figures. In particular, the structural and / or functional elements common to the different embodiments may have the same references and may have identical structural, dimensional and material properties.

[0038] For the sake of clarity, only the steps and elements useful for understanding the embodiments described have been represented and are detailed.

[0039] Unless otherwise specified, when referring to two elements connected to each other, this means directly connected without intermediate elements other than conductors, and when referring to two elements connected (in English "coupled") to each other, this means that these two elements can be connected or be connected by means of one or more other elements.

[0040] In the following description, when reference is made to absolute position qualifiers, such as the terms "front", "back", "top", "bottom", "left", "right", etc., or relative position qualifiers, such as the terms "above", "below", "upper", "lower", etc., or to orientation qualifiers, such as the terms "horizontal", "vertical", etc., reference is made unless otherwise specified to the orientation of the figures.

[0041] Unless otherwise specified, the expressions "about", "approximately", "substantially", and "of the order of" mean to within 10%, preferably to within 5%.

[0042] [Fig. 1] is a block diagram showing a processing device 100 (DEVICE). The device 100 comprises one or more sensors 102 (SENSOR). For example, the sensor(s) 102 are multi-sensors configured to acquire image representations. In particular, the image representations acquired by the sensor(s) 102 are data represented in the form of tensors of order greater than or equal to 3. The data are for example videos, images comprising at least two channels, such as for example color channels, infrared, etc. A tensor of order 3 representing a video can then be seen as a sequence of matrices, each matrix corresponding to an instant of the video. Each element of each matrix is ​​then a gray level value associated with a pixel of an image of the video at a given instant. Images, or video, in color, are represented by tensors of higher order. For example, an RGB color image is represented by a tensor of order 3.

[0043] The representations of images acquired by sensors such as the sensor 102 are generally corrupted by noise. For example, these noises come from outside the devices and / or are noises internal to the sensor 102. Generally, the quantity of noise in an image is evaluated by a signal-to-noise ratio. A data item having a signal-to-noise ratio equal to 0 is pure noise data, that is, data comprising only noise. In particular, in the case where an image acquired by the sensor 102 is pure noise data, this means that no signal was measured during its acquisition. The higher the signal-to-noise ratio of a data item, the less the data item is corrupted by noise.

[0044] As an example, the noise present in the data acquired by the sensor 102 is modeled by Gaussian noise. Thus, in the following, when referring to noise present in a tensor, this noise has the form of a tensor of the same order and dimension and is composed of elements each following a centered normal law and reduced, each element being independent of the others. This modeling is realistic because the noise sources are so diverse and numerous that the central limit theorem applies.

[0045] The device 100 further comprises a non-volatile memory 104 (NV MEM), a volatile memory 106 (RAM) and a processor 108 (CPU) connected to the sensor 102 via a bus 110. For example, the memory 106 is a random access memory (RAM - Random Memory Access) and the processor 108 is a central processing unit (CPU - "Central Processing Unit"). In another example, the memory 106 is a video memory (VRAM - "Video Random Access Memory") and the processor 108 is a graphics processing unit (GPU - "Graphics Processing Unit"). When the sensor 102 acquires data, represented by a tensor, the processor 108 is configured to execute instructions 112 (INSTRUCTIONS). For example, instructions 112 are stored in non-volatile memory 104 and are loaded into volatile memory 106 for execution.According to one embodiment, the instructions 112 are instructions allowing the implementation of a signal detection method in image representations, in the form of tensors of order greater than or equal to 3, acquired by the sensor 102. In particular, the data manipulated during the implementation of the signal detection method are not converted into the form of matrices, or more broadly, into the form of tensors of order less than 3.

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[0048] Figure 2 is an example of graphs representing trace invariants. For a tensor T, we will use Einstein notation for summations. In other words, for a tensor T of order 3, the quantity T is the sum of all elements of the tensor, that is, Tij^Tijk = ] [ / ] [£] ■ Generally speaking, A invariant value for a tensor ye Rn' is a scalar invariant under transformations such that t- ___V r? 0 , where the elements 1 4 - -4 7 h ■ h “ ' uWd -Jd q( 4 are elements of the orthogonal groups O() x ... XO( n^) ■ In the case of a matrix M, values ​​such as the trace of the product MM\ where M' is the transpose of the matrix M, its determinant, or the coefficients of its characteristic polynomial are invariant values. Trace invariants are usually formed by contractions of one or more copies of a tensor. The number of copies then determines the degree of the invariant. Thus, the trace of a matrix is ​​an invariant of order 1. In particular, trace invariants admit representations in the form of graphs. Graphs 200 and 202 illustrate examples of first-order trace invariants. Graphs 204 and 206 illustrate examples of second-order trace invariants.

[0049] Tensor copies are represented by 208 vertices for 3rd order tensors and 210 vertices for a matrix. Each edge, numbered 1, 2 or 3 in [Fig.2], corresponds to an index of the tensor. Thus, the number of edges corresponds to the order of the tensor.

[0050] The graph 200 represents a copy of a tensor of order 3. In particular, the copy represented by the graph 200 is a copy 2"ijjc of a tensor T. The edges numbered 1, 2 and 3 represent the indices i, j and k respectively.

[0051] Graph 202 represents the trace of a matrix. The two edges 1 and 2 meet, which means that the sum is carried out on the diagonal elements of the matrix. Thus, the trace of a matrix is ​​equal to T».

[0052] Graphs 204 and 206 represent trace invariants of order 2 for tensors of order 3. In particular, graph 204 represents the contraction of two copies 208 and the invariant represented is Tijjc. Graph 206 illustrates a contraction of two copies 208, the contraction being carried out on indices having different positions. The junction of the two edges at the top means that the sum is carried out on the first copy having its first index equal to the second index of the second copy. The trace invariant represented is then T

[0053] In the context of graph representation, a tensor symmetrization method consists of summing all possible permutations of the edges, the sum being weighted by the inverse of the number of possible permutations. Thus, in the example of graph 200, and when the tensor T is a cubic tensor of order 3, each element T [ i: ] [ j'] [ k ] of the symmetrized tensor T is equal to (T[i][j]lk]+T[i][^

[0054] Figures 3A and 3B illustrate graphs representing sets of trace invariants.

[0055] In particular, Figure 3A illustrates so-called "melonic graphs" for tensors of order 3. The graphs in this category are formed by self-contraction of two copies of tensors. In the case of tensors of order 3, this category includes 36 graphs and includes in particular graphs 204, noted / ], and 206, noted 26. By fixing the order of the indices of the first copy to {4 j, k], the number of graphs is reduced to 6. Indeed, the trace invariants and Tj^JT are identical, we can therefore restrict ourselves to considering Ti^ as the first copy. By defining a category of graphs as being a set of graphs, each graph of which corresponds to the other graphs of the set up to a ready permutation of indices, the four other graphs of the Melonic category are graphs 302, 304, 306 and 308 representing respectively the trace invariants I2 = T T iijTkjÿ, / 5 = T and 1 6=T ^Tkj; , / 3“ / 4 — T ,Tet / 5 — T jTj^. However, the invariants represented 75 and 7Ô are identical. This means that there are only five possible melon graphs that can be formed, and contracting symmetrized tensors gives different weights to these invariants. In order to avoid symmetrizing the tensors, as described in relation to Figure 2, which is costly in terms of time and resources, we assign symmetrization weights to each invariant. In particular, the weights of the 5 possible trace invariants are {1,1, 1,1, 2}.

[0056] [Fig.3B] illustrates graphs 310, 312, 314 each belonging to other categories of graphs.

[0057] Graph 310 is an example of a so-called “tadpole” graph. The invariant represented by graph 310 is equal to Each graph in the “tadpole” category has its vertices connected by a central edge corresponding to a single index, and the other two edges of each copy join. The “tadpole” category includes 6 different graphs and the symmetrization weights are {1,1, 1,2, 2,2}. The 6 invariants represented by the “tadpole” graphs are I \ = T jj^T r

[0058] Graph 312 is an example of a tetrahedral graph. Tetrahedral graphs represent trace invariants involving 4 copies of a tensor. The trace invariants represented by these graphs are therefore trace invariants of order 4. The invariant represented by graph 312 is equal to Tetrahedral graphs represent 60 different trace invariants, among the 216 invariants without taking into account symmetries, with weights varying between the values ​​{1,2,4).

[0059] Graph 314 is an example of a so-called “pillow” graph formed by double contraction between two pairs of copies of the tensor. The trace invariants represented by the “pillow” graphs are trace invariants of order 4. In particular, graph 314 represents an invariant equal to The “pillow” graphs re have 99 different trace invariants, out of 348, with weights varying between the values ​​{1,2,4}.

[0060] Figures 3A and 3B illustrate examples of graphs for tensors of order 3, but there are of course representations in the form of graphs for tensors of orders higher than 3. The numbers of trace invariants per category are then higher.

[0061] According to one embodiment, the instructions 112 allow the calculation of an invariance value by calculating a trace invariant, or a combination of trace invariants, represented by a single, or several, graph categories. The instructions 212 are further configured so that the invariance value is compared to the dis invariance values ​​for pure noise tensors. In particular, the invariance value is compared to a value based on the expectation of the invariance value for a tensor composed solely of pure noise. In another example, the invariance value is compared to a value based on the expectation and variance of the invariance value for a tensor composed solely of pure noise. Such a tensor is then written as T = Z where Z is, for example, a Gaussian tensor whose each element is independent of the others and follows a centered and reduced normal distribution. In another example, the tensor Z is a tensor modeling noise whose elements are, for example, correlated and / or follow a distribution different from a Gaussian distribution.

[0062] Figures 4A and 4B illustrate analytical calculations of trace invariant moments associated with the distribution of pure noise tensors.

[0063] In particular, Figure 4A illustrates an example of an expectation calculation for a “pillow” type trace invariant for a pure noise tensor of order 3. Expectation calculations, and more generally of moments of any order, are based on a representation of the graph associated with the trace invariant in a covering graph. A covering graph 400 is an example of a covering graph for so-called “pillow” graphs. A covering graph for an invariant of order k, of a tensor of order d is constructed by adding half edges 402, called propagators and represented in dotted lines, to each vertex and then connecting each propagator to another. For a given graph, there are therefore several covering graphs.

[0064] The calculation of the expectation of an invariant represented by a graph is based on the recognition of cycles in the spanning graph. Starting from a first vertex vi, we follow an edge, composed of two indexed half-edges, to a second vertex v2 then we follow the propagator connecting vertex v2 to a vertex v3. From vertex v3 we follow the half-edge starting from vertex 'h having the same index as the half-edge preceding vertex v2. The reading of the graph continues in this way until the first edge traveled falls back, that is to say on the edge going from vertex vi to vertex v2. The spanning graph 400 thus comprises two cycles 402 and 404.

[0065] Figure 4B illustrates a spanning graph 406 connecting two same graphs 408 representing an invariant of order 6 of a tensor of order 5. This type of spanning graph, between two copies of graphs is used to calculate the moment of order 2 of the invariant. Generally, to calculate a moment of order m, m > 1, we will count the number of cycles, in a spanning graph, between a number m of copies of the graph representing the invariant considered.

[0066] Each cycle of the covering graph then contributes a factor n to the value of the moment, where n is the dimension of the tensor. Thus, the value of a moment of order m, for an invariant T and represented by a graph G, is given by the equation:

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[0070]

[0071] [Math 1] £[ / c(r)] = F cvc / «] where the sum is carried out over the set of spanning graphs G ' of the graph G, and the value {nb cycle} corresponds to the number of cycles on each spanning graph. This relationship is verified in the Gaussian case, but has a universal aspect. Indeed, this relationship is also verified for other noise distributions. The universality of this relationship is, for example, discussed in "Universality for Random Tensors" published in the Annals of the IHP Probabilities and Statistics by Gurau, R. in 2014. In the case of tensors of dimensions "ix - x 'G, the calculation of moments is generalized. In one example, in this case, only the invariants associated with graphs having a unique index on each edge are used in the calculations of trace invariants. In another example, a matrix A is constructed from the starting tensor T. For example, for a tensor T of order 3, of dimension fli x n2 x ma(rjcc a CS( a square matrix of dimension nix and each component Ay of this matrix is ​​equal to the sum The following tables group the expectation, variance, and symmetrization weights for the melon and tadpole graphs. In particular, Table 1 groups the melon graphs and Table 2 the tadpole graphs. [Table 1] Subcategory 1 Subcategory 2 Subcategory 3 Invariants AI* hhh Expectation n3 ri2 n Variance 2 / P 2n3 n3 + n Weight 1 1 2 [Tables 2] Subcategory 1 Subcategory 2 Invariants Z'b Z 2' Z 3> z'^ z'6 Expectation n2 H Variance 2n3 n3 + n Weight 1 2 [Fig.5] is a 500 plot illustrating trace invariant distributions. In particular, [Fig.5] illustrates trace invariant distributions for tensors comprising a useful signal, that is to say having a signal-to-noise ratio strictly greater than 0.

[0072] In order to calculate the moments of an invariant for tensors having a signal-to-noise ratio strictly greater than 0, we write each vertex of the associated graph in the form: [Math 2] T; ... ; = Jn 6v ■ ■ ■ v + Z;...; where the part vil'" represents the signal and where Z is a pure noise tensor of the same dimensions and order as the tensor T. The calculation of the expectation of a trace invariant is carried out according to the same cycle counting method as described in relation to figures 4A and 4B. However, when, in a cycle, there is an odd number of elements of the tensor Z, that is to say if the number of vertices traveled during the cycle is odd, the expectation and more generally each moment of odd order is zero for this cycle.

[0073] Graph 500 illustrates distributions of a pillow-type trace invariance value.

[0074] A curve 502 illustrates the distribution of the pillow-type trace invariance values ​​for a pure noise tensor. Curves 504 and 506 respectively illustrate the distributions of these same invariance values ​​when the signal-to-noise ratio p is equal to 1.6 and 2.6. The distributions 504 and 506 then correspond to the distribution 502 shifted by a value, depending on the signal-to-noise ratio.

[0075] In the case of "tadpole", tetrahedral or melonic graphs, the distributions of the trace invariance values ​​have the same shape, and a shift is observed according to the value of the signal-to-noise ratio.

[0076] In the remainder of the description and unless otherwise specified, a moment, in particular the expectation, or the variance of a trace invariant, corresponds to the moment, in particular to the expectation, or to the variance, of the invariant for a pure noise tensor.

[0077] [Fig.6] is a flowchart illustrating steps of a signal detection method, according to an embodiment of the present description.

[0078] In a step 600 (RECEIVE TENSOR), a tensor is provided to the processor 108. For example, the tensor is a digital object, obtained by converting analog data measured by the sensor 102. For example, following reception of the tensor, the processor 108 is configured to symmetrize it.

[0079] In a step 601 (NORMALIZATION) the variance of the components of the tensor is calculated. The tensor is then normalized on the basis of the calculated variance.

[0080] In a step 602 (COMPUTE INVARIANT I), an invariance value / for the symmetrized tensor is calculated by the processor 108. For example, the invariance value corresponds to a trace invariant le, represented by a graph G. In another example, the invariance value is a linear combination of several trace invariants / — °where each is a trace invariant represented by a graph Gj. Graphs G] belong to one or more graph categories. Each coefficient is associated with the graph Gj and has, for example, been calculated beforehand. For example, at least one of the coefficients is equal to the symmetrization weight associated with the graph Gj. For example, at least one of the coefficients is equal to the inverse of the variance of the invariant Ij-

[0081] In a step 603 (COMPUTE MEAN AND VARIANCE), the expectation and variance of the invariance value for a pure noise tensor is calculated. The calculated expectation and variance correspond to the expectation £[ / ] and / or the variance Var[ / ] of the trace invariant, or of the combination of trace invariants

[0082]

[0083] considered in step 601. In the case where a single invariant is considered, the expectation £[ / ] is equal to £[ZG] and the variance Var(I) to Vût(Zg). In the case where the invariant is a combination of several invariants / — the expectation E[l | is equal to ajE[Ic j- variance is obtained by developing the variance of a linear combination. For example, step 602 is performed upstream, for example during the programming of instructions 112. The values ​​of expectation £[ / ] and variance Var [Z] are then, for example, stored in non-volatile memory 104. In another example, expectation E[Z] and variance Var[Z] are calculated on the fly at each execution of instructions 112. In a step 604 (Z < Ee / Y the processor 108 is configured to, by executing the instructions 112, compare the invariance value to a reference value. For example, the reference value is equal to the value E[l] + 2^Var(l) • For example, the reference value is included in the memory 104. In other examples, the reference value is another value, representing the distribution of the invariance values ​​for the invariant or the combination of invariants considered. In another example, the reference value is equal to the expectation £[7], In yet another example, the reference value is equal to £■ / J + 3^Var(E) ■ In the case where the invariance value is greater, for example strictly greater, than the reference value (Y branch at the output of block 604) the processor 108 is configured to determine, in a step 605 (SIGNAL) that the tensor comprises a useful signal, that is to say that the signal-to-noise ratio [5 is strictly greater than 0. In the case where the invariance value is less than the reference value (branch N at the output of block 604), the processor 108 is configured to determine, in a step 606 (NOISE) that the tensor is a pure noise tensor, i.e. that the signal to noise ratio p is equal to 0.

[0084] For example, when the processor 108 determines that the tensor is a pure noise tensor, the latter is removed from the device 100. On the contrary, when the processor 108 determines that the tensor comprises a useful signal, the tensor is for example provided to a data processing circuit. For example, the data processing circuit is configured to perform denoising operations on the tensor. In particular, when the tensor is an image representation, such as a color image, or a video, the data processing circuit is configured to perform image processing operations.

[0085] [Fig.7] is a flowchart illustrating steps of another signal detection method.

[0086] By way of example, the method described in relation to [Fig.7] comprises steps 600 to 602 described in relation to [Fig.6].

[0087] In a step 700 (COMPUTE MEAN AND VARIANCE FOR DIFFERENT P), an expectation value Ep[Z] and variance Var^I^ of an invariance value of a tensor having a signal-to-noise ratio P are calculated. For example, step 700 is carried out for several values ​​of p, where P may for example be zero. These values ​​are for example calculated upstream, for example during the programming of the instructions 112. In another example, these values ​​are calculated on the fly, during the execution, by the processor 108, of the instructions 112.

[0088] In a step 702 (DETERMINE P), the processor 108 is configured to determine the value of the signal-to-noise ratio of the tensor received in step 600. As an example, the invariance value I is compared to the different expectations EpfZ] calculated during step 700. The signal-to-noise ratio retained is the value of P minimizing the value | JE^Z] [. In other examples, the invariance value Z is compared to the different values ​​Ep[Z] + 2Varp(I). The signal-to-noise ratio retained is the value of P minimizing the value | / - ^[Z] + 2\IVarp(Z) | •

[0089] For example, when it is determined that the signal-to-noise ratio is other than 0, the tensor is provided to a data processing circuit, for example configured to perform image processing operations, in association with the estimated value of the signal-to-noise ratio.

[0090] However, as illustrated in Fig. 5, the distributions of a trace invariant according to different values ​​of P overlap. This induces uncertainty in the signal detection result. Indeed, when carrying out the methods described in relation to Figs. 6 and 7 on the basis of the invariant used for [Fig.5], there is a risk that a tensor comprising a useful signal is determined to be a pure noise tensor, or vice versa.

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[0094] According to one embodiment, the invariance value is calculated based on a combination of at least one trace invariant for which the overlap interval between the distributions is reduced. For an invariance value I, a distance between the distributions associated with a pure noise tensor and a tensor comprising a useful signal with a signal-to-noise ratio p is represented by an objective function: [Math 3] ms(Lp)-mx(t) where msm P) d OS(AP) are respectively the expectation oN(l)-as(ip) ' and the standard deviation of the distribution of an invariant, or combination of invariants, for a tensor having a signal-to-noise ratio equal to P and where mN (Z ) and a^,( I ) are the expectation and the standard deviation of the distribution of the same invariant, or even combination of invariants, for a pure noise tensor. The idea is then to look for an invariance value in the form of a combination / = a J g ■' For which the quantity f is large enough to avoid detection errors. The parameter space then describing the invariant Z is the t-simplex AZ- where t is the number of invariants Ig, considered in the combination. Thus, looking at the numerator of the objective function applied to a weighted invariant, we notice that for at least trace invariants of order 2, the numerator of is in depending on the type of invariant chosen and, due to the contribution of order p for each vertex, is of the order of ^p2. Thus, by summing invariants of order 2, it is sufficient to take into account the contribution of the signal in ^p2 in the numerator and to multiply it with the sum of the weights in the numerator. In the case of invariants of degree 4, the numerator is more complex and has the form P^n ) «p2 + n2p4- For some graphs, such as tetrahedral graphs, and some "pillow" graphs the value ( n ) is less than np2 when the dimension n is sufficiently large. Thus the contribution / j2p4 is factored into the numerator. Looking at the denominator, and more specifically Gy(Z, P), the largest contribution is approximated by 2av(Z) • These approximations show that for invariants of order 2, or of order 4 fulfilling the condition P / in ) < n2p4, the quantity Ct A” ) / IL Œ admits a minimum. Moreover, under the condition that Cov(lG„ Ig) is negligible in front of Var(jGj) and Var( IG.), this quantity is minimal when the weights aj are equal to fq y Var( Zg )'°n is a normalization constant such that = 1-

[0095] Figures 8A and 8B are graphs illustrating the behavior of the objective function. In particular, Figures 8A and 8B illustrate the behavior of the numerator of the objective function for several invariants and several graphs.

[0096] A curve 800 is the equation curve as a function of P. Figure 8A illustrates several curves 802, each illustrating the behavior of ms(I, fi) -mN(I), as a function of [3 and for several tetrahedral type invariants. Figure 8B illustrates several curves 804, and 806 each illustrating the behavior of I, fi) -mN(l) , as a function of p and for a pillow invariant. Both Figures 8A and 8B show a gap between the behavior of the invariants and ^2^4. This gap is due to the P[ terms described previously. However, in the case of tetrahedral graphs, the gap between curves 802 and curve 800 is small. The influence of the P] term is then negligible when the dimension n of the tensor is large, for example when n > 100. On the contrary, in the case of pillow graphs, the gap between curves 804 and 800 shows that the P] term is not negligible for these invariants. The gap between curves 806 and 800 is small, however, so there are pillow graphs for which the Pj term is negligible.

[0097] In particular, when the term P] is negligible when n is large, the objective function is such that [Math 4] m (7m i °ù s corresponds to the order of the invariants. In the case where the invariance value is calculated from invariants of different orders, the value of ' is an approximation. For example, the value of $ corresponds to the average of the orders of the trace invariants used. Minimizing the objective function consists of looking for a combination of values ​​for each a', under the condition that 1 and such that, for this combination of coefficients, the value of the objective function is as small as possible.

[0098] Figures 9A, 9B, 10A and 10B are graphs illustrating the distribution of weights provided by a symmetrization process.

[0099] In particular, Figures 9A and 9B illustrate weights for the 60 different tetrahedral graphs Gz. Figures 10A and 10B illustrate weights for the 99 different “pillow” graphs Gi.

[0100] Figures 9A and 10A are graphs comprising 60 and 99 points respectively. Each point has as abscissa the index i of the graph considered and as ordinate the value of] / yassociated.

[0101] Figures 9B and 10B are graphs comprising 60 and 99, respectively points. Each point has as abscissa (Invariant( / ;)) the index i of the graph considered and as ordinate the value of Var^ Iq ) associated, where is the symmetrization weight of the invariant Ij.

[0102] Figures 9A and 9B show that, in the case of tetrahedral graphs, the weights produced by symmetrization and the values ​​[ / Var[ Ig} are proportional. Thus, in this case, symmetrization is equivalent to weighting the graphs by the inverse of the variance. On the contrary, Figures 10A and 10B show that, in the case of pillow graphs, the symmetrization weights w> and the values ​​| [Yar^Ig} are not proportional.

[0103] The values ​​of the weights used for figures 9B and 10B are, for example, obtained using numerical methods making it possible to count the number of repetitions in the 216, or 348, possible invariants for tetrahedral graphs, or "pillow". For each invariant, the variance is, for example, obtained numerically, for example, from a large number of samples, for example between 500 and 2000, of pure noise tensors. By way of example, the numerical calculation of the variance is carried out upstream of the signal detection method as described in relation to figures 6 and / or 7. By way of example, the numerical calculation of the variance is carried out on a computer, before the programming of the instructions 112.

[0104] Figures 1 1A and 1 1B are graphs illustrating gradient descents associated with the objective function f$(l) ■ In particular, Figures 1 1A and 1 1B illustrate gradient descents respectively carried out on the sub-simplex of Melonic graphs or the sub-simplex of "tadpole" graphs, from 30 different initializations of the coefficients ^j. Gradient descent makes it possible to optimize the values ​​of the coefficients, that is to say to find a combination minimizing the value of the objective function, for a fixed set of graphs. In the remainder of the description, the term minimizing the objective function means selecting the combination of values ​​of the coefficients for which, for all the other combinations tested numerically, the value of the objective function is greater than that associated with the minimizing combination. In certain cases, at least one coefficient is determined to be harmful.Figures 1 IA and 1 IB illustrate the evolution of the values ​​f^(I), for each initialization, following several steps of gradient descent. Whatever the initialization, Figures 11A and 11B show that there is a combination of invariants for which the value of the function f(I) is minimal. The combinations of invariants resulting from the gradient descent process therefore make it possible to have a distribution associated with pure noise as far as possible from the distributions associated with a non-zero signal-to-noise ratio.

[0105] Figures 12A and 12B are graphs illustrating the values ​​of the objective function for different graphs and as a function of the value of the signal-to-noise ratio.

[0106] In particular, Figure 12A illustrates curves 1200, 1201, 1202 and 1203 respectively representing the value f$(I) as a function of [3, for an invariant Z being a combination of “tadpole”, melonic, “pillow” and tetrahedral trace invariants. Curve 1204 represents the value / ^( / ) as a function of [3, for an invariant Z being a combination of trace invariants belonging to several categories. In particular, the combinations of invariants considered are obtained following the performance of a gradient descent, in order to determine coefficient values ​​for which the value of the objective function is minimal.

[0107] [Fig.l2B] illustrates curves 1205, 1206, 1207 and 1208, similar to curves 1200, 1201, 1202 and 1203 except that the coefficients of the invariants are equal to the inverse of the variance of the associated invariant. As described in connection with Figures 8A, 8B, 9A, 9B and 10A, 10B, the inverse of the variance of a tetrahedral invariant is proportional to the weight of the graph.

[0108] Figures 13A, 13B, 13C and 13D are graphs illustrating distributions of trace invariants. In particular, in each [Fig.l3A] to 13D, the left distribution is a distribution of an invariance value for a pure noise tensor and the right distribution is associated with a tensor comprising a useful signal having a signal-to-noise ratio equal to 3. In addition, the dimension of the tensors used for developing the graphs is equal to 100.

[0109] The distributions illustrated by [Fig.l3A] are those associated with a combination of trace invariants only of the "pillow" type, each invariant being weighted by the inverse of its variance. The distributions illustrated by [Fig.l3B] are those associated with the same combination of invariants but weighted by the associated symmetrization weights. The overlap interval between the two distributions is less when the invariants are weighted by the inverse of the variance. Indeed, in the case of "pillow" type invariants, as described in relation to [Fig.lOB], the inverse of the variance is not equivalent to the symmetrization weight.

[0110] The distributions illustrated by [Fig. 13C] are those associated with a combination of only tetrahedral trace invariants, each invariant being weighted by the inverse of its variance or by the associated symmetrization weight.

[0111] The distributions illustrated in [Fig. 13D] are those associated with a combination of pillow, tadpole, and tetrahedral trace invariants, each invariant being weighted by a value determined following the performance of a gradient descent. For example, pillow-type invariants are weighted by the inverse of their variance, and tetrahedral, tadpole, or melonic, are weighted by the associated symmetrization weight.

[0112] The overlap interval is less when the invariance value is calculated from a combination of invariants of all types.

[0113] Figures 14A, 14B and 14C are graphs illustrating success rates in signal detection, according to one embodiment of the present disclosure;

[0114] [Fig. 14A] illustrates success rates in the application of the signal detection method as described in relation to [Fig. 6] when the invariance value is a combination of pillow invariants. In particular, a curve 1400 illustrates the success rate when the pillow invariant combination is weighted by the inverse of the variance. A curve 1401 illustrates the success rate when the pillow invariant combination is weighted by the symmetrization weights. For example, the weights and invariants used are the same as those used to obtain the distributions illustrated in [Fig. 13A] and 13B. The success rate is therefore better when the weighting is carried out by the inverses of variance, as suggested by Figures 13A and 13B.

[0115] [Fig. 14B] illustrates success rates in applying the signal detection method as described in relation to [Fig. 6]. In particular, a curve 1402 illustrates the success rate for a combination of invariants of all types and a curve 1403 illustrates the success rate for a combination comprising only tetrahedral type invariants. For example, the weights and invariants used are the same as those used to obtain the distributions illustrated in Figures 13C and 13D. The success rate is therefore better when the invariance value is calculated from several types of trace invariants as suggested in Figures 13C and 13D.

[0116] [Fig.l4C] groups curves 1402 and 1403 with a curve 1404 illustrating the success rates for an invariance value being a combination of 28 “pillow” type invariants, 3 of which are weighted by the associated symmetrization weight and the other 25 by the inverse of their variance.

[0117] As an example, the success rates were calculated from a large number of samples, for example between 500 and 2000, of tensors whose signal-to-noise ratio is known. The method described in relation to [Fig.6] is for example carried out on each sample. The result provided by the processor 108 is then compared with reality. It is observed that the higher the signal-to-noise ratio, the higher the success rate. In particular, the success rate is equal to 1 when the signal-to-noise ratio is greater than 3.

[0118] Figure 15 is a graph illustrating weights obtained by gradient descent. In particular, Figure 15 illustrates 4 categories of invariants, each category being separated by vertical lines 1500, 1501 and 1502. To the right of line 1502, points associated with trace invariants of the “pillow” type have the ordinate ( log( az ) ) the logarithm of the weighting value obtained by performing a gradient descent process. A horizontal line 1503 separates the pillow invariants into two parts. Above line 1503 are invariants that allow a satisfactory success rate to be obtained, for example the success rates illustrated by curve 1404. Below line 1503 are invariants that do not give satisfactory results. To the left of line 1500, points associated with melon trace invariants are illustrated. Between lines 1500 and 1501, points associated with tadpole trace invariants are illustrated. Between lines 1501 and 1502, points associated with tetrahedral trace invariants are illustrated.

[0119] [Fig. 16] is a flowchart illustrating a method of selecting a set of trace invariants, according to an embodiment of the present disclosure.

[0120] By way of example, the method described in relation to [Fig. 16] is carried out by a device external to the device 100 such as a computer. By way of example, the external device comprises a non-volatile moire in which are stored indications of resources, such as memory and / or time resources, necessary for the calculation of trace invariants and / or combination of trace invariants. By way of example, the memory stores a list indexing a plurality of combinations of invariants associated with weights determined for example by a gradient descent method. In another example, for each invariant of a combination, the associated weight is the symmetrization weight, or the inverse of the variance. By way of example, in association with each combination, the memory stores an indication of a number of operations allowing the calculation of the associated invariance value.For example, in association with each combination, the memory further stores an indication of resources required and / or time required to calculate the associated invariance value. For example, the time indication is of the form "small", "medium" or "large" associated with, for example, a memory capacity range.

[0121] In a step 1600 (INFORMATION FURNITURE) information about the device 100 is provided to the external device. The information includes, for example, the memory resource of the device 100. For example, the memory resource corresponds to the capacity of the volatile memory 106. The information further includes, for example, the performance of the processor 108. The information includes, for example, the order of the tensors acquired by the sensor 102 as well as the dimensions of the tensors. For example, the information further includes an indication of time, for example of the form “small”, “medium” or “large”, in which the calculation of the invariance value, or the signal detection method as described in relation to [Fig. 6], is to be performed. In one example, only the capacity of the memory 106 as well as a number of operations are provided to the external device. The number of operations corresponds, for example, to a maximum number of operations for calculating the trace invariant in order to satisfy, for example, a computation time constraint.

[0122] In a step 1601 (INVARIANT ESTIMATION), the external device estimates a combination of invariants adapted to the device 100. For example, the estimation is carried out by reading the list stored in the non-volatile memory. The combination of invariants retained is for example that corresponding the most to the information provided during step 1600. In another example, certain criteria, such as the memory resource, are prioritized.

[0123] In a step 1602 (ESTIMATION OPERATIONS) a number of operations necessary for the calculation of each of the trace invariants included in the combination is estimated. In another example, a number of operations necessary for the calculation of the invariance value, associated with the combination, is estimated during step 1602. For example, the number of operations is estimated on the basis of the dimensions and the order of the tensor.

[0124] In a step 1603 (PROGRAMMING INSTRUCTIONS) the device 100 is for example programmed in order to implement the method described in relation to FIG. 6 from the calculation of invariance values ​​on the basis of the combination estimated during step 1601. By way of example, step 1603 comprises the programming of the instructions 1603 so that during their execution the invariance value, on the basis of the combination estimated in step 1601, is calculated. By way of example, step 1603 further comprises the calculation of the reference value I ref and the programming of an instruction, in the instructions 112, controlling the comparison of the invariance value with the reference value. Step 1603 further comprises the storage of the instructions 112 thus programmed in the device 100.

[0125] Figure 17 is a graph 1700 illustrating success rates in signal detection. In particular, curves 1702 and 1704 illustrate success rates, on a scale from 0 to 1, and as a function of the value of the signal-to-noise ratio |3.

[0126] Curve 1702 illustrates the success rates (DETECTION SUCCESS) for carrying out a signal detection method as described in relation to [Fig.6] and on the basis of an invariance value comprising only tetrahedral type invariants. Curve 1704 illustrates the success rates following the implementation of a matrix signal detection method based on the conversion of tensors into matrices. For example, curves 1702 and 1704 are obtained by processing the same tensor values. In particular, the tensors used are of order 3 and of dimension 200x200x200 and the success rates are calculated from 1000 samples. In particular, the matrix method implemented is described in the publication “Detection of signal in spiked rectangular models. » published in 2021 in “International Conference on Machine Learning” by Jung, Ji Hyung, Hye Won Chung and Ji Oon Lee. Regardless of the value of the signal-to-noise ratio, the method described in relation to [Fig.6] obtains a higher success rate than the matrix method.

[0127] An advantage of the described embodiments is that they allow the implementation of a signal detection method on data represented by tensors of orders greater than or equal to 3, without converting them into matrices.

[0128] Another advantage of the described embodiments is that they allow the calculation of the invariance value to be adapted so as to minimize the failure rate in the detection method.

[0129] Various embodiments and variants have been described. Those skilled in the art will understand that certain features of these various embodiments and variants could be combined, and other variants will occur to those skilled in the art. The estimation of a combination of invariants allowing the calculation of the invariance value can be carried out on criteria other than memory and / or time resource criteria.

[0130] Finally, the practical implementation of the embodiments and variants described is within the reach of those skilled in the art from the functional indications given above.

Claims

Claims

1. Method for detecting a useful signal, the method comprising: - acquiring a raw signal, by a sensor (102); - providing the raw signal, to a processing device (108), the raw signal being represented by a tensor of order d greater than or equal to 3; - calculating, by the processing device, an invariance value ( / ) associated with the tensor, the invariance value being calculated on the basis of at least one trace invariant under the orthogonal group of degree d ( O(nyl) For tensors of order d; - comparing, by the processing device (108), the invariance value associated with the tensor with a first reference value ( Iref); - based on the comparison, providing, by the processing device, an estimate of the signal-to-noise ratio ( / ?) of the raw signal; and - if the estimated signal-to-noise ratio is different from 0, providing the tensor to a circuit configured to process the raw signal.

2. The method of claim 1, wherein the sensor (102) is configured to acquire image representations and the circuit configured to process the raw signal is an image processing circuit.

3. A method according to claim 1 or 2, wherein the invariance value associated with the tensor is a linear combination of a plurality of trace invariants Ij for the orthogonal group (O(n)) for tensors of order d, the combination being of the form djlf °where the values ​​are weighting coefficients.

4. A method according to claim 3, wherein the linear combination comprises melonic trace and / or tadpole and / or tetrahedral and / or pillow invariants.

5. The method of claim 4, wherein the weighting coefficient of a pillow-type trace invariant is equal to the inverse of the variance of the invariant for a pure noise tensor.

6. A method according to claim 4 or 5, wherein the weighting coefficient of a melanoid trace and / or tadpole and / or tetrahedral invariant is equal to the symmetrization weight of the invariant.

7. A method according to any one of claims 1 to 6, wherein the first reference value is a function of the expectation of the invariance value for a pure noise tensor.

8. The method of claim 7, wherein the first reference value is equal to / ^ / ] +2^Var(I) , where £[ / ] and Var(l) are respectively the expectation and variance of the invariance value for a pure noise tensor.

9. A method according to any one of claims 1 to 8, wherein, if the invariance value is greater than the first reference value, the processing device (108) is configured to determine that the raw signal acquired by the sensor (102) comprises a useful signal.

10. A method according to any one of claims 1 to 9, further comprising, when it is determined that the invariance value is greater than the first reference value: - comparing the invariance value with a second reference value that is a function of the expectation of the invariance value for a tensor associated with a signal-to-noise ratio of value [1.

11. A device (100) comprising: - a sensor configured to acquire a raw signal; - a processing device configured to execute instructions (112) stored in a non-volatile memory (104) of the device, the execution of the instructions making it possible to detect whether the raw signal comprises a useful signal, by: - ​​shaping the raw signal in the form of a tensor of order greater than 3; - calculating an invariance value of the tensor; - comparing the invariance value with a reference value; - based on the comparison, estimating the signal-to-noise ratio present in the raw signal; and - if it is determined that the signal-to-noise ratio is non-zero, providing the tensor to a circuit configured to perform raw signal processing operations.

12. The device of claim 11, wherein the sensor is configured to acquire image representations and wherein the circuit configured to perform raw signal processing operations is an image processing circuit.

13. A method of determining a combination of trace invariants, the combination being of the form y üjlf °ù 'cs h are invariants of trace and the values ​​aj are weighting coefficients, adapted to a device (100), the method comprising: - providing indication of the device's memory resources to an external device; - providing the indication of a processing time to the external device; - providing an indication of dimensions of the order of tensors to the external device; - searching for a set of trace invariants, in association with a set of weights, forming the combination, among a plurality of trace invariants, each set of trace invariants being associated with a cost and each cost value being stored in a memory of the external device in association with an identifier of the associated set, the search for the set of invariants being carried out on the basis of the memory resources and / or the calculation time and / or the indication of the dimensions provided; - providing the set of trace invariants and weights to the device so that an invariance value is calculated, by the device, based on the determined combination of invariants.

14. The method of claim 13, wherein the weights associated with each trace invariant in each combination are determined by performing gradient descent on an objective function determining a distance between the distribution of the invariance value associated with the combination for a pure noise tensor and for a tensor having a non-zero signal-to-noise ratio.

15. A method according to claim 13 or 14, wherein each trace invariant is a melanoid and / or tadpole and / or tetrahedral and / or pillow trace invariant.

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