WO1991018357A1

WO1991018357A1 - Imaging method and uses of same

Info

Publication number: WO1991018357A1
Application number: PCT/FI1991/000161
Authority: WO
Inventors: Pekka HIISMÄKI
Original assignee: Valtion Teknillinen Tutkimuskeskus
Priority date: 1990-05-24
Filing date: 1991-05-23
Publication date: 1991-11-28
Also published as: FI902600A; FI902600A0

Abstract

An imaging method for forming a bidimensional image of a self-radiating object (O) or of an object that is selectively penetrable by radiation. In the method, a discrete aperture is employed which has an area wider than a spot-like aperture and which consists of a finite number of pixels belonging to the same periodic lattice, the radiation used for the imaging being confined to pass through said aperture. In the aperture, an exchangeable series of masks is installed, so that, of the object, a pseudo-image is stored per each component code. The image of the object (O) is synthesized out of said pseudo-images by means of a decoding algorithm. By means of the masks, the radiation field that passes through the aperture is modulated in accordance with the component codes of the CV codes in accordance with the present invention defined for the L-pixel discrete aperture.

Description

Imaging method and uses of same

The invention concerns an imaging method for forming a bidimensional image of a self-radiating object or of an object that is selectively penetrable by radi¬ ation.

Further, the invention concerns the uses of the method.

In prior art, when a bidimensional image is formed of a bidimensional or, often, of a three-dimensional object, the technique to be applied depends on the particles available for the transmission of the image. It is essential whether the passage of the carrier particles can be affected in a controlled way by optical means by means of lenses or mirrors or not. If not, the imaging must be based on a precisely defined opening or aperture, by whose means it can be achieved that the image corresponds to the object as unequivocally as possible and in a correct way in respect of its dimensional proportions. The basic solution is a spot-like aperture, well-known examples of which are the "camera obscura" and a spot anode of a fluoroscopic apparatus. Qualitatively, the image produced by a spot-like aperture is optimal, but a limiting factor is often constituted by the intensity. A small, spot-like aperture allows just a little portion of the intensity arriving on the plane of the aperture to pass through the aperture, or a suffi- ciently high brightness cannot be produced in the spot-like source. In view of solving this problem, in prior art, so-called coded apertures are known. In respect of said prior-art technique, reference is made to the paper by G.K. Skinner, "X-ray Imaging with Coded Masks", Scientific American 66...71, August (1988), wherein the applications suggested are confined to X-ray astronomy.

The development in the use of coded apertures has progressed from unidimen- sional problems to bidimensional ones. It is a general objective in the image formation transmitted by means of particles to obtain an optimal signal-to-noise ratio and to avoid systematic image errors. Codes known in unidimensional imaging are periodic, pseudorandom codes and finite, complementary codes of Golay, in whose respect reference is made to the paper by M.J.E. Golay, "Complementary Series", IRE Trans on Inf. Theory IT-7. 82...87, (1961). When applied correctly, said codes do not involve systematic image errors. In bidimen¬ sional imaging, the only prior-art codes that, when applied correctly, do not cause systematic errors are pseudorandom codes. However, it is a drawback of these codes that the pixel-specific variance of the final image is invariable and proportional to the number of all the detected particles. Thus, a strong object present in the image covers weak objects, which are difficult to detect, by means of its noise. In view of avoiding this problem, finite codes should be employed in stead of periodic ones. As is well known, such a finite scalar code does not exist.

The object of the present invention is to provide a novel imaging method by whose means the drawbacks discussed above are avoided.

A further object of the invention is to create novel uses of the method in accordance with the invention.

In view of achieving the objectives stated above and those that will come out later, the invention is mainly characterized in

that, in the method, a discrete aperture is employed which has an area wider than a spot-like aperture and which consists of a finite number of pixels belong¬ ing to the same periodic lattice, the radiation used for the imaging being confined to pass through said aperture,

that in said aperture, an exchangeable series of masks is installed, so that, of the object, a pseudo-image is stored per each component code,

that the image of the object (O) is synthesized out of said pseudo-images by means of a decoding algorithm,

that, by means of said masks, the radiation field that passes through the aperture is modulated in accordance with the component codes of the CV codes defined for the L-pixel discrete aperture, which CV code is a combination of n scalar binary codes Ml, M2,...Mn, each of which binary codes obtains a value 0 or 1 with each pixel (i,j) of the aperture, and which binary codes themselves, or the autocorrelation functions Ml#Ml,...Mn#Mn of which binary codes, satisfy the following conditions (I and II):

I: Ml + M2 + ...Mn = LF

II: M1#M1 + M2#M2 +...Mn#Mn = (1 - m I_ 5(i,0 - (j,0) + m-F#F,

wherein 1 and m < 1 are little integers, δ(i,0) is a delta function, which obtains the value 0 in all other cases, except that it obtains the value 1 when the arguments are the same, i.e. i = 0, and F is full mask of the aperture, which obtains the value 1 with every pixel of the aperture,

that as the pseudo-images Rl, R2,...Rn to be formed of the object (O), substan¬ tially the following convolutions (III) of the codes Ml, M2,...Mn and of the object (O) are used:

πi: Rl = M1*0, R2 = M2*0,...Rn = Mn*0

and that the final image (I) is calculated by means of the following decoding algorithm (IV):

IV: I = M1#R1 + M2#R2 + .. Mn#Rn -(m/l F#(Rl + R2 +... Rn)

or by means of an equivalent algorithm which gives a sharp image of the object (O).

In the following, the invention will be described in detail with reference to some exemplifying embodiments of the invention illustrated in the figures in the accompanying drawing, the invention being not confined to the details of said embodiments. Figure 1 is a block diagram illustrating the different steps of the imaging method in accordance with the invention.

Figure 2 illustrates the seed codes of the vector codes in accordance with the invention and the doubling operations carried out with said seed codes.

Figure 3 is a schematic illustration of an X-ray telescope that makes use of the method of the invention.

Figure 4 is a schematic illustration of an application of the invention to radio¬ scopy.

Figure 5 illustrates an exemplifying embodiment of the invention, showing the original object "CV", four different masks and the four different images taken of the original object through said masks, and a decoded image.

The different stages of imaging are shown schematically by Fig. 1, wherein O is the bidimensional object or the bidimensional projection of a three-dimensional object to be imaged, M is the "point spread function" that defines the imaging system, R is the "pseudo-image" stored by the detector, D is the decoding function used in the processing of the pseudo-image, and I is the final image formed of the object.

In Fig. 1, * represents a convolution operation. In the choice of M and D in the invention, the aim is that D*M should be reduced to a multiple of a δ -function. Herein, bidimensional objects, apertures, and images are dealt with as discrete functions, which are numerical values given by means of elements, pixels, which form a bidimensional lattice.

As is shown in Fig. 3, the aperture A is formed on the aperture plane T by a finite, unequivocally defined set of pixels, which is expressed by the formula

(1) (i,j)_A e A . It is a feature common of the codes defined with this aperture that they are lost, i.e. they obtain the value 0 with all pixels outside the aperture A. A full code F is defined as follows:

(2) F_u = l (i,j) e A

= 0 in all other cases.

A polarity code C defined with A, which code can obtain the values + 1 or -1 with the pixels included in A, can always be written in the form

(3) C = C⁺ + C = 2-C⁺ - F,

wherein C⁺ and C^" are binary, i.e. can obtain the values 0 or 1 only, complemen¬ tary codes which satisfy the condition

(4) C⁺ + C = F.

The correlation function of two codes defined with the same aperture is defined as a sum of the products of the code values of the pixels that are placed one on top of the other, for every possible transition vector when the codes are made to glide over each other as multiples of the lattice vectors. The correlation operation is expressed by means of the symbol #. An identity

(5) C#C + F#F = 2.(C⁺#C⁺ + C#C)

reveals a connection between the autocorrelation functions of the codes defined above.

In the following, a two-component vector code will be examined, whose compo- nent codes U and D are codes of the polarity type so that U ("up") refers to the upper component and D to the lower ("down") component. The aim is to find code pairs U and D which satisfy the condition

(6) U#U + D#D = 2.L.δ(i,0>δ(j,0) , wherein L is the number of pixels in the aperture. If such codes as result in a sharp δ-function are found, at the same time, also the binary codes U⁺, U^", D⁺ and D^" have been found, which, by virtue of the equations (5) and (6), satisfy the condition

(7) U⁺#ir + U ^"# IT + D⁺#D⁺ + D #D^" - F#F = L.δ(i,0 δ(j,0),

which can be used for decoding of a series of pseudo-images measured by means of four binary codes. With a full code F, measurement need not be carried out, for the record corresponding to it is obtained by summing up the pseudo-images measured by means of complementary codes. More general codes may also be aimed at, for example, so that the number of component codes is higher than four or that they do not have to be complementary in pairs, but that some little multiple of a full code is produced only out of the sum of all of the component codes, but such codes do not seem to provide any advantage over the codes complementary in pairs.

Referring to Fig. 2, it is ascertained that the simplest aperture comprises one pixel only, i.e. L = 1. For this aperture, it is possible to define two orthogonal code vectors:

(8) NE = SE = II -1

To facilitate the memorizing, the denotations have been chosen in accordance with the points of the compass; NE comes from the point "north-east", and SE from the point "south-east". The points SW = -NE and NW = -SE are also code vectors of an aperture lxl. An L-pixel aperture A is now examined, and it is assumed that, for said aperture, scalar codes U(A) and D(A) have been found, which satisfy the condition (6). New codes can now be found by means of the following doubling rule. D o u b l i n g r u l e:

The original aperture is copied on the aperture plane twice in its original position or one time or both times as rotated over 180 degrees so that the copies do not even partly overlap each other, and one of the copies is filled with NE vectors whose signs have been chosen in accordance with the U(A) code of the original aperture, and the other copy is filled with SE vectors whose signs have been chosen in accordance with the D(A) code of the original aperture.

The new code obtained by means of the doubling rule obviously also satisfies the equation (6), for, with internal transition vectors of the copies, this follows from the fact that U(A) and D(A) satisfied the equation (6) and, with transition vectors extending from one copy to the other, this follows from the fact that the NE and SE vectors are perpendicular to one another. By applying the doubling rule, it is possible to find complementary vector codes defined with apertures of arbitrary magnitudes. To be able to start, simple "seed codes" are needed, of which three have been found. They and the first doubling operation are illus¬ trated in Fig. 2. Even though the examples always show a rectangular lattice plane consisting of square pixels, this is not essential. Exactly the same codes can be employed for any lattice with oblique angles whatsoever, for example for a hexagonal lattice consisting of hexagons.

In order that the advantages of the CV codes in accordance with the present invention over the prior-art pseudorandom codes should come out, it is necess- ary to examine the variance of the image signals. The pixel elements of the detector store four pseudo-images:

(9) Rl = IT* O + Bl + Nl

R2 = U* O + B2 + N2 R3 = D⁺* O + B3 + N3

R4 = D* O + B4 + N4 ,

wherein B1...B4 represent an unmodulated background and N1...N4 represent random noise. The stored signals R1...R4 are Poisson-distributed random quantities, which are independent from each other and whose covariance matrix is

(10) σ²R(α, _)_u = E{[R_αi - E(R_Qi)].[R^ - E(R^)]} = = E No_fNβ = δ(_α,_J8).δ_i,i.E{Rα_i},

wherein E{} means the expectation value. The nature of the background signals depends on the imaging problem in the particular case. In some cases, it can be assumed that the following equation is true:

(11) Bl = B2 = B3 = B4 = B.

In such a case, the background is fully unmodulated, but in the other respects arbitrary. Now, by virtue of the equation (7), the decoding algorithm will be

(12) I = U⁺#R1 + U -# R2 + D⁺#R3 + D __ R4 - *SF#(R1+R2 +R3 +R4)

= L-O + (U⁺-^J/₂F)#(N1 - N2) + (D₊-V_F)#(N3 - N4) .

In this case, B no longer occurs in the decoded image. For the covariance matrix of the decoded image, the following equation is obtained:

(13) σ²I_u = y₂.∑

wherein R_k is defined by means of the equation

(14) R_k = Rl_k + R2_k + R3_k + R4_k = 4.[ 2F*0 + B]_k .

The variance is obtained as

(15) σ²I_iti = {F * [ViF * O + B]}, .

If the object has a separate spot source, it causes a variance in the surrounding of its own image at the maximum at a distance where the autocorrelation function of full code is still different from zero. This is why even weak sources in the object distribution can be noticed unless they are placed entirely side by side with a strong source.

In the following, some exemplifying embodiments and applications of the method of the invention will be described.

In X-ray astronomy, it is desired to chart the sources of X-radiation in the sky. Owing to the absorption by the atmosphere, the telescope must be placed in a satellite. For soft X-rays, it is possible to use prior-art mirror optics; for hard X- rays, coded apertures have been employed. If the object remains stationary during the imaging, the four separate measurements necessary for the use of the CV-codes in accordance with the invention can be made one after the other by alternatingly exchanging one of the masks prepared in accordance with the component codes onto the aperture. In the contrary case, it is possible to use four parallel measurements, as is illustrated in Fig. 3. This solution is, better than pseudorandom codes, suitable for the detection of weak sources when there are also strong sources in the field of view.

In radioscopy, the achievement of sufficient surface brightness at the source of radiation is a problem in particular with displaceable sources, and in neutron radiography even otherwise. In prior art, only spot-like apertures have been known. As is well known, the size of the aperture has been chosen as a compro¬ mise between resolution and intensity. Fig. 4 is a schematic illustration of the possibility of use of CV codes in radioscopy. Even if the mask M placed on the aperture operated deficiently so that the absorbing pixel is partly penetrable, this would not necessarily cause a major problem, for, according to the equation (12), the unmodulated background is eliminated in the decoding stage.

In Fig. 4, S represents the source of radiation, O represents the object to be radiographed, M represents a mask in accordance with the invention placed on the aperture, and D represents the radiation detector.

Fig. 5 is a detailed illustration of an exemplifying embodiment of the invention. In Fig. 5, the original object O = "CV" is placed to the right above. At its side, there are four 16-pixel masks Ml, M2, M3 and M4, which form the CV code. The four images Kl, K2, K3 and K4 in the middle represent the object "CV" as imaged through each of the masks Ml, M2, M3 and M4, and at the bottom there is the decoded image K, which is an accurate copy of the original object O = "CV". Other finite codes do not possess this property.

In the following, the patent claims will be given, and the various details of the invention may show variation within the scope of the inventive idea defined in said claims and differ from the details stated above for the sake of example only.

Claims

1. Imaging method for forming a bidimensional image of a self-radiating object (O) or of an object that is selectively penetrable by radiation, c h a r a c - t e r i z e d in

I: Ml + M2 + ...Mn = 1-F

E: M1#M1 + M2#M2 +...Mn#Mn = (1 - m).I_ δ(i,0 δ(j,0) + m.F#F,

wherein 1 and m < 1 are little integers, δ(i,0) is a delta function, which obtains the value 0 in all other cases, except that it obtains the value 1 when the arguments are the same, i.e. i = 0, and F is full mask of the aperture, which obtains the value 1 with every pixel of the aperture, that as the pseudo-images Rl, R2,...Rn to be formed of the object (O), substan¬ tially the following convolutions (HI) of the codes Ml, M2,...Mn and of the object (O) are used:

IE: Rl = M O, R2 = M2*0,...Rn = Mn*0

IV: I = M1#R1 + M2#R2 + .. Mn#Rn -(m/l F#(Rl + R2 +... Rn)

2. Imaging method as claimed in claim 1, c h a r a c t e r i z e d in that, of the object to be imaged, the pseudo-image defined above is stored in digital form per each component code.

3. Use of a method as claimed in claim 1 or 2 in a X-ray telescope when the sources of X-radiation in the sky are charted, said telescope being placed in a satellite.

4. Use as claimed in claim 3, wherein the object remains stationary during the imaging so that the four different measurements needed for the use of the CV- codes in accordance with the invention are carried out one after the other by alteraatingly exchanging one of the masks prepared in accordance with the component codes onto the aperture.

5. Use as claimed in claim 3 for detection of weak X-ray sources when the field of view also includes strong sources, by using four parallel measurements (Fig.

3).

6. Use of a method as claimed in claim 1 or 2 for radioscopy.