DE102014113520B4 - Method for low-loss transformation and/or compression of a data stream - Google Patents

Abstract

Method for the low-loss transformation and/or compression of a data stream of input signals (S12Bit) with a first bit depth into a data stream of output signals (S8Bit) with a second bit depth using a transfer function in which a noise component of the input signals (S12Bit) is taken into account, the transfer function is designed such that the noise component in the data stream of output signals (S8Bit) is at least approximately constant, and wherein the transfer function further comprises:- at least one logarithmic function, in which a logarithm of at least the input signal (S12Bit) and the noise component is formed; or- at least one area hyperbolic cosine function of the input signal (S12Bit), the noise component and a proportional statistical noise component which the input signal (S12Bit) has in addition to the noise component.

Description

The invention relates to a method for low-loss transformation and/or compression of a data stream. The invention also relates to a method for increasing the contrast of a data stream and an image processing unit.

Modern existing image sensors (for example thermal, visual or the like) have a high dynamic range or a high bit or sampling depth of for example 12, 14 or 16 bits (referred to generally as n bits below). However, this internally available data cannot be transmitted or processed in many systems, since there are often standard interfaces that are often only designed for 8 bits. Likewise, there is often a need to transmit smaller amounts of data when transmitting image signals.

Of course, this problem also affects other types of signals, such as audio signals, measurement signals, voltage signals or the like, from a wide variety of sensors.

Known systems linearly convert the signals received by the sensor in the sensor dynamic range from the internal to the externally available bit depth, for example. In the process, image information is lost to a considerable extent. Lossless methods, such as ZIP format or the like, can reduce internal data to the available bandwidth, but do not deliver directly readable signals (e.g. audio signals or image signals), but rather a data stream that has to be recalculated downstream to image or sound. In addition, such methods require a comparatively high computing power in the system, in particular in the camera, and generate an additional delay in the image data or other data.

the U.S. 4,458,267 A relates to a digital X-ray system.

In addition, GOWEN, R.A.; SMITH, A.: Square root data compression. In: AlP Review of Scientific Instruments, Volume 74, August 2003, Number 8, 3853-3861. http://dx.doi.org/10.1063/1.1593811.

In addition, BERNSTEIN, Gary M. [et al.]: Noise and bias in square-root compression schemes. 01/13/2010. 22 p. URL: https://arxiv.org/pdf/0910.4571.pdf [accessed on 01/24/2022].

Proceeding from this, the object of the present invention is to create a method for low-loss transformation and/or compression of a data stream which avoids the disadvantages of the prior art, in which in particular only a small part of the useful information is lost and the data can be used directly .

This object is achieved according to the invention by a method for low-loss transformation and/or compression of a data stream of input signals with a first bit depth into a data stream of output signals with a second bit depth using a transfer function in which a noise component of the input signals is taken into account.

In the method according to the invention, the output signal also consists of data that can be used directly or image data that can be viewed directly. The applied transformation and/or compression can, if necessary, be reversed to a large extent by means of a corresponding inverse function in the receiving system. In addition, for example in the case of image data, existing image optimization functions that have already been introduced can be applied directly to the generated image data. Local optimizations (manually or automatically) can also be used for image optimization for a viewer.

The invention is based on the consideration that the available bit resources are distributed as effectively as possible among the various signals by means of a noise-adapted transformation. If the signal distribution is assumed to be arbitrary over the whole possible range of values, the optimal solution is to allocate the same small number of bits to the noise of any given signal value.

wobei R ein Rauschanteil ist. Der Rauschanteil kann ein Ausleserauschen oder Elektronenrauschen sein. Er kann auch als n_RMS ^e- bezeichnet werden. Das Signalrauschen ΔS, das bei der Aufnahme von Bildern entsteht, ist von der Helligkeit jedes Bildpunkts abhängig. Dunkle Bildpunkte bzw. Pixel besitzen deutlich weniger Signalrauschen ΔS als helle Bildpunkte. Wie aus 1 ersichtlich, besteht das Signalrauschen ΔS im Wesentlichen aus der Quadratwurzel des Signals (Helligkeit des Bildpunkts) selbst. In 1 ist auf der horizontalen Achse (Abszisse) das Bildsignal S und auf der vertikalen Achse (Ordinate) das Signalrauschen ΔS aufgetragen.For example, an image signal S (with negligible so-called dark current noise) has the noise or the signal noise $\Delta \text{S}=\sqrt{\text{S}+{\text{<figure-callout id="2" label="R" filenames="DE102014113520B4\_0038.png,DE102014113520B4\_0039.png" state="{{state}}">R</figure-callout>}}^2},$

where R is a noise component. The noise component can be read noise or electron noise. It can also be denoted as n _RMS ^e- . The signal noise ΔS that occurs when taking pictures depends on the brightness of each pixel. Dark picture elements or pixels have significantly less signal noise ΔS than bright picture elements. How out 1 As can be seen, the signal noise ΔS essentially consists of the square root of the signal (brightness of the pixel) itself. In 1 the image signal S is plotted on the horizontal axis (abscissa) and the signal noise ΔS is plotted on the vertical axis (ordinate).

Advantageously, only the signal noise ΔS is impaired during the transformation and/or compression. Although you no longer get a bit-identical image, but since the changes only affect the noise, the essential information in the image is retained even after the transformation or compression. In the case of image signals, brighter areas have higher signal noise and are therefore coded differently than dark areas. The noise component R, which is independent of the image brightness, in particular the readout noise or the electron noise, becomes more important when considering the noise in the case of dark pixels, while it does not make any significant contributions in the case of bright pixels. The signal noise ΔS also scales with the square root of the signal S in thermal images. However, thermal images are characterized by a clear background. In 2 a signal noise ΔS is shown for image signals S with an offset. How out 2 As can be seen, the curve does not begin with an input signal of 0. The method according to the invention can advantageously also be applied to such offset-prone signals. However, depending on the offset, the compression effect can vary in magnitude.

The transfer function is designed in such a way that the noise component in the data stream of output image signals is at least approximately constant. Since it is the noise that limits the dynamics of a signal representation, it is advantageous to find a transformation or compression under the condition that the noise of the target representation, which has a bit depth of 8 bits, for example, is constant or at least approximately, in particular within a tolerance range, is constant.

The transformation and/or the compression can be at least partially reversible. Accordingly, the applied transformation can, if necessary, be completely or at least largely reversed by means of a corresponding inverse function in the receiving system.

In an example not belonging to the invention, the transfer function can comprise at least one root function, in particular a square root function, in which the radicand is formed at least by the input signal S _n and the noise component R.

ergeben, wobei S_m das Ausgangssignal, S_n das Eingangssignal, n die erste Bittiefe, m die zweite Bittiefe, S_nmax ein maximales Eingangssignal und R der Rauschanteil sein kann.In an example not belonging to the invention, the transfer function can change to ${\text{S}}_{\text{m}}=\left(2^{\text{m}}-1\right)\frac{\sqrt{{\text{S}}_{\text{n}}+{\text{<figure-callout id="2" label="R" filenames="DE102014113520B4\_0038.png,DE102014113520B4\_0039.png" state="{{state}}">R</figure-callout>}}^2}-\text{R}}{\sqrt{{\text{S}}_{\text{n max}}+{\text{<figure-callout id="2" label="R" filenames="DE102014113520B4\_0038.png,DE102014113520B4\_0039.png" state="{{state}}">R</figure-callout>}}^2}-\text{R}}$

where S _m is the output signal, S _n is the input signal, n is the first bit depth, m is the second bit depth, S _{nmax can be} a maximum input signal and R can be the noise component.

As a first alternative according to the invention, the transfer function comprises at least one logarithm function, in which a logarithm of at least the input signal S _n and the noise component R is formed. As an alternative to the square root function, a logarithmic transfer function can also be used.

ergeben, wobei S_m das Ausgangssignal, S_n das Eingangssignal, n die erste Bittiefe, m die zweite Bittiefe, S_nmax ein maximales Eingangssignal, α ein Justierparameter zur Anpassung an weitere Systemeigenschaften und R der Rauschanteil sein kann.The transfer function can change ${\text{S}}_{\text{m}}=\frac{\left(2^{\text{m}}-1\right)\cdot \text{ln}\left(1+\mathrm{a}\cdot \frac{{\text{S}}_{\text{n}}}{\text{R}}\right)}{\text{ln}\left(1+\mathrm{a}\cdot \frac{{\text{S}}_{\text{n max}}}{\text{R}}\right)}$

where S _m is the output signal, S _n is the input signal, n is the first bit depth, m is the second bit depth, S _{nmax is} a maximum input signal, α can be an adjustment parameter for adapting to other system properties and R can be the noise component.

In addition to the noise component R, the input signal S _n can have a proportional statistical noise component. The transfer function can comprise at least one hyperbolic area cosine function of the input signal, the noise component and the proportional statistical noise component.

If there is a statistical noise term proportional to the signal, an area cosine function can be used as a second alternative according to the invention. The statistical noise term can be characterized by a fraction α _i which is, for example, of the order of about 0.5 to about 2%.

ergeben, wobei S_m das Ausgangssignal, S_n das Eingangssignal, n die erste Bittiefe, m die zweite Bittiefe, S_nmax ein maximales Eingangssignal, α_i ein Bruchteil für den proportionalen statistischen Rauschanteil und R der Rauschanteil sein kann.The transfer function can change $$\begin{array}{l}{\text{S}}_{\text{m}}=\left(2^{\text{m}}-1\right)\frac{\text{ln}\left|\frac{1+2{\mathrm{a}}_{\text{i}}{}^2{\text{S}}_{\text{n}}+\sqrt{{\left(1+2{\mathrm{a}}_{\text{i}}{}^2{\text{S}}_{\text{n}}\right)}^2-1+4{\mathrm{a}}_{\text{i}}{}^2{\text{<figure-callout id="2" label="R" filenames="DE102014113520B4\_0038.png,DE102014113520B4\_0039.png" state="{{state}}">R</figure-callout>}}^2}}{1+2{\mathrm{a}}_{\text{i}}\text{R}}\right|}{\text{ln}\left|\frac{1+2{\mathrm{a}}_{\text{i}}{}^2{\text{S}}_{\text{n max}}+\sqrt{{\left(1+2{\mathrm{a}}_{\text{i}}{}^2{\text{S}}_{\text{n max}}\right)}^2-1+4{\mathrm{a}}_{\text{i}}{}^2{\text{<figure-callout id="2" label="R" filenames="DE102014113520B4\_0038.png,DE102014113520B4\_0039.png" state="{{state}}">R</figure-callout>}}^2}}{1+2{\mathrm{a}}_{\text{i}}\text{R}}\right|}\\ \end{array}$$

where S _m is the output signal, S _n is the input signal, n is the first bit depth, m is the second bit depth, S _{nmax is} a maximum input signal, α _i is a fraction for the proportional statistical noise component, and R is the noise component.

It is advantageous if the transfer function is implemented as a look-up table.

The transformation and/or compression can be carried out using a look-up table, which means that hardly any computing power is required in the system. This also avoids an additional delay in image signals, which can be undesirable in camera systems or even unacceptable depending on the application.

The input signals can be in the form of input image signals and the output signals can be in the form of output image signals.

1. a) eine verlustarme Transformation und/oder Kompression des Datenstroms von Eingangsbildsignalen mit der Eingangsbittiefe als erster Bittiefe in einen Datenstrom von Zwischenbildsignalen mit der Eingangsbittiefe als zweiter Bittiefe mittels des erfindungsgemäßen Verfahrens zur verlustarmen Transformation und/oder Kompression eines Datenstroms durchgeführt wird, wonach
2. b) eine Kontrastanhebung in dem Datenstrom von Zwischenbildsignalen erfolgt, und wonach
3. c) in dem Datenstrom von Zwischenbildsignalen eine Anzahl, insbesondere der untersten, Bits der Zwischenbildsignale derart entfernt wird, dass ein Datenstrom von Ausgangsbildsignalen mit der Ausgangsbittiefe erhalten wird.

Claim 7 relates to a method for increasing the contrast of a data stream of input image signals with an input bit depth, which is transmitted in a data stream of output image signals with an output bit depth, wherein:

1. a) a low-loss transformation and/or compression of the data stream of input image signals with the input bit depth as the first bit depth into a data stream of intermediate image signals with the input bit depth as the second bit depth is carried out using the method according to the invention for low-loss transformation and/or compression of a data stream, after which
2. b) contrast is increased in the data stream of intermediate image signals, and after that
3. c) in the data stream of intermediate image signals, a number, in particular the lowest, bits of the intermediate image signals are removed in such a way that a data stream of output image signals with the output bit depth is obtained.

In the case of low-contrast images, histogram equalization functions or contrast enhancements are often used. However, since the methods described take signal noise (during recording) into account, such corrections should not be carried out before the method according to the invention is applied.

In step c), the number of bits to be removed can result from the difference between the number of bits in the input bit depth and the number of bits in the output bit depth.

Claim 9 specifies a signal processing unit.

Advantageous refinements and developments of the invention result from the dependent claims. Exemplary embodiments of the invention are described in principle below with reference to the drawing.

• 1 ein Diagramm eines Signalrauschens bei Bildaufnahmen;
• 2 ein Diagramm eines Signalrauschens bei Bildaufnahmen mit einem Offset;
• 3 ein vereinfachtes Diagramm einer Wurzelübertragungsfunktion, welche nicht zur Erfindung gehört;
• 4 ein vereinfachtes Diagramm einer 12-Bit-zu-8-Bit-Look-Up-Tabelle für eine Wurzelübertragungsfunktion;
• 5 ein vereinfachtes Diagramm einer logarithmischen Übertragungsfunktion;
• 6 ein vereinfachtes Diagramm einer Abhängigkeit zwischen Signal und Signalrauschen bei einer logarithmischen Übertragungsfunktion;
• 7 ein vereinfachtes Diagramm einer 12-Bit-zu-8-Bit-Look-Up-Tabelle für eine logarithmische Übertragungsfunktion;
• 8 ein vereinfachtes Diagramm einer 12-Bit-zu-8-Bit-Look-Up-Tabelle für eine Area-Kosinus-Übertragungsfunktion mit einem Rauschterm von 0,5 %; und
• 9 ein vereinfachtes Diagramm einer 12-Bit-zu-8-Bit-Look-Up-Tabelle für eine Area-Kosinus-Übertragungsfunktion mit einem Rauschterm von 2 %.

Show it:

• 1 a diagram of a signal noise in image recordings;
• 2 a diagram of a signal noise when recording images with an offset;
• 3 a simplified diagram of a root transfer function not belonging to the invention;
• 4 a simplified diagram of a 12-bit to 8-bit look-up table for a root transfer function;
• 5 a simplified diagram of a logarithmic transfer function;
• 6 a simplified diagram of a dependency between signal and signal noise in a logarithmic transfer function;
• 7 Figure 12 is a simplified diagram of a 12-bit to 8-bit look-up table for a logarithmic transfer function;
• 8th Figure 12 is a simplified diagram of a 12-bit to 8-bit look-up table for an area cosine transfer function with a 0.5% noise term; and
• 9 a simplified diagram of a 12-bit to 8-bit look-up table for an area cosine transfer function with a 2% noise term.

The invention will be described below using input image signals as input signals and output image signals as output signals. Of course, other types of signals such as voltage signals, measurement signals, audio signals, etc. can also be considered as input or output signals.

According to the invention, a method is proposed for the low-loss transformation and/or compression of a data stream of input image signals S _12-bit with a first bit depth of 12 bits into a data stream of output image signals S _8-bit with a second bit depth of 8-bits by means of a transfer function in which a noise component of the input image signals S _{12-bit is} taken into account will. As an example, a first bit depth of 12 bits and a second image depth of 8 bits are assumed here. Of course, any other bit depths are conceivable here.

The method according to the invention can run on a signal processing unit or image processing unit which is set up to carry out the method, for example as a computer program in a memory element of the signal processing unit or image processing unit.

Dieses Signalrauschen ΔS, das bei der Aufnahme von Bildern entsteht, ist abhängig von der Helligkeit jedes Bildpunkts bzw. Pixels. Dunkle Pixel besitzen deutlich weniger Rauschen als helle Pixel. Im Wesentlichen besteht das Signalrauschen ΔS aus der Quadratwurzel des Signals S (Helligkeit des jeweiligen Pixels) selbst. Ein von der Bildhelligkeit unabhängiger Rauschanteil R, welcher beispielsweise das Ausleserauschen oder das Elektronenrauschen der CCD-Elemente der Bildsensoren (thermisch, visuell oder dergleichen) sein kann, gewinnt bei dunklen Pixeln bei der Betrachtung des Signalrauschens an Bedeutung, während er bei hellen Pixeln weniger in Erscheinung tritt. Der Rauschanteil R kann auch als n_RMS ^e- bezeichnet werden, wobei mit e- die Ladungselektronen bezeichnet werden.In general, the signal S has signal noise $\Delta \text{S}=\sqrt{\text{S}+{\text{<figure-callout id="2" label="R" filenames="DE102014113520B4\_0038.png,DE102014113520B4\_0039.png" state="{{state}}">R</figure-callout>}}^2}.$

This signal noise ΔS, which occurs when taking pictures, depends on the brightness of each picture element or pixel. Dark pixels have significantly less noise than bright pixels. The signal noise ΔS essentially consists of the square root of the signal S (brightness of the respective pixel) itself. A noise component R that is independent of the image brightness, which can be, for example, the readout noise or the electron noise of the CCD elements of the image sensors (thermal, visual or similar). , becomes more important when considering signal noise for dark pixels, while it becomes less apparent for bright pixels. The noise component R can also be denoted as n _RMS ^e- , where e- denotes the charge electrons.

Since it is the signal noise ΔS that limits the dynamics of the signal representation S or S _n (with a first bit depth n), it is advantageous to find a transformation and/or compression of the data stream of input image signals S _n in which the signal noise of the Target representation or the output image signals S _m (with a second bit depth m) with a signal noise of ΔS _m is constant.

The following explanations describe a target representation S 8 _bits with a bit depth m of 8 bits. However, the method can also be used accordingly for other bit depths or sampling depths m of the target representation S _m . The constant 255 is then generally replaced by 2 ^m-1 , resulting in ΔS _m or S _m as a result.

The transfer function is designed in such a way that the noise component R is at least approximately constant in the data stream of output video signals S _m . The transformation and/or the compression can be at least partially or completely reversible.

The transfer function can advantageously be implemented as a look-up table, e.g. on the signal processing unit.

In an example that does not belong to the invention, the transfer function can include at least one root function, in particular a square root function, in which the radicand is formed at least by the input signal S _n and the noise component R.

ergeben. Dabei ist S_m das Ausgangsbildsignal, S_n das Eingangsbildsignal, n die erste Bittiefe, m die zweite Bittiefe und R der Rauschanteil. S_nmax stellt das maximale Eingangsbildsignal dar und kann mit der maximalen Ladungskapazität eines CCD-Elements, zum Beispiel in Höhe von 20.000 Elektronen (vorliegend mit e^- bezeichnet) gleichgestellt werden. Der Rauschanteil R bzw. das Ausleserauschen des CCD-Elements kann zum Beispiel 20 Elektronen (e^-) umfassen. Die vorstehend genannten Werte stellen typische Parameter eines CCD-Sensors dar. Andere Sensorarten (zum Beispiel CMOS usw.) können andere Parameter aufweisen. Der funktionelle Zusammenhang ist jedoch im Wesentlichen gleich.The transfer function can thus be general ${\text{S}}_{\text{m}}=\left(2^{\text{m}}-1\right)\frac{\sqrt{{\text{S}}_{\text{n}}+{\text{<figure-callout id="2" label="R" filenames="DE102014113520B4\_0038.png,DE102014113520B4\_0039.png" state="{{state}}">R</figure-callout>}}^2}-\text{R}}{\sqrt{{\text{S}}_{\text{n max}}+{\text{<figure-callout id="2" label="R" filenames="DE102014113520B4\_0038.png,DE102014113520B4\_0039.png" state="{{state}}">R</figure-callout>}}^2}-\text{R}}$

result. In this case, S _m is the output image signal, S _n is the input image signal, n is the first bit depth, m is the second bit depth and R is the noise component. S _nmax represents the maximum input image signal and can be equated with the maximum charge capacity of a CCD element, for example equal to 20,000 electrons (denoted here by e ^- ). The noise component R or the readout noise of the CCD element can, for example, comprise 20 electrons (e ^- ). The above values represent typical parameters of a CCD sensor. Other sensor types (e.g. CMOS, etc.) may have other parameters. However, the functional relationship is essentially the same.

The root transfer function can be found as follows.

was sich lösen lässt durch $$\Rightarrow {\text{S}}_{8\text{Bit}}=2\cdot \text{const}.\left(\sqrt{\text{S}+{\text{R}}^2}-\text{R}\right),$$

wobei die Integrationskonstante so gewählt wurde, dass S = 0 <=> S_8BR = 0.Assuming constant noise in the output image signals S _m or S _8Bit , the result is: $$\Delta {\text{S}}_{\mathrm{8th}\text{bit}}=\frac{{\text{dS}}_{\mathrm{8th}\text{bit}}}{\text{dS}}\Delta \text{S}=\frac{{\text{dS}}_{\mathrm{8th}\text{bit}}}{\text{dS}}\sqrt{\text{S}+{\text{<figure-callout id="2" label="R" filenames="DE102014113520B4\_0038.png,DE102014113520B4\_0039.png" state="{{state}}">R</figure-callout>}}^2}=\text{const}\mathrm{.,}$$

what can be solved by $$\Rightarrow {\text{S}}_{\mathrm{8th}\text{bit}}=2\cdot \text{const}.\left(\sqrt{\text{S}+{\text{R}}^2}-\text{R}\right),$$

where the constant of integration was chosen such that S = 0 <=> S _8BR = 0.

The constant const. depends on the maximum input image signal S _nmax , as well as on the independent noise component R and is calculated as follows: $$\Delta {\text{S}}_{\mathrm{8th}\text{bit}}=\text{const}.=\frac{255/2}{\sqrt{{\text{S}}_{\text{n max}}+{\text{<figure-callout id="2" label="R" filenames="DE102014113520B4\_0038.png,DE102014113520B4\_0039.png" state="{{state}}">R</figure-callout>}}^2}-\text{R}}.$$

The charge signal (number of charge electrons e ^- ) S is then transformed into an 8-bit signal S _8Bit accordingly: $${\text{S}}_{\mathrm{8th}\text{bit}}=255\frac{\sqrt{\text{S}+{\text{R}}^2}}{\sqrt{{\text{S}}_{\text{n max}}+{\text{<figure-callout id="2" label="R" filenames="DE102014113520B4\_0038.png,DE102014113520B4\_0039.png" state="{{state}}">R</figure-callout>}}^2}-\text{R}}.$$

Here, the photocharge signal S is represented by: $$\text{S}=\frac{{\text{S}}_{\text{n max}}}{2^{\text{n}}-1}{\text{S}}_{\text{n}}.$$

In 3 a square root transfer function is shown. The input image signal S _{12 bit} is entered on the horizontal axis (abscissa). The output image signal S _8-bit is plotted on the vertical axis (ordinate).

The inverse function for the square root transfer function that may be required for display is derived from the 8-bit output image signal S _8Bit as follows: (6) $$\text{S}={\left[\frac{{\text{S}}_{\mathrm{8th}\text{bit}}}{255}\left(\sqrt{{\text{S}}_{\text{n max}}+{\text{<figure-callout id="2" label="R" filenames="DE102014113520B4\_0038.png,DE102014113520B4\_0039.png" state="{{state}}">R</figure-callout>}}^2}-\text{R}\right)+{\text{R}}^2\right]}^2-{\text{<figure-callout id="2" label="R" filenames="DE102014113520B4\_0038.png,DE102014113520B4\_0039.png" state="{{state}}">R</figure-callout>}}^2.$$

In 4 the application of the root transfer function is shown as an example in the form of a look-up table. How out 4 As can be seen, the 1-bit difference signal is independent of the signal level only slightly larger than the signal noise. This means that the transformation is almost dynamic. In 4 the 12-bit input image signal S _12Bit is plotted on the abscissa axis. The left ordinate shows the 8-bit output image signal S _8Bit and the right ordinate shows the signal noise.

ergeben, wobei S_m das Ausgangssignal, S_n das Eingangssignal, n die erste Bittiefe, m die zweite Bittiefe, S_nmax ein maximales Eingangssignal, α ein Justierparameter zur Anpassung an weitere Systemeigenschaften und R der Rauschanteil sein kann.According to the invention, in one embodiment, the transfer function can comprise at least one logarithm function, in which a logarithm of at least the input signal S _n and the noise component R is formed. The transfer function can be general ${\text{S}}_{\text{m}}=\frac{\left(2^{\text{m}}-1\right)\cdot \text{ln}\left(1+\mathrm{a}\cdot \frac{{\text{S}}_{\text{n}}}{\text{R}}\right)}{\text{ln}\left(1+\mathrm{a}\cdot \frac{{\text{S}}_{\text{n max}}}{\text{R}}\right)}$

where S _m is the output signal, S _n is the input signal, n is the first bit depth, m is the second bit depth, S _{nmax is} a maximum input signal, α can be an adjustment parameter for adapting to other system properties and R can be the noise component.

A logarithmic transfer function with an adjustment parameter α = 1 is in 5 shown. In this case, the input image signal S _{12 bits} is again plotted on the abscissa axis and the output image signal S _{8 bits} is plotted on the ordinate axis.

The 8-bit signal representation then results accordingly $${\text{S}}_{\mathrm{8th}\text{bit}}=\frac{255\cdot \text{ln}\left(1+\mathrm{a}\frac{\text{S}}{\text{R}}\right)}{\text{ln}\left(1+\mathrm{a}\cdot \frac{{\text{S}}_{\text{n max}}}{\text{R}}\right)}.$$

As already explained above, the adjustment parameter α can be used to adapt to other system properties.

In this case, the signal noise results in $$\Delta {\text{S}}_{\mathrm{8th}\text{bit}}=\frac{255}{\text{ln}\left(1+\mathrm{a}\cdot \frac{{\text{S}}_{\text{n max}}}{\text{R}}\right)}\cdot \frac{\sqrt{\text{S}+{\text{R}}^2}}{\text{S}+\frac{\text{R}}{\mathrm{a}}}.$$

und die Ableitung $$\begin{array}{l}\frac{\text{dS}}{{\text{dS}}_{8\text{Bit}}}=\frac{\text{R}}{255\mathrm{\alpha }}{\left(1+\mathrm{\alpha }\cdot \frac{{\text{S}}_{\text{n max}}}{\text{R}}\right)}^{\frac{{\text{S}}_{8\text{Bit}}}{255}}\cdot \text{ln}\left(1+\mathrm{\alpha }\cdot \frac{{\text{S}}_{\text{n max}}}{\text{R}}\right)\\ =\frac{\text{S}+\frac{\text{R}}{\mathrm{\alpha }}}{255}\cdot \text{ln}\left(1+\mathrm{\alpha }\cdot \frac{{\text{S}}_{\text{n max}}}{\text{R}}\right)\end{array}$$

betrachtet. 6 shows the dependency between the 12-bit input image signal S _12Bit and the signal noise ΔS for five different adjustment parameters α, namely 0.0025, 0.5, 1, 2 and 4 - Readout noise determines what can be seen very clearly in the selected function, while for larger input image signals the total noise is dominated by the square root of the input image signal and the influence of the readout noise becomes weaker and weaker. The so-called dark current noise is generally irrelevant and can be neglected in the present case. How further from 6 As can be seen, the noise begins with relatively large bit values with a small input image signal S _{12 bits} and falls quickly below the 1-bit limit at medium brightness, finally becoming a fraction of a bit in the high brightness range (about 15% with an adjustment parameter of α = 1 ) to reach. This means that in the case of brightness, one bit of the 8-bit output image signal S _{8Bit represents} a significantly greater difference in the original signal than the noise equivalent, and the possible signal-to-noise ratio is thus noticeably reduced. This can also be seen by looking at the inverse function $$\text{S=}\frac{\text{R}}{\mathrm{a}}\left[{\left(1+\mathrm{a}\cdot \frac{{\text{S}}_{\text{n max}}}{\text{R}}\right)}^{\frac{{\text{S}}_{\mathrm{8th}\text{bit}}}{255}}-1\right]$$

and the derivation $$\begin{array}{l}\frac{\text{dS}}{{\text{dS}}_{\mathrm{8th}\text{bit}}}=\frac{\text{R}}{255\mathrm{a}}{\left(1+\mathrm{a}\cdot \frac{{\text{S}}_{\text{n max}}}{\text{R}}\right)}^{\frac{{\text{S}}_{\mathrm{8th}\text{bit}}}{255}}\cdot \text{ln}\left(1+\mathrm{a}\cdot \frac{{\text{S}}_{\text{n max}}}{\text{R}}\right)\\ =\frac{\text{S}+\frac{\text{R}}{\mathrm{a}}}{255}\cdot \text{ln}\left(1+\mathrm{a}\cdot \frac{{\text{S}}_{\text{n max}}}{\text{R}}\right)\end{array}$$

considered.

In 7 1 shows an exemplary implementation of a look-up table for a logarithmic transfer function with an input _image signal S 12 bits with a bit depth of 12 bits and an output image signal S 8 _bits with 8 bits. Again, different adjustment parameters α of 0.025, 0.5, 1, 2 and 4 are assumed. The 12-bit input image signal S _12Bit is plotted on the abscissa axis and the 8-bit output image signal S _8Bit is plotted on the ordinate axis. The logarithmic function appears suitable for reducing the number of quantization levels since it approximately preserves the contrast ratios or modulation ratios regardless of the background radiation level. However, the constancy of the noise representation is better guaranteed with a root function as the transfer function. However, if a very small adjustment parameter, such as α = 0.0025, is used for a logarithmic transfer function, a result similar to the root transfer function can be achieved.

If the input image signal S _n has a proportional statistical noise component or noise term in addition to the noise component R, the transfer function can, according to the invention in an alternative embodiment, comprise at least one area hyperbolic cosine function of the input image signal S _n , the noise component R and the proportional statistical noise component.

wobei S_m das Ausgangssignal, S_n das Eingangssignal, n die erste Bittiefe, m die zweite Bittiefe, S_nmax ein maximales Eingangssignal, α_i ein Bruchteil für den proportionalen statistischen Rauschanteil und R der Rauschanteil sein kann.The general transfer function is: $${\text{S}}_{\text{m}}=\left(2^{\text{m}}-1\right)\frac{\text{ln}\left|\frac{1+2{\mathrm{a}}_{\text{i}}{}^2{\text{S}}_{\text{n}}+\sqrt{{\left(1+2{\mathrm{a}}_{\text{i}}{}^2{\text{S}}_{\text{n}}\right)}^2-1+4{\mathrm{a}}_{\text{i}}{}^2{\text{<figure-callout id="2" label="R" filenames="DE102014113520B4\_0038.png,DE102014113520B4\_0039.png" state="{{state}}">R</figure-callout>}}^2}}{1+2{\mathrm{a}}_{\text{i}}\text{R}}\right|}{\text{ln}\left|\frac{1+2{\mathrm{a}}_{\text{i}}{}^2{\text{S}}_{\text{n max}}+\sqrt{{\left(1+2{\mathrm{a}}_{\text{i}}{}^2{\text{S}}_{\text{n max}}\right)}^2-1+4{\mathrm{a}}_{\text{i}}{}^2{\text{<figure-callout id="2" label="R" filenames="DE102014113520B4\_0038.png,DE102014113520B4\_0039.png" state="{{state}}">R</figure-callout>}}^2}}{1+2{\mathrm{a}}_{\text{i}}\text{R}}\right|},$$

where S _m is the output signal, S _n is the input signal, n is the first bit depth, m is the second bit depth, S _{nmax is} a maximum input signal, α _i is a fraction for the proportional statistical noise component, and R is the noise component.

The fraction α _i can be of the order of 0.5 to 2%. If you introduce the fraction α _i into the formula for the noise ΔS, you get: $$\Delta \text{S}=\sqrt{\text{S}+{\text{<figure-callout id="2" label="R" filenames="DE102014113520B4\_0038.png,DE102014113520B4\_0039.png" state="{{state}}">R</figure-callout>}}^2+{\left({\mathrm{a}}_{\text{i}}\text{S}\right)}^2}.$$

If one now proceeds as with the root transfer function, one looks for an 8-bit representation S _8Bit of the signal S, with which the condition can be fulfilled that the variance ΔS _8Bit of the 8-bit output signal S _8Bit for all values of S is constant. This is equivalent to the following condition: $$\Delta {\text{S}}_{\mathrm{8th}\text{bit}}=\frac{{\text{dS}}_{\mathrm{8th}\text{bit}}}{\text{dS}}\Delta \text{S=}\frac{{\text{dS}}_{\mathrm{8th}\text{bit}}}{\text{dS}}\sqrt{\text{S}+{\text{<figure-callout id="2" label="R" filenames="DE102014113520B4\_0038.png,DE102014113520B4\_0039.png" state="{{state}}">R</figure-callout>}}^2+{\left({\mathrm{a}}_{\text{i}}\text{S}\right)}^2}=\text{const}.=:{\text{<figure-callout id="0" label="c" filenames="DE102014113520B4\_0036.png,DE102014113520B4\_0037.png" state="{{state}}">c</figure-callout>}}_0.$$

worin wiederum die Integrationskonstante derart gewählt ist, dass S = 0 <=> S_8Bit = 0.This differential equation is solved by an area cosine function (the inverse of the hyperbolic cosine): $$\Delta {\text{S}}_{\mathrm{8th}\text{bit}}=\frac{{\text{c}}_0}{{\mathrm{a}}_{\text{i}}}\text{ln}\left|\frac{1+2{\mathrm{a}}_{\text{i}}{}^2\text{S}+\sqrt{{\left(1+2{\mathrm{a}}_{\text{i}}{}^2\text{S}\right)}^2-1+4{\mathrm{a}}_{\text{i}}{}^2{\text{<figure-callout id="2" label="R" filenames="DE102014113520B4\_0038.png,DE102014113520B4\_0039.png" state="{{state}}">R</figure-callout>}}^2}}{1+2{\mathrm{a}}_{\text{i}}\text{R}}\right|,$$

where in turn the constant of integration is chosen such that S = 0 <=> S _8Bit = 0.

und folglich $${\text{S}}_{8\text{Bit}}\left(\text{S}\right)=255\frac{\text{ln}\left|\frac{1+2{\mathrm{\alpha }}_{\text{i}}{}^2\text{S}+\sqrt{{\left(1+2{\mathrm{\alpha }}_{\text{i}}{}^2\text{S}\right)}^2-1+4{\mathrm{\alpha }}_{\text{i}}{}^2{\text{R}}^2}}{1+2{\mathrm{\alpha }}_{\text{i}}\text{R}}\right|}{\text{ln}\left|\frac{1+2{\mathrm{\alpha }}_{\text{i}}{}^2{\text{S}}_{\text{n max}}+\sqrt{{\left(1+2{\mathrm{\alpha }}_{\text{i}}{}^2{\text{S}}_{\text{n max}}\right)}^2-1+4{\mathrm{\alpha }}_{\text{i}}{}^2{\text{R}}^2}}{1+2{\mathrm{\alpha }}_{\text{i}}\text{R}}\right|}.$$

The constant c ₀ = ΔS _8bits is determined by the condition S _8bits (Qmax) = S _nmax = 255, viz $${\text{<figure-callout id="0" label="c" filenames="DE102014113520B4\_0036.png,DE102014113520B4\_0037.png" state="{{state}}">c</figure-callout>}}_0=\Delta {\text{S}}_{\mathrm{8th}\text{bit}}=\frac{255\mathrm{a}}{\text{ln}\left|\frac{1+2{\mathrm{a}}_{\text{i}}{}^2{\text{S}}_{\text{n max}}+\sqrt{{\left(1+2{\mathrm{a}}_{\text{i}}{}^2{\text{S}}_{\text{n max}}\right)}^2-1+4{\mathrm{a}}_{\text{i}}{}^2{\text{<figure-callout id="2" label="R" filenames="DE102014113520B4\_0038.png,DE102014113520B4\_0039.png" state="{{state}}">R</figure-callout>}}^2}}{1+2{\mathrm{a}}_{\text{i}}\text{R}}\right|}$$

and consequently $${\text{S}}_{\mathrm{8th}\text{bit}}\left(\text{S}\right)=255\frac{\text{ln}\left|\frac{1+2{\mathrm{a}}_{\text{i}}{}^2\text{S}+\sqrt{{\left(1+2{\mathrm{a}}_{\text{i}}{}^2\text{S}\right)}^2-1+4{\mathrm{a}}_{\text{i}}{}^2{\text{<figure-callout id="2" label="R" filenames="DE102014113520B4\_0038.png,DE102014113520B4\_0039.png" state="{{state}}">R</figure-callout>}}^2}}{1+2{\mathrm{a}}_{\text{i}}\text{R}}\right|}{\text{ln}\left|\frac{1+2{\mathrm{a}}_{\text{i}}{}^2{\text{S}}_{\text{n max}}+\sqrt{{\left(1+2{\mathrm{a}}_{\text{i}}{}^2{\text{S}}_{\text{n max}}\right)}^2-1+4{\mathrm{a}}_{\text{i}}{}^2{\text{<figure-callout id="2" label="R" filenames="DE102014113520B4\_0038.png,DE102014113520B4\_0039.png" state="{{state}}">R</figure-callout>}}^2}}{1+2{\mathrm{a}}_{\text{i}}\text{R}}\right|}.$$

mit den Abkürzungen: $$\begin{array}{l}\text{A}=\sqrt{1-4{\mathrm{\alpha }}_{\text{i}}{}^{{\text{R}}^{2}2}},\\ \text{C}=\text{arccosh}\frac{1}{\text{A}}=\text{ln}\left|1/\text{A}+\sqrt{1/{\text{A}}^2-1)}\right|\text{ und}\\ \text{B}=\text{arccosh}\frac{1+2{\mathrm{\alpha }}_{\text{i}}{}^2{\text{S}}_{\text{n max}}}{\text{A}}-\text{C}=\text{ln}\left|\left(1+2{\mathrm{\alpha }}_{\text{i}}{}^2{\text{S}}_{\text{n max}}\right)/\text{A}+\sqrt{\left(1+2{\mathrm{\alpha }}_{\text{i}}{}^2{\text{S}}_{\text{n max}}\right)/{\text{A}}^2-1)}\right|-\text{C}\text{.}\end{array}$$

The inverse function is given by $$\begin{array}{l}\text{S}\left({\text{S}}_{\mathrm{8th}\text{bit}}\right)=\frac{\text{A}\cdot \text{arccos h}\left(\text{B}+\text{C}\cdot {\text{S}}_{\mathrm{8th}\text{bit}}/255\right)-1}{2{\mathrm{a}}_{\text{<figure-callout id="2" label="i" filenames="DE102014113520B4\_0038.png,DE102014113520B4\_0039.png" state="{{state}}">i</figure-callout>}}{}^2}\\ =\frac{\text{A}\cdot \text{ln}\left|\text{B}+\text{C}\cdot {\text{S}}_{\mathrm{8th}\text{bit}}/255+\sqrt{{\left(\text{B}+\text{C}\cdot {\text{S}}_{\mathrm{8th}\text{bit}}/255\right)}^2-1}\right|-1}{2{\mathrm{a}}_{\text{<figure-callout id="2" label="i" filenames="DE102014113520B4\_0038.png,DE102014113520B4\_0039.png" state="{{state}}">i</figure-callout>}}{}^2}\end{array}$$

with the abbreviations: $$\begin{array}{l}\text{A}=\sqrt{1-4{\mathrm{a}}_{\text{<figure-callout id="2" label="i R" filenames="DE102014113520B4\_0038.png,DE102014113520B4\_0039.png" state="{{state}}">i</figure-callout>}}{}^{{\text{R}}^{}}{{}^{2}2}^{}},\\ \text{C}=\text{arccosh}\frac{1}{\text{A}}=\text{ln}\left|1/\text{A}+\sqrt{1/{\text{A}}^2-1)}\right|\text{and}\\ \text{B}=\text{<figure-callout id="1" label="arccosh" filenames="DE102014113520B4\_0038.png,DE102014113520B4\_0039.png" state="{{state}}">arccosh</figure-callout>}\frac{1+2{\mathrm{a}}_{\text{i}}{}^2{\text{S}}_{\text{n max}}}{\text{A}}-\text{C}=\text{ln}\left|\left(1+2{\mathrm{a}}_{\text{i}}{}^2{\text{S}}_{\text{n max}}\right)/\text{A}+\sqrt{\left(1+2{\mathrm{a}}_{\text{i}}{}^2{\text{S}}_{\text{n max}}\right)/{\text{A}}^2-1)}\right|-\text{C}\text{.}\end{array}$$

As an example for a statistical noise term α _i of 0.5% 8th the realization of a 12-bit to 8-bit look-up table using the area cosine law. Analog is in 9 such a realization for a statistical noise term α _i of 2% is shown. In 8th the lower horizontal axis shows a photocharge with a number of electrons e ^- and the upper horizontal axis shows the 12-bit input image signal S _12Bit . The 8-bit output image signal S 8Bit is plotted on the left-hand ordinate axis and the signal noise of the 8-bit output _{image signal S 8Bit is} plotted on the right-hand ordinate axis. As mentioned above, in 9 the same values are plotted for a noise term α _i of 2%. A so-called fixed-pattern noise basically represents a statistical noise term mentioned above. However, this can be eliminated afterwards, ie after the compression or transformation, if the inhomogeneity caused by the fixed-pattern noise is known at any time. This can be done, for example, by averaging over a number of images with different image content.

1. a) eine verlustarme Transformation und/oder Kompression des Datenstroms von Eingangsbildsignalen mit der Eingangsbittiefe als erster Bittiefe in einen Datenstrom von Zwischenbildsignalen mit der Eingangsbittiefe als zweiter Bittiefe mittels eines erfindungsgemäßen Verfahrens zur verlustarmen Transformation und/oder Kompression durchgeführt wird, wonach
2. b) eine Kontrastanhebung in dem Datenstrom von Zwischenbildsignalen erfolgt, und wonach
3. c) in dem Datenstrom von Zwischenbildsignalen eine Anzahl, insbesondere der untersten, Bits der Zwischenbildsignale derart entfernt wird, dass ein Datenstrom von Ausgangsbildsignalen mit der Ausgangsbittiefe m erhalten wird.

Furthermore, a method for increasing the contrast of a data stream of input image signals with an input bit depth, which is transmitted in a data stream of output image signals with an output bit depth, is proposed, wherein:

1. a) a low-loss transformation and/or compression of the data stream of input image signals with the input bit depth as the first bit depth into a data stream of intermediate image signals with the input bit depth as the second bit depth is carried out using a method for low-loss transformation and/or compression according to the invention, after which
2. b) contrast is increased in the data stream of intermediate image signals, and after that
3. c) in the data stream of intermediate image signals, a number, in particular the lowest, bits of the intermediate image signals are removed in such a way that a data stream of output image signals with the output bit depth m is obtained.

In step c), the number of bits to be removed can result from the difference between the number of bits in the input bit depth and the number of bits in the output bit depth.

Histogram equalization functions or contrast enhancements are often used for low-contrast images. However, since the methods described take into account the signal noise (during recording), it is advantageous not to carry out such corrections before using the method according to the invention for low-loss transformation and/or compression, for example using the root transfer function. For example, additional enhancement methods can be applied to low-contrast images after the square root transfer function has been applied.

gegeben,
wobei L + 1 = 2ⁿ die Zahl der möglichen Grauwerte eines Eingangsbildsignals S_L ist, das seinerseits die n-Bit-Repräsentation eines Ladungssignals S bezeichnet, eventuell nach einer Transformation wie etwa mittels der Wurzelübertragungsfunktion. L_min bzw. L_max bezeichnen die Anzahl des niedrigsten bzw. höchsten Histogrammwerts, dessen Vorkommen von 0 verschieden ist.A contrast-enhanced signal S _CE is given by the formula $${\text{S}}_{\text{CE}}\left({\text{S}}_{\text{L}}\right)-\text{L}\frac{{\text{S}}_{\text{L}}-{\text{L}}_{\text{at least}}}{{\text{L}}_{\text{Max}}-{\text{L}}_{\text{at least}}}$$

given,
where _L + 1 = 2 ⁿ is the number of possible gray values of an input image signal SL, which in turn denotes the n-bit representation of a charge signal S, possibly after a transformation such as by means of the root transfer function. L _min and L _max denote the number of the lowest and highest histogram value whose occurrence is different from 0.

The variance ΔS _CE of the contrast-enhanced signal S _CE is: $$\Delta {\text{S}}_{\text{CE}}\left({\text{S}}_{\text{L}}\right)=\frac{\text{L}}{{\text{L}}_{\text{Max}}-{\text{L}}_{\text{at least}}}\Delta {\text{S}}_{\text{L}}$$

und variiert beispielsweise von 0,1 % von L (S = 0) bis 0,7 % von L (S = S_max) für Q_max = 20.000 e- (Elektronen), R = 20 e-, n = 12.In case S _L represents the direct linear contrast-enhanced n-bit representation, the variance ΔS _L of S _L is given by: $$\Delta {\text{S}}_{\text{L}}=\frac{\text{L}}{{\text{S}}_{\text{n max}}}\sqrt{\text{S}+{\text{<figure-callout id="2" label="R" filenames="DE102014113520B4\_0038.png,DE102014113520B4\_0039.png" state="{{state}}">R</figure-callout>}}^2}$$

and varies, for example, from 0.1% of L (S = 0) to 0.7% of L (S = S _max ) for Q _max = 20,000 e- (electrons), R = 20 e-, n = 12.

und hat im Beispiel unabhängig von S den konstanten Werten 0,4 % von L.In case _SL is the n-bit representation after applying the transform with the root transfer function, the variance of _SL is given by $$\Delta {\text{S}}_{\text{L}}=\frac{\text{L}}{2\sqrt{{\text{S}}_{\text{n max}}+{\text{<figure-callout id="2" label="R" filenames="DE102014113520B4\_0038.png,DE102014113520B4\_0039.png" state="{{state}}">R</figure-callout>}}^2}}$$

and in the example has the constant value 0.4% of L independently of S.

für den linearen Fall bzw. $$\Delta {\text{S}}_{\text{CE}}\left({\text{S}}_{\text{L}}\right)=\frac{\text{L}}{{\text{L}}_{\text{max}}-{\text{L}}_{\text{min}}}\frac{\text{L}}{2\sqrt{{\text{S}}_{\text{nmax}}+{\text{R}}^2}}$$

für den Fall mit Wurzeltransformation.Using equation (19) above, one obtains for the respective variances of the contrast-enhanced signal: $$\Delta {\text{S}}_{\text{CE}}\left({\text{S}}_{\text{L}}\right)=\frac{\text{L}}{{\text{L}}_{\text{Max}}-{\text{L}}_{\text{at least}}}\frac{\text{L}}{{\text{S}}_{\text{n max}}}\sqrt{\text{S}+{\text{<figure-callout id="2" label="R" filenames="DE102014113520B4\_0038.png,DE102014113520B4\_0039.png" state="{{state}}">R</figure-callout>}}^2}$$

for the linear case or $$\Delta {\text{S}}_{\text{CE}}\left({\text{S}}_{\text{L}}\right)=\frac{\text{L}}{{\text{L}}_{\text{Max}}-{\text{L}}_{\text{at least}}}\frac{\text{L}}{2\sqrt{{\text{S}}_{\text{n max}}+{\text{<figure-callout id="2" label="R" filenames="DE102014113520B4\_0038.png,DE102014113520B4\_0039.png" state="{{state}}">R</figure-callout>}}^2}}$$

for the case with root transformation.

In both cases, if contrast enhancement is possible, that is, if L _max + L _min < L, the variance is multiplied by the same gain factor as the signal itself. Therefore, the low bits that one wants to remove when compressing are in the Tat was less significant in terms of variance than without contrast enhancement. The transformation using a root transfer function with constant variance is very well suited for low-loss compression.

worin SH Zahlen im kumulierten Histogramm bezeichnet mit SH_min := SH(L_min) und SH_max := SH(L_max) = SH(L) = Gesamtzahl der Bildpunkte.The signal after histogram equalization S _HE is given by the formula $${\text{S}}_{\text{HE}}\left({\text{S}}_{\text{L}}\right)=\text{L}\frac{\text{SH}\left({\text{S}}_{\text{L}}\right)-{\text{SH}}_{\text{at least}}}{{\text{SH}}_{\text{Max}}-{\text{SH}}_{\text{at least}}},$$

where SH denotes numbers in the cumulative histogram with SH _min := SH(L _min ) and SH _max := SH(L _max ) = SH(L) = total number of pixels.

Denoting the histogram with H, one obtains for the variance ΔS _HE of the signal S _HE after the histogram adjustment: $$\Delta {\text{S}}_{\text{HE}}\left({\text{S}}_{\text{L}}\right)=\text{L}\frac{\Delta \text{SH}\left({\text{S}}_{\text{L}}\right)}{{\text{SH}}_{\text{Max}}-{\text{SH}}_{\text{at least}}}\approx \text{L}\frac{\text{H}\left({\text{S}}_{\text{L}}\right)}{{\text{SH}}_{\text{Max}}-{\text{SH}}_{\text{at least}}}\Delta {\text{S}}_{\text{L}}.$$

With a constant histogram H within the limits of occurrence L _max and L _min , the formula is reduced to the formula for direct contrast enhancement (19). In the general case, however, H varies within these limits and hence the variance multiplier of ΔS _L will also vary around a constant value, which means worse low-loss compression performance for a certain number of _SL values. Therefore, in terms of low-loss compression, it seems to be very advantageous to apply an n-to-n-bit transformation with a square root transfer function to the full n-bit representation of the signal, then perform a direct contrast enhancement and only then the lower (n - m) bits (input bit depth - output bit depth).

Claims (9)

Method for the low-loss transformation and/or compression of a data stream of input signals (S _12Bit ) with a first bit depth into a data stream of output signals (S _8Bit ) with a second bit depth by means of a transfer function in which a noise component of the input signals (S _12Bit ) is taken into account, wherein the transfer function is designed such that the noise component in the data stream of output signals (S _8Bit ) is at least approximately constant, and wherein the transfer function further comprises: - at least one logarithmic function, in which a logarithm of at least the input signal (S _12Bit ) and the noise component is formed; or - at least one area hyperbolic cosine function of the input signal (S _12Bit ), the noise component and a proportional statistical noise component which the input signal (S _12Bit ) has in addition to the noise component. procedure after claim 1 , wherein the transformation and/or the compression is at least partially reversible. procedure after claim 1 or 2 , where the transfer function increases to ${\text{S}}_{\text{m}}=\frac{\left(2^{\text{m}}-1\right)\cdot \text{ln}\left(1+\mathrm{a}\cdot \frac{{\text{S}}_{\text{n}}}{\text{R}}\right)}{\text{ln}\left(1+\mathrm{a}\cdot \frac{{\text{S}}_{\text{n max}}}{\text{R}}\right)}$

where S _m is the output signal, S _n is the input signal, n is the first bit depth, m is the second bit depth, S _{nmax is} a maximum input signal, α is an adjustment parameter for adapting to further system properties and R is the noise component. procedure after claim 1 or 2 , where the transfer function increases to $${\text{S}}_{\text{m}}=\left(2^{\text{m}}-1\right)\frac{\text{ln}\left|\frac{1+2{\mathrm{a}}_{\text{i}}{}^2{\text{S}}_{\text{n}}+\sqrt{{\left(1+2{\mathrm{a}}_{\text{i}}{}^2{\text{S}}_{\text{n}}\right)}^2-1+4{\mathrm{a}}_{\text{i}}{}^2{\text{R}}^2}}{1+2{\mathrm{a}}_{\text{i}}\text{R}}\right|}{\text{ln}\left|\frac{1+2{\mathrm{a}}_{\text{i}}{}^2{\text{S}}_{\text{n max}}+\sqrt{{\left(1+2{\mathrm{a}}_{\text{i}}{}^2{\text{S}}_{\text{n max}}\right)}^2-1+4{\mathrm{a}}_{\text{i}}{}^2{\text{R}}^2}}{1+2{\mathrm{a}}_{\text{i}}\text{R}}\right|}$$

where S _m is the output signal, S _n is the input signal, n is the first bit depth, m is the second bit depth, S _{nmax is} a maximum input signal, α _i is a fraction for the proportional statistical noise component, and R is the noise component. Procedure according to one of Claims 1 until 4 , where the transfer function is implemented as a look-up table. Procedure according to one of Claims 1 until 5 , where the input signals are input image signals (S _12Bit ) and the output signals are output image signals (S _8Bit ). Method for increasing the contrast of a data stream of input image signals (S _12Bit ) with an input bit depth, which is transferred into a data stream of output image signals (S _8Bit ) with an output bit depth, wherein: a) low-loss transformation and/or compression of the data stream of input image signals (S _12Bit ) with the input bit depth as the first bit depth into a data stream of intermediate image signals with the input bit depth as the second bit depth by means of a method according to claim 6 is carried out, after which b) the contrast is increased in the data stream of intermediate image signals, and after which c) a number of bits, in particular the lowest bits, of the intermediate image signals are removed in the data stream of intermediate image signals in such a way that a data stream of output image signals (S _8Bit ) with the output bit depth is obtained. procedure after claim 7 , wherein in step c) the number of bits to be removed results from the difference between the number of bits of the input bit depth and the number of bits of the output bit depth. Signal processing unit, which is used to carry out a method according to one of Claims 1 until 8th is set up.

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