EP4728736A1 - Adaptive fourier mapping for implicit neural representation - Google Patents

Abstract

A method for encoding comprising: obtaining a coding unit of a picture; applying a joint learning phase allowing learning jointly parameters of an implicit neural network and coefficients of a transformation, the learning comprising a minimization of a loss function depending jointly on the parameters of the implicit neural network and of the coefficients of the transformation, the implicit neural network being applied to coordinates of samples of the coding unit transformed by the transformation; encoding the learned parameters of the implicit neural network and coefficients of the transformation in output data.

Description

2023PF00472 ADAPTIVE FOURIER MAPPING FOR IMPLICIT NEURAL REPRESENTATION 1. CROSS REFERENCE TO RELATED APPLICATIONS This application claims priority to European Application No.23305947.6, filed June 14, 2023, which is incorporated herein by reference in its entirety. 2. TECHNICAL FIELD At least one of the present embodiments generally relates to a method and a device for encoding picture or video data based on an Implicit Neural Representation. 3. BACKGROUND Implicit Neural Representation (INR) based compression techniques are relatively new compression techniques that can be applied to 2D picture, video, 3D scenes or objects. These techniques have a far lower computational complexity than end-to-end neural network based compression approaches. An INR network is typically a neural network, composed of multiple neural layers, such as fully connected layers. Each neural layer can be described as a function that first multiplies an input signal by a tensor, adds a vector called the bias and then applies a nonlinear function on the resulting values. The shape (and other characteristics) of the tensor and the type of non-linear functions are called the architecture of the network. The input signal may be modified by a transformation before being used as input for the neural network. This transformation can be a Fourier mapping, coordinate transformation, normalization etc. Document Tancik, M. S.-K. (2020). Fourier features let networks learn high frequency functions in low dimensional domains. Advances in Neural Information Processing Systems, (pp. 7537-7547) shown that a mapping into Fourier features enables a Multi-layer Perceptron (MLP) learn high-frequency components of an input signal. Otherwise, the MLP has a spectral bias and is unable to learn the high frequencies of the input signal, which degrades considerably a visual quality when reconstructing the encoded signal. 2023PF00472 A random selection of Fourier mapping is considered as sub-optimal when applied locally to a sub-part of a signal, such as a block (or a coding unit (CU)) of a picture. It is desirable to propose solutions allowing to overcome the above issues. In particular, it is desirable to propose solutions improving a local use of a Fourier mapping on a sub-part of a signal. 4. BRIEF SUMMARY In a first aspect, one or more of the present embodiments provide a method for encoding comprising: obtaining a coding unit of a picture; applying a joint learning phase allowing learning jointly parameters of an implicit neural representation and coefficients of a transformation, the learning comprising a minimization of a loss function depending jointly on the parameters of the implicit neural representation and of the coefficients of the transformation, the implicit neural representation being applied to coordinates of samples of the coding unit transformed by the transformation; encoding the learned parameters of the implicit neural representation and coefficients of the transformation in output data. In an embodiment, the coefficients are quantized before being encoded in the output data to obtain quantized coefficients. In an embodiment, the method comprises obtaining updated parameters of the implicit neural representation by learning parameters of the implicit neural representation when the implicit neural representation is applied to coordinates of samples of the coding unit transformed by a transformation based on second coefficients resulting from an inverse quantization of the quantized coefficients, the learning comprising a minimization of a loss function depending on the parameters of the implicit neural representation and wherein the coefficients of the transformation are considered fixed and resulting from the inverse quantization of the quantized coefficients. In an embodiment, the transformation is a Fourier mapping. 2023PF00472 In an embodiment, the method comprises, obtaining a random Fourier mapping and learning preliminary parameters of the implicit neural representation when the implicit neural representation is applied to coordinates of samples of the coding unit transformed by the random Fourier mapping, the learning comprising a minimization of a loss function depending on the parameters of the implicit neural representation and wherein the coefficients of the transformation are considered fixed and equal to coefficients of the random Fourier mapping, and, using the preliminary parameters of the implicit neural representation and the coefficients of the Fourier mapping to initialize the joint learning phase. In an embodiment, the coefficients of the transformation comprise a scale parameter. In an embodiment, responsive to obtaining a random Fourier mapping, the method comprises encoding the coefficients learned during the joint learning phase in a form of a difference between the coefficients learned during the joint learning phase and the coefficients of the random Fourier mapping. In a second aspect, one or more of the present embodiments provide a method decoding comprising: obtaining input data representing a coding unit of a picture; decoding coefficients of a transformation from the input data; decoding parameters of an implicit neural representation from the input data; applying the transformation based on the decoded coefficients to coordinates of samples of the coding unit to obtain mapped coordinates; and, applying the implicit neural representation based on the decoded parameters to the mapped coordinates. In an embodiment, during the decoding of the coefficients, an inverse quantization is applied to data representing the coefficients to obtain the decoded coefficients. In an embodiment, a quantization parameter used during the inverse quantization is decoded from the input data. In an embodiment, the transformation is a Fourier mapping. 2023PF00472 In an embodiment, the method comprises obtaining a random Fourier mapping, the data representing the coefficients being residuals representing a difference between coefficients of the Fourier mapping and coefficients of the obtained random Fourier mapping, the coefficients of the Fourier mapping being obtained by adding the residuals to the coefficients of the obtained random Fourier mapping. In a third aspect, one or more of the present embodiments provide a device for encoding comprising electronic circuitry configured for: obtaining a coding unit of a picture; applying a joint learning phase allowing learning jointly parameters of an implicit neural representation and coefficients of a transformation, the learning comprising a minimization of a loss function depending jointly on the parameters of the implicit neural representation and of the coefficients of the transformation, the implicit neural representation being applied to coordinates of samples of the coding unit transformed by the transformation; encoding the learned parameters of the implicit neural representation and coefficients of the transformation in output data. In an embodiment the coefficients are quantized before being encoded in the output data to obtain quantized coefficients. In an embodiment, the electronic circuitry is further configured for obtaining updated parameters of the implicit neural representation by learning parameters of the implicit neural representation when the implicit neural representation is applied to coordinates of samples of the coding unit transformed by a transformation based on second coefficients resulting from an inverse quantization of the quantized coefficients, the learning comprising a minimization of a loss function depending on the parameters of the implicit neural representation and wherein the coefficients of the transformation are considered fixed and resulting from the inverse quantization of the quantized coefficients. In an embodiment the transformation is a Fourier mapping. In an embodiment, the electronic circuitry is further configured for obtaining a random Fourier mapping and learning preliminary parameters of the implicit neural representation when the implicit neural representation is applied to coordinates of 2023PF00472 samples of the coding unit transformed by the random Fourier mapping, the learning comprising a minimization of a loss function depending on the parameters of the implicit neural representation and wherein the coefficients of the transformation are considered fixed and equal to coefficients of the random Fourier mapping, and, using the preliminary parameters of the implicit neural representation and the coefficients of the Fourier mapping to initialize the joint learning phase. In an embodiment the coefficients of the transformation comprise a scale parameter. In an embodiment, responsive to obtaining a random Fourier mapping, the electronic circuitry is further configured for encoding the coefficients learned during the joint learning phase in a form of a difference between the coefficients learned during the joint learning phase and the coefficients of the random Fourier mapping. In a fourth aspect, one or more of the present embodiments provide a device for decoding comprising electronic circuitry configured for: obtaining input data representing a coding unit of a picture; decoding coefficients of a transformation from the input data; decoding parameters of an implicit neural representation from the input data; applying the transformation based on the decoded coefficients to coordinates of samples of the coding unit to obtain mapped coordinates; and, applying the implicit neural representation based on the decoded parameters to the mapped coordinates. In an embodiment, during the decoding of the coefficients, an inverse quantization is applied to data representing the coefficients to obtain the decoded coefficients. In an embodiment, a quantization parameter used during the inverse quantization is decoded from the input data. In an embodiment, the transformation is a Fourier mapping. In an embodiment, the electronic circuitry is further configured for obtaining a random Fourier mapping, the data representing the coefficients being residuals representing a difference between coefficients of the Fourier mapping and coefficients of the obtained random Fourier mapping, the coefficients of the Fourier mapping being 2023PF00472 obtained by adding the residuals to the coefficients of the obtained random Fourier mapping. In a fifth aspect, one or more of the present embodiments provide a non- transitory information storage medium storing program code instructions for implementing the method according to the first or the second aspect. In a sixth aspect, one or more of the present embodiments provide computer program comprising program code instructions for implementing the method according to the first or the second aspect. In a seventh aspect, one or more of the present embodiments provide signal generated by the method of the first aspect or by the device of the third aspect. 5. BRIEF SUMMARY OF THE DRAWINGS Fig. 1 illustrates an example of context in which various embodiments may be implemented; Fig. 2A illustrates schematically an example of hardware architecture of a processing module able to implement an encoding module or a decoding module in which various aspects and embodiments are implemented; Fig. 2B illustrates a block diagram of an example of a first system in which various aspects and embodiments are implemented; Fig.2C illustrates a block diagram of an example of a second system in which various aspects and embodiments are implemented; Fig.3 illustrates a simple neural network used for implicit neural representation; Fig. 4A illustrates a typical process to encode a signal using an implicit neural representation; Fig. 4B illustrates a typical process to decode a signal using an implicit neural representation; Fig. 5 illustrates an example of partitioning undergone by a picture of pixels of an original video sequence; Fig. 6 illustrates schematically a process to encode a coding unit using local implicit neural representation; 2023PF00472 Fig.7 describes schematically an example of quantization process; and, Fig.8 illustrates schematically a process to decode a coding unit using local INR. 6. DETAILED DESCRIPTION Fig.1 describes an example of a context in which following embodiments can be implemented. In Fig. 1, a system 11, that could be a camera, a storage device, a computer, a server or any device capable of delivering a video stream, transmits a video stream to a system 13 using a communication channel 12. The video stream is either encoded and transmitted by the system 11 or received and/or stored by the system 11 and then transmitted. The communication channel 12 is a wired (for example Internet or Ethernet) or a wireless (for example WiFi, 3G, 4G or 5G) network link. The system 13, that could be for example a set top box, receives and decodes the video stream to generate a sequence of decoded pictures. The obtained sequence of decoded pictures is then transmitted to a display system 15 using a communication channel 14, that could be a wired or wireless network. The display system 15 then displays said pictures. In an embodiment, the system 13 is comprised in the display system 15. In that case, the system 13 and display 15 are comprised in a TV, a computer, a tablet, a smartphone, a head-mounted display, etc. Fig. 2A illustrates schematically an example of hardware architecture of a processing module 200 able to implement an encoding module or a decoding module capable of implementing respectively a method for encoding of Fig.6 and a method for decoding of Fig. 8 modified according to different aspects and embodiments. The encoding module is for example comprised in the system 11 when this apparatus is in charge of encoding the video stream. The decoding module is for example comprised in the system 13. The processing module 200 comprises, connected by a communication bus 2005: a processor or CPU (central processing unit) 2000 encompassing one or more microprocessors, general purpose computers, special purpose computers, and processors based on a multi-core architecture, as non-limiting examples; a random access memory (RAM) 2001; a read only memory (ROM) 2002; a storage unit 2003, which can include non-volatile memory and/or volatile memory, 2023PF00472 including, but not limited to, Electrically Erasable Programmable Read-Only Memory (EEPROM), Read-Only Memory (ROM), Programmable Read-Only Memory (PROM), Random Access Memory (RAM), Dynamic Random Access Memory (DRAM), Static Random Access Memory (SRAM), flash, magnetic disk drive, and/or optical disk drive, or a storage medium reader, such as a SD (secure digital) card reader and/or a hard disc drive (HDD) and/or a network accessible storage device; at least one communication interface 2004 for exchanging data with other modules, devices or equipment. The communication interface 2004 can include, but is not limited to, a transceiver configured to transmit and to receive data over a communication channel. The communication interface 2004 can include, but is not limited to, a modem or network card. If the processing module 200 implements a decoding module, the communication interface 2004 enables for instance the processing module 200 to receive encoded video streams and to provide a sequence of decoded pictures. If the processing module 200 implements an encoding module, the communication interface 2004 enables for instance the processing module 200 to receive a sequence of original picture data to encode and to provide an encoded video stream. The processor 2000 is capable of executing instructions loaded into the RAM 2001 from the ROM 2002, from an external memory (not shown), from a storage medium, or from a communication network. When the processing module 200 is powered up, the processor 2000 is capable of reading instructions from the RAM 2001 and executing them. These instructions form a computer program causing, for example, the implementation by the processor 2000 of a decoding method as described in relation with Fig. 8, an encoding method described in relation to Fig. 6, these methods comprising various aspects and embodiments described below in this document. All or some of the algorithms and steps of the methods of Figs.6 and 8 may be implemented in software form by the execution of a set of instructions by a programmable machine such as a DSP (digital signal processor) or a microcontroller, or be implemented in hardware form by a machine or a dedicated component such as a FPGA (field-programmable gate array) or an ASIC (application-specific integrated circuit). As can be seen, microprocessors, general purpose computers, special purpose computers, processors based or not on a multi-core architecture, DSP, microcontroller, 2023PF00472 FPGA and ASIC are electronic circuitry adapted to implement (i.e., configured for implementing) at least partially the methods of Figs.6 and 8. Fig. 2C illustrates a block diagram of an example of the system 13 in which various aspects and embodiments are implemented. The system 13 can be embodied as a device including the various components described below and is configured to perform one or more of the aspects and embodiments described in this document. Examples of such devices include, but are not limited to, various electronic devices such as personal computers, laptop computers, smartphones, tablet computers, digital multimedia set top boxes, digital television receivers, personal video recording systems, connected home appliances and head mounted display. Elements of system 13, singly or in combination, can be embodied in a single integrated circuit (IC), multiple ICs, and/or discrete components. For example, in at least one embodiment, the system 13 comprises one processing module 200 that implements a decoding module. In various embodiments, the system 13 is communicatively coupled to one or more other systems, or other electronic devices, via, for example, a communications bus or through dedicated input and/or output ports. In various embodiments, the system 13 is configured to implement one or more of the aspects described in this document. The input to the processing module 200 can be provided through various input modules as indicated in block 231. Such input modules include, but are not limited to, (i) a radio frequency (RF) module that receives an RF signal transmitted, for example, over the air by a broadcaster, (ii) a component (COMP) input module (or a set of COMP input modules), (iii) a Universal Serial Bus (USB) input module, and/or (iv) a High Definition Multimedia Interface (HDMI) input module. Other examples, not shown in FIG.2C, include composite video. In various embodiments, the input modules of block 231 have associated respective input processing elements as known in the art. For example, the RF module can be associated with elements suitable for (i) selecting a desired frequency (also referred to as selecting a signal, or band-limiting a signal to a band of frequencies), (ii) down-converting the selected signal, (iii) band-limiting again to a narrower band of frequencies to select (for example) a signal frequency band which can be referred to as a channel in certain embodiments, (iv) demodulating the down-converted and band- limited signal, (v) performing error correction, and (vi) demultiplexing to select the desired stream of data packets. The RF module of various embodiments includes one 2023PF00472 or more elements to perform these functions, for example, frequency selectors, signal selectors, band-limiters, channel selectors, filters, downconverters, demodulators, error correctors, and demultiplexers. The RF portion can include a tuner that performs various of these functions, including, for example, down-converting the received signal to a lower frequency (for example, an intermediate frequency or a near-baseband frequency) or to baseband. In one set-top box embodiment, the RF module and its associated input processing element receives an RF signal transmitted over a wired (for example, cable) medium, and performs frequency selection by filtering, down- converting, and filtering again to a desired frequency band. Various embodiments rearrange the order of the above-described (and other) elements, remove some of these elements, and/or add other elements performing similar or different functions. Adding elements can include inserting elements in between existing elements, such as, for example, inserting amplifiers and an analog-to-digital converter. In various embodiments, the RF module includes an antenna. Additionally, the USB and/or HDMI modules can include respective interface processors for connecting system 13 to other electronic devices across USB and/or HDMI connections. It is to be understood that various aspects of input processing, for example, Reed-Solomon error correction, can be implemented, for example, within a separate input processing IC or within the processing module 200 as necessary. Similarly, aspects of USB or HDMI interface processing can be implemented within separate interface ICs or within the processing module 200 as necessary. The demodulated, error corrected, and demultiplexed stream is provided to the processing module 200. Various elements of system 13 can be provided within an integrated housing. Within the integrated housing, the various elements can be interconnected and transmit data therebetween using suitable connection arrangements, for example, an internal bus as known in the art, including the Inter-IC (I2C) bus, wiring, and printed circuit boards. For example, in the system 13, the processing module 200 is interconnected to other elements of said system 13 by the bus 2005. The communication interface 2004 of the processing module 200 allows the system 13 to communicate on the communication channel 12. As already mentioned above, the communication channel 12 can be implemented, for example, within a wired and/or a wireless medium. 2023PF00472 Data is streamed, or otherwise provided, to the system 13, in various embodiments, using a wireless network such as a Wi-Fi network, for example IEEE 802.11 (IEEE refers to the Institute of Electrical and Electronics Engineers). The Wi- Fi signal of these embodiments is received over the communications channel 12 and the communications interface 2004 which are adapted for Wi-Fi communications. The communications channel 12 of these embodiments is typically connected to an access point or router that provides access to external networks including the Internet for allowing streaming applications and other over-the-top communications. Other embodiments provide streamed data to the system 13 using the RF connection of the input block 231. As indicated above, various embodiments provide data in a non- streaming manner. Additionally, various embodiments use wireless networks other than Wi-Fi, for example a cellular network or a Bluetooth network. The system 13 can provide an output signal to various output devices, including the display system 15, speakers 26, and other peripheral devices 27. The display system 15 of various embodiments includes one or more of, for example, a touchscreen display, an organic light-emitting diode (OLED) display, a curved display, and/or a foldable display. The display 15 can be for a television, a tablet, a laptop, a cell phone (mobile phone), a head mounted display or other devices. The display system 15 can also be integrated with other components (for example, as in a smart phone), or separate (for example, an external monitor for a laptop). The other peripheral devices 27 include, in various examples of embodiments, one or more of a stand-alone digital video disc (or digital versatile disc) (DVR, for both terms), a disk player, a stereo system, and/or a lighting system. Various embodiments use one or more peripheral devices 27 that provide a function based on the output of the system 13. For example, a disk player performs the function of playing an output of the system 13. In various embodiments, control signals are communicated between the system 13 and the display system 15, speakers 26, or other peripheral devices 27 using signaling such as AV.Link, Consumer Electronics Control (CEC), or other communications protocols that enable device-to-device control with or without user intervention. The output devices can be communicatively coupled to system 13 via dedicated connections through respective interfaces 232, 233, and 234. Alternatively, the output devices can be connected to system 13 using the communications channel 12 via the communications interface 2004 or a dedicated communication channel 2023PF00472 corresponding to the communication channel 14 in Fig. 2A via the communication interface 2004. The display system 15 and speakers 26 can be integrated in a single unit with the other components of system 13 in an electronic device such as, for example, a television. In various embodiments, the display interface 232 includes a display driver, such as, for example, a timing controller (T Con) chip. The display system 15 and speaker 26 can alternatively be separate from one or more of the other components. In various embodiments in which the display system 15 and speakers 26 are external components, the output signal can be provided via dedicated output connections, including, for example, HDMI ports, USB ports, or COMP outputs. Fig. 2B illustrates a block diagram of an example of the system 11 in which various aspects and embodiments are implemented. System 11 is very similar to system 13. The system 11 can be embodied as a device including the various components described below and is configured to perform one or more of the aspects and embodiments described in this document. Examples of such devices include, but are not limited to, various electronic devices such as personal computers, laptop computers, smartphones, tablet computers, a camera and a server. Elements of system 11, singly or in combination, can be embodied in a single integrated circuit (IC), multiple ICs, and/or discrete components. For example, in at least one embodiment, the system 11 comprises one processing module 200 that implements an encoding module. In various embodiments, the system 11 is communicatively coupled to one or more other systems, or other electronic devices, via, for example, a communications bus or through dedicated input and/or output ports. In various embodiments, the system 11 is configured to implement one or more of the aspects described in this document. The input to the processing module 200 can be provided through various input modules as indicated in block 231 already described in relation to Fig.2C. Various elements of system 11 can be provided within an integrated housing. Within the integrated housing, the various elements can be interconnected and transmit data therebetween using suitable connection arrangements, for example, an internal bus as known in the art, including the Inter-IC (I2C) bus, wiring, and printed circuit boards. For example, in the system 11, the processing module 200 is interconnected to other elements of said system 11 by the bus 2005. The communication interface 2004 of the processing module 200 allows the 2023PF00472 system 200 to communicate on the communication channel 12. Data is streamed, or otherwise provided, to the system 11, in various embodiments, using a wireless network such as a Wi-Fi network, for example IEEE 802.11 (IEEE refers to the Institute of Electrical and Electronics Engineers). The Wi- Fi signal of these embodiments is received over the communications channel 12 and the communications interface 2004 which are adapted for Wi-Fi communications. The communications channel 12 of these embodiments is typically connected to an access point or router that provides access to external networks including the Internet for allowing streaming applications and other over-the-top communications. Other embodiments provide streamed data to the system 11 using the RF connection of the input block 231. As indicated above, various embodiments provide data in a non-streaming manner. Additionally, various embodiments use wireless networks other than Wi-Fi, for example a cellular network or a Bluetooth network. The data provided to the system 11 can be provided in different format. In various embodiments, these data are raw data provided for example by a picture acquisition module connected to the system 11 or comprised in the system 11. In that case, the processing module take in charge the encoding of these data. The system 11 can provide an output signal to various output devices capable of storing and/or decoding the output signal such as the system 13. Various implementations involve decoding. “Decoding”, as used in this application, can encompass all or part of the processes performed, for example, on a received encoded video stream (i.e., received video data) in order to produce a final output suitable for display. In various embodiments, such processes include processes performed by a decoder of various implementations described in this application in relation to Fig.8. Various implementations involve encoding. In an analogous way to the above discussion about “decoding”, “encoding” as used in this application can encompass all or part of the processes performed, for example, on an input video sequence in order to produce an encoded video stream. In various embodiments, such processes include processes performed by an encoder of various implementations described in this application in relation to Fig.6. When a figure is presented as a flow diagram, it should be understood that it 2023PF00472 also provides a block diagram of a corresponding apparatus. Similarly, when a figure is presented as a block diagram, it should be understood that it also provides a flow diagram of a corresponding method/process. The implementations and aspects described herein can be implemented in, for example, a method or a process, an apparatus, a software program, a data stream, or a signal. Even if only discussed in the context of a single form of implementation (for example, discussed only as a method), the implementation of features discussed can also be implemented in other forms (for example, an apparatus or program). An apparatus can be implemented in, for example, appropriate hardware, software, and firmware. The methods can be implemented, for example, in a processor, which refers to processing devices in general, including, for example, a computer, a microprocessor, an integrated circuit, or a programmable logic device. Processors also include communication devices, such as, for example, computers, cell phones, portable/personal digital assistants ("PDAs"), and other devices that facilitate communication of information between end-users. Reference to “one embodiment” or “an embodiment” or “one implementation” or “an implementation”, as well as other variations thereof, means that a particular feature, structure, characteristic, and so forth described in connection with the embodiment is included in at least one embodiment. Thus, the appearances of the phrase “in one embodiment” or “in an embodiment” or “in one implementation” or “in an implementation”, as well any other variations, appearing in various places throughout this application are not necessarily all referring to the same embodiment. Additionally, this application may refer to “determining” various pieces of information. Determining the information can include one or more of, for example, estimating the information, calculating the information, predicting the information, retrieving the information from memory or obtaining the information for example from another device, module or from user. Further, this application may refer to “accessing” various pieces of information. Accessing the information can include one or more of, for example, receiving the information, retrieving the information (for example, from memory), storing the information, moving the information, copying the information, calculating the information, determining the information, predicting the information, or estimating the information. 2023PF00472 Additionally, this application may refer to “receiving” various pieces of information. Receiving is, as with “accessing”, intended to be a broad term. Receiving the information can include one or more of, for example, accessing the information, or retrieving the information (for example, from memory). Further, “receiving” is typically involved, in one way or another, during operations such as, for example, storing the information, processing the information, transmitting the information, moving the information, copying the information, erasing the information, calculating the information, determining the information, predicting the information, or estimating the information. It is to be appreciated that the use of any of the following “/”, “and/or”, and “at least one of”, “one or more of” for example, in the cases of “A and/or B” and “at least one of A and B”, “one or more of A and B” is intended to encompass the selection of the first listed option (A) only, or the selection of the second listed option (B) only, or the selection of both options (A and B). As a further example, in the cases of “A, B, and/or C” and “at least one of A, B, and C”, “one or more of A, B and C” such phrasing is intended to encompass the selection of the first listed option (A) only, or the selection of the second listed option (B) only, or the selection of the third listed option (C) only, or the selection of the first and the second listed options (A and B) only, or the selection of the first and third listed options (A and C) only, or the selection of the second and third listed options (B and C) only, or the selection of all three options (A and B and C). This may be extended, as is clear to one of ordinary skill in this and related arts, for as many items as are listed. Also, as used herein, the word “signal” refers to, among other things, indicating something to a corresponding decoder. For example, in certain embodiments the encoder signals a use of some INR parameters and Fourier mapping coefficients. In this way, in an embodiment the same parameters can be used at both the encoder side and the decoder side. Thus, for example, an encoder can transmit (explicit signaling) a particular parameter to the decoder so that the decoder can use the same particular parameter. Conversely, if the decoder already has the particular parameter as well as others, then signaling can be used without transmitting (implicit signaling) to simply allow the decoder to know and select the particular parameter. By avoiding transmission of any actual functions, a bit savings is realized in various embodiments. It is to be appreciated that signaling can be accomplished in a variety of ways. For example, one 2023PF00472 or more syntax elements, flags, and so forth are used to signal information to a corresponding decoder in various embodiments. While the preceding relates to the verb form of the word “signal”, the word “signal” can also be used herein as a noun. As will be evident to one of ordinary skill in the art, implementations can produce a variety of signals formatted to carry information that can be, for example, stored or transmitted. The information can include, for example, instructions for performing a method, or data produced by one of the described implementations. For example, a signal can be formatted to carry the encoded video stream (i.e. encoded data). Such a signal can be formatted, for example, as an electromagnetic wave (for example, using a radio frequency portion of spectrum) or as a baseband signal. The formatting can include, for example, encoding an encoded video stream and modulating a carrier with the encoded video stream. The information that the signal carries can be, for example, analog or digital information. The signal can be transmitted over a variety of different wired or wireless links, as is known. The signal can be stored on a processor-readable medium. Fig.3 illustrates a simple neural network used for implicit neural representation (INR). Such a neural network used for INR can be referred to as an INR network. For clarity, we use for illustration a 2D signal such as a picture, but INR can be used for signals of any dimension. INR parameterizes a signal as a function (300), which takes coordinates (310) as input and outputs potentially approximated signal values (320) at these coordinates. INR has recently been applied to pictures, 2D videos or 3D objects among other applications. In the picture case, the inputs (310) can be sample coordinates (x,y) of picture samples and the INR outputs (320) are the picture sample values. Picture samples values can be original sample values of an original picture or residual values representative of a difference between predictor samples and the original samples. A picture sample can be a single component signal (such as a grey scale picture) or a multi-component signal comprising a plurality of components such as for example a RGB, YUV or YUV+d picture where d represents a depth component. In the video case, the output is similar, but the input can include a picture index t in addition to the sample coordinates. The INR can be used to reconstruct a signal by computing picture sample values for some or each sample coordinates (x,y). An INR network (300) is typically a neural network composed of multiple neural layers, such as fully connected layers. In Fig. 3, the network has four neural 2023PF00472 layers. Intermediate outputs are represented by circles. Each neural layer can be described as a function that first multiplies the input by a tensor, adds a vector called the bias and then applies a nonlinear function on the resulting values. In the present document, we may also refer to a neural layer simply as a layer. Tensors shapes (and other characteristics of the tensors) and non-linear functions types of the neural network defines an architecture of the neural network. In the following, tensor values and bias values are denoted by the term weights. The weights and, if applicable, the parameters of the non-linear functions, are called parameters ^^ of the neural network. The architecture and the parameters ^^ define a model. In the following we use ^^_ఏ to denote an INR function parameterized by ^^. Fig.4A illustrates a typical process to encode a signal using INR. The process of Fig. 4A is executed for example by the processing module 200 of the system 11. In a step 401, the processing module 200 obtains an input signal and applies a learning phase during which the INR parameters ^^ (or a subset of them) of the INR network allowing reconstructing the input signal from the samples coordinates are learned. In an embodiment, the INR parameters ^^ are learned by minimizing a loss function such as for example, the loss function of equation eq.1 below: ^^ ^^ ^^ ^^ ൌ ^^^ ^^, ^^ _^^^ ^ ^^ ^^^ ^^^ (eq.1) where ^^ is a distortion which quantifies the difference between the reconstructed signal obtained by applying the INR function ^^_ఏ to input coordinate and the original signal ^^, ^^ is a bitrate of the encoded INR parameters ^^ and ^^ is a Lagrangian parameter representing a trade-off parameter between the distortion ^^ and the bitrate ^^. ^^ could be any distortion measure, such as mean squared error as equation eq.2. ^^_ெௌா ൌ ^{^} ெ_ே∑_௫,௬ ^ ^^^ ^^, ^^^ െ ^^ _^^^ ^^, ^^^^^ଶ (eq.2) M and N are a width and a height of a picture when the signal is a picture. Other metrics such as LPIPS (Learned Perceptual Image Patch Similarity) can also be used in this case. The optimization of the INR parameters (or weights) ^^ is typically performed 2023PF00472 by a machine learning approach such as a batch gradient descent method. In a step 402, the processing module 200 encodes the INR parameters ^^ (or a subset of them) in an output bitstream (i.e., in output data). When the signal is a picture, the processing module 200 also adds information representative of the picture such as the width and the height of the picture. Fig.4B illustrates a typical process to decode data using INR. The process of Fig. 4B is executed for example by the processing module 200 of the system 13. In a step 411, the processing module 200 obtains input data, for instance, corresponding to the output data generated by the processing module 200 of the system 11 when applying the method of Fig. 4A. The input data comprises encoded INR parameters ^^. During step 411, the processing module 200 decodes the INR parameters ^^ from the input data and regenerate the INR network applying the INR function ^^_ఏ. When the signal is a picture, the processing module 200 also decodes the information representative of the picture. In a step 412, the processing module 200 applies the regenerated INR network (i.e., the processing module 200 applies the INR function ^^_ఏ) to samples coordinates to generate a reconstructed version of the input signal obtained by the system 11 in step 401. If the input signal is a picture, the processing module 200 applies the regenerated INR network to at least a sub-part of the samples coordinates (x,y) of the picture. As an example, for a 256x256 samples picture, these coordinates could be all pairs (x,y) for all x∈{0,1,…,255} and y∈{0,1,…,255}. Other choices are possible, for example to generate an up-sampled, down-sampled or extended version of the input picture. Using one INR network globally for a whole signal makes learning difficult, as all parameters contribute to all values and lead to a large network as it must encode all details of the signal. A solution to address this issue is to divide the signal in portions and to define a local INR network for each portion. When the signal is a picture, the portion of a picture could be a slice, a tile, a coding unit, etc. Fig.5 illustrates an example of partitioning undergone by a picture of pixels 51 of an original video sequence 20. A picture is divided into a plurality of coding entities. First, as represented by reference 53 in Fig. 5, a picture is divided in a grid of blocks called coding tree units (CTU). A CTU consists of an ^^ ൈ ^^ block of luminance samples together with two 2023PF00472 corresponding blocks of chrominance samples. N is generally a power of two having a maximum value of “128” for example. Second, a picture is divided into one or more groups of CTU. For example, it can be divided into one or more tile rows and tile columns, a tile being a sequence of CTU covering a rectangular region of a picture. In some cases, a tile could be divided into one or more bricks, each of which consisting of at least one row of CTU within the tile. Above the concept of tiles and bricks, another encoding entity, called slice, exists, that can contain at least one tile of a picture or at least one brick of a tile. In the example in Fig.5, as represented by reference 52, the picture 51 is divided into three slices S1, S2 and S3 of the raster-scan slice mode, each comprising a plurality of tiles (not represented), each tile comprising only one brick. As represented by reference 54 in Fig. 5, a CTU may be partitioned into the form of a hierarchical tree of one or more sub-blocks called coding units (CU). The CTU is the root (i.e., the parent node) of the hierarchical tree and can be partitioned in a plurality of CU (i.e. child nodes). Each CU becomes a leaf of the hierarchical tree if it is not further partitioned in smaller CU or becomes a parent node of smaller CU (i.e., child nodes) if it is further partitioned. In the example of Fig.5, the CTU 54 is first partitioned in “4” square CU using a quadtree type partitioning. The upper left CU is a leaf of the hierarchical tree since it is not further partitioned, i.e., it is not a parent node of any other CU. The upper right CU is further partitioned in “4” smaller square CU using again a quadtree type partitioning. The bottom right CU is vertically partitioned in “2” rectangular CU using a binary tree type partitioning. The bottom left CU is vertically partitioned in “3” rectangular CU using a ternary tree type partitioning. During the coding of a picture, the partitioning is adaptive, each CTU being partitioned so as to optimize a compression efficiency of the CTU criterion. In the present application, the term “block” or “picture block” can be used to refer to any one of a CTU and a CU. In the present application, the terms “reconstructed” and “decoded” may be used interchangeably, the terms “pixel” and “sample” may be used interchangeably, the terms “image,” “picture”, “sub-picture”, “slice” and “frame” may be used interchangeably. Usually, but not necessarily, the term “reconstructed” is used at the encoder side while “decoded” is used at the decoder side. 2023PF00472 In the following, it is considered that the processing module 200 of the system 11 obtains a picture divided in coding units (CU) and that the encoding process of Fig. 4 is applied to each coding unit independently. An INR network is therefore obtained for each CU with INR parameters ^^ adapted to this CU. The bitstream outputted by the encoding process of Fig.4 represents therefore a plurality of sets of INR parameters ^^, one for each CU. As already mentioned in introduction, the input coordinates (x,y) may be modified by a transformation before being used as input for the INR. This transformation can be a Fourier mapping, a coordinate transformation, a normalization etc. Document Tancik, M. S.-K. (2020). Fourier features let networks learn high frequency functions in low dimensional domains. Advances in Neural Information Processing Systems, (pp.7537-7547) shown that a mapping into Fourier features (i.e., a Fourier mapping) enables a Multi-layer Perceptron (MLP) learn high-frequency components of an input signal. Otherwise, the MLP has a spectral bias and is unable to learn the high frequencies of the input signal, which degrades considerably a visual quality when reconstructing the encoded signal. It has been shown that a random selection of the Fourier mapping is optimal when applied to a whole picture. In practice, to guarantee reproducibility, this random Fourier mapping is used in all INR overfitting (so that close pictures have close INR representation, which is crucial). In the context of local INR network applied to a portion of a signal (typically a CU of a picture), the random Fourier mapping is suboptimal. The following embodiments propose to locally adapt the Fourier mapping to each CU. The random Fourier mapping is replaced by a locally optimized Fourier mapping. Technically, the Fourier mapping of a sample coordinate ^^ ൌ ^ ^^, ^^^ is defined as: ^^^ ^^^ ൌ ^ ^^_^ cos^2 ^^ ^^_^ ^^^, ^^_^ sin^2 ^^ ^^_^ ^^^, … , ^^_^ cos^2 ^^ ^^_^ ^^^, ^^_^ sin^2 ^^ ^^_^ ^^^^^் Hence, the mapping depends on the coefficients ^^_^ , ^^_^where the coefficients ^^_^ are the Fourier basis frequencies when the mapping is seen as a Fourier approximation of a kernel function. The Fourier basis frequencies ^^_^ are sampled randomly from a Gaussian distribution with an appropriate scale parameter ^^. When using local INR network, a local optimization of the Fourier mapping coefficients ^^_^ , ^^_^ for each local 2023PF00472 INR network leads to better results. Fig. 6 illustrates schematically a process to encode a coding unit using local INR. The process of Fig.6 is executed for example by the processing module 200 of the system 11. It is supposed here that a signal obtained by the processing module 200 is a picture and that this picture had been partitioned in a plurality of portions such as square and rectangular coding units of various sizes. In the example of Fig. 6, the process is applied to a coding unit (CU). However, the same process could be applied identically to other types of portions of a picture such as slices, tiles, CTU, etc. In the example of Fig.6, the CU comprises original samples of a picture. However, the process of Fig.6 could be also applied to a CU comprising residuals resulting from a prediction of a CU of original samples by a predictor. In a step 600, the processing module 200 obtains a coding unit (CU), called current CU in the following. In a step 604, the processing module 200 applies a joint learning phase during which the INR parameters ^^ (or a subset of them) of the INR network and Fourier mapping coefficients ^^_^ , ^^_^ and scale parameter ^^ allowing reconstructing the current CU from samples coordinates are learned jointly. In an embodiment, the INR parameters ^^, the Fourier mapping coefficients ^^_^ , ^^_^ and the scale parameter ^^ are learned on the samples of the CU by function such as for example, the loss function of equation eq.3 below: ^^ ^^ ^^ ^^ ൌ ^^^ ^^, ^^ _^^ ∘ ^^^ ^ ^^ ^^^ ^^^ (eq.3) where ^^ represents the Fourier mapping and ^^ _^^ ∘ ^^ represents an application of the Fourier mapping ^^ followed by an application of the INR function ^^_ఏ on the CU samples coordinates (x,y). In an embodiment ^^ is a mean squared error represented by equation eq.2. The minimization uses for example a recursive gradient descent process applying gradient descent of the loss function Loss. At each iteration ^^ of the recursive process, the parameters of the INR ^^ and the coefficients of the Fourier mapping ^^_^ , ^^_^ are updated as: Θ_௧ା^ ൌ Θ_௧ െ λ∇_^ ^^ ^^ ^^ ^^, where Θ_௧ represents the INR parameters ^^ and Fourier mapping coefficients ^^_^ , ^^_^ at the iteration t. In this optimization, the parameter 2023PF00472 λ is denoted the learning rate. The learning phase results in a set of INR parameters ^^^{^^௧}, a set of Fourier mapping coefficients ^^^{^^௧ ^^௧} ^ , ^^_^ and a scale parameter ^^^{^^௧} optimized for the current CU. In a step 607, the processing module 200 encodes the INR parameters ^^^{^^௧}, Fourier mapping coefficients ^^^{^^௧ ^^௧} ^ , ^^_^ and the scale parameter ^^^{^^௧} in output data. In an embodiment, in order to decrease the bitrate cost of Fourier mapping coefficients, the Fourier mapping coefficients ^^^{^^௧ ^^௧ ^^௧ ^^௧} ^ , ^^_^ ^^_^ , ^^_^ are quantized in a step 605 between steps 604 and 607. Fig. 7 describes schematically an example of quantization process. In a step 701, the processing module 200 determines the maximum value ^^_^^௫ of the Fourier mapping coefficients ^^^{^^௧} ^ and the maximum value ^^_^^௫ of the Fourier mapping coefficients ^^^{^^௧} ^ . In a step 702, the processing module 200 normalize the Fourier mapping coefficients ^^^{^^௧ ^^௧} ^ and ^^_^ as follows. ^_{^ ൌ} ^{^^} ^^௧ ^ ^{^ ^ ^} _^^^^௫ In a step 703, the a fixed bit quantization ^^ ^{^ ^} u_{sing 2 bits to obtain quantized Fourier mapping coefficients ^} ^{^} _{^^ ൌ ^^} ^{^} _^^^ ^{^} _{ൌ ^^ ^^ ^^ ^^ ^^^ ^^} ^{^} _{∗ ^2} ^{^} _{െ 1^^ and ^} ^{^} _{^ ൌ ^^} ^{^} _^^^ ^{^^} _{ൌ ^^ ^^ ^^ ^^ ^^^ ^^^} ^{^} _{∗ ^2} ^{^} _{െ 1^^. q a} , the F_{ourier mapping coefficients ^^^^ and ^} ^{^} _{^^ are encoded in the output data along with the} INR parameters ^^^{^^௧}. In an embodiment, the quantization parameter q is fixed and known by the decoder. In that case, nothing is coded in the output data for the quantization parameter q. In a variant, the quantization parameter is also learned during step 604 to obtain a learned quantization parameter ^^^{^^௧}. In that case, an information representing the learned quantization parameter ^^^{^^௧} is encoded in the output data. In an embodiment, the INR parameters ^^^{^^௧} are also quantized applying a process similar to the process of Fig.7. The INR parameters ^^^{^^௧} were learned considering the set of Fourier mapping coefficients ^^^{^^௧} ^ , ^^^{^^௧} ^ optimized for the current CU but not the quantized version of t_{hese Fourier mapping coefficients ^^^^ and ^} ^{^} _{^^. Reconstructing the current CU using the} 2023PF00472 quantized Fourier mapping coefficients ^^^_^ and ^^{^}^_^ is possible but would be sub-optimal. In an embodiment, INR parameters ^^^{^^௧} are updated in a step 606 between step 605 and 607 in a second learning phase but now considering the quantized Fourier mapping coefficients ^^^_^ and ^^{^}^_^. In other words, the Fourier mapping coefficients ^^^{^^௧}, ^^^{^^௧} are replac ^{^^௩ொ} ^ _^ ed by the inverse quantized Fourier mapping coefficients ^^^_^ = ^_^ ^{ି^} _{^ ^^^} ^{^^} ^^௩ொ ^{^^} ^_{^ ൌ} ^{^} ଶ_{^ି^ ∗ ^} ^{^} _^^ = ^^^{ି^} _൫ ^^{^}^_^൯ ൌ ^{^} ଶ_^ି^ ∗ ^^_^^௫ for the learning of the ^^^{௨^௧} are learned by minimizing a loss function such as for example, the loss function of equation eq.1. In that case, in step 607, the INR parameters ^^^{^^௧} are replaced by the updated INR parameters ^^^{௨^௧} in the output data. In an embodiment, the process of Fig.6 comprises a preliminary learning phase in steps 601, 602 and 603 between step 600 and 604. In the step 601, the processing module 200 obtains a pre-generated random Fourier mapping for mapping the coordinates of the current block (x,y) into samples values (RGB, YUV, etc). In the step 602, the processing module 200 applies a learning phase during which the INR parameters ^^ (or a subset of them) of the INR network allowing reconstructing the current CU from samples coordinates are learned considering the Fourier mapping coefficients ^^_^ , ^^_^ of the random Fourier mapping. In an embodiment, the INR parameters ^^ are learned by minimizing a loss function such as for example, the loss function of equation eq. 1. The learning phase results in a set of preliminary INR parameters ^^^{^^^^^^} optimized for the current CU. In the step 603, the processing module 200 adapts a scale parameter ^^ according to the local content of the current CU. In other words, the processing module 200 defines the scale parameter ^^ to better capture local spectrum of the current CU based on the heuristic approaches such as kth percentile of pair-wise distance, median of pair- wise distances between the image pixels. The family of pair-wise distances are a good proxy to define the scale parameter ^^ in a kernel function. Since the Fourier mapping is the approximation of the kernel function, thus defining the scale parameter ^^ of the Gaussian distribution to sample the random frequency basis according to these heuristics could result in near-optimal Fourier mapping. The preliminary INR parameters ^^^{^^^^^^}, the Fourier mapping coefficients 2023PF00472 ^^_^ , ^^_^ of the random Fourier mapping and the scale parameter ^^ are then used for initializing the joint learning phase of step 604. In an embodiment, the scale parameter ^^ is not learned during step 604 to obtain the scale parameter ^^^{^^௧}. Instead, the scale parameter ^^ is used in place of the scale parameter ^^^{^^௧}. If pre-generated random Fourier mapping coefficients are nearly optimal, then transmitting the optimized Fourier mapping coefficients ^^^{^^௧ ^^௧} ^ and ^^_^ (or there _{quantized version ^^^^ and ^} ^{^} _{^^), as described until now, might increases the file size with} minimal gain in the reconstruction quality. To avoid this, in an embodiment, it is proposed to update the pre-generated random Fourier mapping coefficients with a residual value. For instance, the optimized Fourier mapping coefficients ^^^{^^௧ ^^௧} ^ and ^^_^ are computed as follows: ^^^{^^௧} ^ ൌ ^^_^ ^ ∆ ^^_^ ^^^{^^௧} ^ ൌ ^^_^ ^ ∆ ^^_^ Where ^^_^ and ^^_^ are the Fourier mapping coefficients of the random Fourier mapping and ∆ ^^_^= ^^^{^^௧} ^ െ ^^_^ and ∆ ^^_^ ൌ ^^^{^^௧} ^ െ ^^_^ are the residuals. In this embodiment, on the residuals ∆ ^^_^ and ∆ ^^_^ (or a quantized version of the residuals ∆ ^^ and ∆ ^^ ) are encoded ^{^^௧ ^^௧} ^ _^ in the output data instead of ^^_^ and ^^_^ . In order to let the decoder know which random Fourier mapping was used by the encoder, the random Fourier mapping was selected in a set of random Fourier mappings known both by the encoder and the decoder and an index of the random Fourier mapping of the set used by the encoder is encoded in the output data. In this case the transmission cost will be minimal. In alternative embodiments, only the ^^_^ or only the ^^_^coefficients may be optimized in step 604 and transmitted in step 607. The non-optimized Fourier mapping coefficients in that case are equal to corresponding coefficients of the random Fourier mapping. Again, an index of the random Fourier mapping of the set used by the encoder is encoded in the output data. Fig. 8 illustrates schematically a process to decode a coding unit using local INR. The process of Fig.8 is executed for example by the processing module 200 of 2023PF00472 the system 13. The processing module 200 receives all CU of the picture and reconstruct the picture from the reconstructed CU. The process of Fig. 8 is applied to each CU of the picture successively. In a step 800, the processing module 200 obtains input data representative of a current CU. The input data corresponds to the output data generated in step 607. In a step 801, the processing module 200 decodes Fourier mapping coefficients from the output data. If the Fourier mapping coefficients were quantized but the quantization parameter q is known by the processing module 200, the processing module 200 inverse quantize the Fourier mapping coefficients using the quantization parameter q. If the quantization parameter q was also optimized, the processing module decodes the quantization parameter ^^^{^^௧} from the input data and inverse quantize the Fourier mapping coefficients using the quantization parameter ^^^{^^௧}. If only a residual was encoded for the Fourier mapping coefficients, the processing module 200 decodes the residuals ∆ ^^_^ and ∆ ^^_^ (or a quantized version of the residuals ∆ ^^_^ and ∆ ^^_^), decodes the index of the random Fourier mapping used by the encoder to obtain the coefficients ∆ ^^_^ and ∆ ^^_^ of the random Fourier mapping and obtains the Optimized Fourier coefficients as follows: ^^^{^^௧} ^ ൌ ^^_^ ^ ∆ ^^_^ If only the Fourier (respectively the Fourier Mapping coefficients ^^^{^^௧} ^ ) were encoded in the input data, the processing module 200 decodes the encoded coefficients and replaces the missing (not coded) Fourier mapping coefficients by Fourier mapping coefficients of a random Fourier mapping indicated by an index decoded from the input data. In a step 802, the processing module 200 decodes the INR parameters from the input data. In a step 803, the processing module 200 applies the Fourier mapping with the decoded Fourier mapping coefficients on the samples coordinates (x,y) of the current CU. A result of this Fourier mapping is a set of mapped coordinates. In a step 804, the processing module 200 applies the INR network with the decoded INR parameters on the mapped coordinates to obtain a reconstructed version 2023PF00472 of the current CU. We described above a number of embodiments. Features of these embodiments can be provided alone or in any combination. Further, embodiments can include one or more of the following features, devices, or aspects, alone or in any combination, across various claim categories and types: ^ A bitstream or signal that includes one or more of the described INR parameters and Fourier mapping coefficients, or variations thereof. ^ Creating and/or transmitting and/or receiving and/or decoding a bitstream or signal that includes one or more of the described INR parameters and Fourier mapping coefficients, or variations thereof. ^ A TV, set-top box, cell phone, tablet, or other electronic device that performs at least one of the embodiments described. ^ A TV, set-top box, cell phone, tablet, or other electronic device that performs at least one of the embodiments described, and that displays (e.g. using a monitor, screen, or other type of display) a resulting picture. ^ A TV, set-top box, cell phone, tablet, or other electronic device that tunes (e.g. using a tuner) a channel to receive a signal including an encoded video stream, and performs at least one of the embodiments described. ^ A TV, set-top box, cell phone, tablet, or other electronic device that receives (e.g. using an antenna) a signal over the air that includes an encoded video stream, and performs at least one of the embodiments described. ^ A server, camera, cell phone, tablet or other electronic device that transmits (e.g. using an antenna) a signal over the air that includes an encoded video stream, and performs at least one of the embodiments described. ^ A server, camera, cell phone, tablet or other electronic device that tunes (e.g. using a tuner) a channel to transmit a signal including an encoded video stream, and performs at least one of the embodiments described.

Claims

2023PF00472 Claims 1. A method for encoding comprising: obtaining a coding unit of a picture; applying a joint learning phase allowing learning jointly parameters of an implicit neural representation and coefficients of a transformation, the learning comprising a minimization of a loss function depending jointly on the parameters of the implicit neural representation and of the coefficients of the transformation, the implicit neural representation being applied to coordinates of samples of the coding unit transformed by the transformation; and, encoding the learned parameters of the implicit neural representation and coefficients of the transformation in output data. 2. The method of claim 1 wherein the coefficients are quantized before being encoded in the output data to obtain quantized coefficients. 3. The method of claim 2 comprising obtaining updated parameters of the implicit neural representation by learning parameters of the implicit neural representation when the implicit neural representation is applied to coordinates of samples of the coding unit transformed by a transformation based on second coefficients resulting from an inverse quantization of the quantized coefficients, the learning comprising a minimization of a loss function depending on the parameters of the implicit neural representation and wherein the coefficients of the transformation are considered fixed and resulting from the inverse quantization of the quantized coefficients. 4. The method of claim 1, 2 or 3 wherein the transformation is a Fourier mapping. 5. The method of claim 4 comprising, obtaining a random Fourier mapping and learning preliminary parameters of the implicit neural representation when the implicit neural representation is applied to coordinates of samples of the coding unit transformed by the random Fourier mapping, the learning comprising a minimization 2023PF00472 of a loss function depending on the parameters of the implicit neural representation and wherein the coefficients of the transformation are considered fixed and equal to coefficients of the random Fourier mapping, and, using the preliminary parameters of the implicit neural representation and the coefficients of the Fourier mapping to initialize the joint learning phase. 6. The method of claim 4 or 5 wherein the coefficients of the transformation comprise a scale parameter. 7. The method of any previous claim wherein, responsive to obtaining a random Fourier mapping, the method comprises encoding the coefficients learned during the joint learning phase in a form of a difference between the coefficients learned during the joint learning phase and the coefficients of the random Fourier mapping. 8. A method for decoding comprising: obtaining input data representing a coding unit of a picture; decoding coefficients of a transformation from the input data; decoding parameters of an implicit neural representation from the input data; applying the transformation based on the decoded coefficients to coordinates of samples of the coding unit to obtain mapped coordinates; and, applying the implicit neural representation based on the decoded parameters to the mapped coordinates. 9. The method of claim 8 wherein, during the decoding of the coefficients, an inverse quantization is applied to data representing the coefficients to obtain the decoded coefficients. 10. The method of claim 9 wherein a quantization parameter used during the inverse quantization is decoded from the input data. 11. The method of claim 8, 9 or 10 wherein the transformation is a Fourier mapping. 2023PF00472 12. The method of claim 11 wherein, the method comprises obtaining a random Fourier mapping, the data representing the coefficients being residuals representing a difference between coefficients of the Fourier mapping and coefficients of the obtained random Fourier mapping, the coefficients of the Fourier mapping being obtained by adding the residuals to the coefficients of the obtained random Fourier mapping. 13. A device for encoding comprising electronic circuitry configured for: obtaining a coding unit of a picture; applying a joint learning phase, allowing learning jointly parameters of an implicit neural representation and coefficients of a transformation, the learning comprising a minimization of a loss function depending jointly on the parameters of the implicit neural representation and of the coefficients of the transformation, the implicit neural representation being applied to coordinates of samples of the coding unit transformed by the transformation; and, encoding the learned parameters of the implicit neural representation and coefficients of the transformation in output data. 14. The device of claim 13 wherein the coefficients are quantized before being encoded in the output data to obtain quantized coefficients. 15. The device of claim 14 wherein the electronic circuitry is further configured for obtaining updated parameters of the implicit neural representation by learning parameters of the implicit neural representation when the implicit neural representation is applied to coordinates of samples of the coding unit transformed by a transformation based on second coefficients resulting from an inverse quantization of the quantized coefficients, the learning comprising a minimization of a loss function depending on the parameters of the implicit neural representation and wherein the coefficients of the transformation are considered fixed and resulting from the inverse quantization of the quantized coefficients. 16. The device of claim 13, 14 or 15 wherein the transformation is a Fourier mapping. 2023PF00472 17. The device of claim 16 wherein the electronic circuitry is further configured for obtaining a random Fourier mapping and learning preliminary parameters of the implicit neural representation when the implicit neural representation is applied to coordinates of samples of the coding unit transformed by the random Fourier mapping, the learning comprising a minimization of a loss function depending on the parameters of the implicit neural representation and wherein the coefficients of the transformation are considered fixed and equal to coefficients of the random Fourier mapping, and, using the preliminary parameters of the implicit neural representation and the coefficients of the Fourier mapping to initialize the joint learning phase. 18. The device of claim 16 or 17 wherein the coefficients of the transformation comprise a scale parameter. 19. The device of any previous claim from claim 13 to 18 wherein, responsive to obtaining a random Fourier mapping, the electronic circuitry is further configured for encoding the coefficients learned during the joint learning phase in a form of a difference between the coefficients learned during the joint learning phase and the coefficients of the random Fourier mapping. 20. A device for decoding comprising electronic circuitry configured for: obtaining input data representing a coding unit of a picture; decoding coefficients of a transformation from the input data; decoding parameters of an implicit neural representation from the input data; applying the transformation based on the decoded coefficients to coordinates of samples of the coding unit to obtain mapped coordinates; and, applying the implicit neural representation based on the decoded parameters to the mapped coordinates. 21. The device of claim 20 wherein, during the decoding of the coefficients, an inverse quantization is applied to data representing the coefficients to obtain the decoded coefficients. 2023PF00472 22. The device of claim 21 wherein a quantization parameter used during the inverse quantization is decoded from the input data. 23. The device of claim 20, 21 or 22 wherein the transformation is a Fourier mapping. 24. The device of claim 23 wherein, the electronic circuitry is further configured for obtaining a random Fourier mapping, the data representing the coefficients being residuals representing a difference between coefficients of the Fourier mapping and coefficients of the obtained random Fourier mapping, the coefficients of the Fourier mapping being obtained by adding the residuals to the coefficients of the obtained random Fourier mapping. 25. Non-transitory information storage medium storing program code instructions for implementing the method according to any previous claims from claim 1 to 12. 26. A computer program comprising program code instructions for implementing the method according to any previous claims from claim 1 to 12. 27. A signal generated by the method of claim 1 to 7 or by the device of claim 13 to 19.