Updated dictionary-driven implicit neural representation for image and video compression

Abstract

A decoding method is disclosed. Coefficients, dictionary updates and parameters of a second set of layers of an INR (Implicit Neural Representation) network decomposed into a first set of layers and a second set of layers are decoded. The first set of layers is obtained based on a linear combination of basis functions weighted by the coefficients, the basis functions being basis functions of a dictionary updated by the dictionary updates. An image or 3D scene is reconstructed based on said INR network using said first set of layers and said second set of layers.

Description

[0001] UPDATED DICTIONARY-DRIVEN IMPLICIT NEURAL

[0002] REPRESENTATION FOR IMAGE AND VIDEO COMPRESSION

[0003] CROSS REFERENCE TO RELATED APPLICATIONS

[0004] This application claims the benefit of European Application No. 24305214.9, filed on February 09, 2024 which is incorporated herein by reference in its entirety.

[0005] TECHNICAL FIELD

[0006] The present embodiments generally relate to a method and an apparatus for neural compression.

[0007] BACKGROUND

[0008] Neural compression or learning-based compression is the application of neural networks and other machine learning methods to data compression. Those techniques are currently being investigated by MPEG, and there is a new ad-hoc group which focuses on the Implicit Neural Representation-based compression (INR-based) within Working Group 4. Typically, INR- based compression techniques have a far lower computational complexity than end-to-end neural compression approaches.

[0009] SUMMARY

[0010] In one implementation, the weights of the Implicit Neural Representation (INR) network may be approximated through a dictionary basis, and this dictionary may be learnt from a large collection of data and known to both encoder and decoder. The dictionary may be updated. In an example, the updates may be obtained by the encoder and transmitted to the decoder.

[0011] In one implementation, the information content in the signal may be modeled as a composition of global and local information. The global information is common and shared for all the natural signals, and this can be learned from a large collection of data. However, the local information is specific to each signal. The INR network may thus be decomposed into head and tail layers, where the head layers are responsible for the global information and tail for the local information. The weights of the head layers may be approximated through a dictionary basis, and this dictionary may be learnt from a large collection of data and known to both encoder and decoder. The dictionary may be updated. In an example, the updates are obtained by the encoder and transmitted to the decoder. Thus, only the weights of the tail layers are transmitted with the updates and some extra information about the head layers.

[0012] BRIEF DESCRIPTION OF THE DRAWINGS

[0013] FIG. 1 illustrates a block diagram of a system within which aspects of the present embodiments may be implemented;

[0014] FIG. 2 illustrates a simple neural network used for Implicit Neural Representation (INR);

[0015] FIG. 3 illustrates a typical process to encode a signal using INR;

[0016] FIG.4 depicts a flowchart of encoding method according to an example ;

[0017] FIG. 5 depicts a flowchart of decoding method according to an example;

[0018] FIG.6 depicts a flowchart of encoding method according to an example ;

[0019] FIG. 7 depicts a flowchart of decoding method according to an example and

[0020] FIG. 8 depicts a flowchart of decoding method according to another example.

[0021] DETAILED DESCRIPTION

[0022] This application describes a variety of aspects, including tools, features, embodiments, models, approaches, etc. Many of these aspects are described with specificity and, at least to show the individual characteristics, are often described in a manner that may sound limiting. However, this is for purposes of clarity in description, and does not limit the application or scope of those aspects. Indeed, all of the different aspects can be combined and interchanged to provide further aspects. Moreover, the aspects can be combined and interchanged with aspects described in earlier filings as well.

[0023] The aspects described and contemplated in this application can be implemented in many different forms. FIGs. 1, 2 and 3 below provide some embodiments, but other embodiments are contemplated and the discussion of FIGs. 1, 2 and 3 does not limit the breadth of the implementations. At least one of the aspects generally relates to video encoding and decoding, and at least one other aspect generally relates to transmitting a bitstream generated or encoded. These and other aspects can be implemented as a method, an apparatus, a computer readable storage medium (e.g. a non-transitory computer readable storage medium) having stored thereon instructions for encoding or decoding video data according to any of the methods described, and / or a computer readable storage medium having stored thereon a bitstream generated according to any of the methods described.

[0024] In the present application, the terms “reconstructed” and “decoded” may be used interchangeably, the terms “encoded” or “coded” may be used interchangeably, the terms “pixel” and “sample” may be used interchangeably and the terms “image,” “picture” and “frame” may be used interchangeably.

[0025] Various methods are described herein, and each of the methods comprises one or more steps or actions for achieving the described method. Unless a specific order of steps or actions is required for proper operation of the method, the order and / or use of specific steps and / or actions may be modified or combined. Additionally, terms such as “first”, “second”, etc. may be used in various embodiments to modify an element, component, step, operation, etc., such as, for example, a “first decoding” and a “second decoding”. Use of such terms does not imply an ordering to the modified operations unless specifically required. So, in this example, the first decoding need not be performed before the second decoding, and may occur, for example, before, during, or in an overlapping time period with the second decoding.

[0026] For the sake of clarity, satisfying, failing to satisfy a condition and configuring condition parameter(s) are described throughout embodiments described herein as relative to a threshold (e.g., greater, or lower than), a (e.g., threshold) value, configuring the (e.g., threshold) value, etc.). For example, satisfying a condition may be described as being above a (e.g., threshold) value, and failing to satisfy a condition (e.g., performance criteria) may be described as being below a (e.g., threshold) value. Embodiments described herein are not limited to thresholdbased conditions. Any kind of other condition and parameter(s) (such as e.g., belonging or not belonging to a range of values) may be applicable to embodiments described herein.

[0027] The present aspects are not limited to VVC or HEVC, and can be applied, for example, to other standards and recommendations, whether pre-existing or future-developed, and extensions of any such standards and recommendations (including VVC and HEVC). Unless indicated otherwise, or technically precluded, the aspects described in this application can be used individually or in combination.

[0028] FIG. 1 illustrates a block diagram of an example of a system in which various aspects and embodiments can be implemented. System 100 may be embodied as a device including the various components described below and is configured to perform one or more of the aspects described in this application. 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 servers. Elements of system 100, singly or in combination, may be embodied in a single integrated circuit, multiple ICs, and / or discrete components. For example, in at least one embodiment, the processing and encoder / decoder elements of system 100 are distributed across multiple ICs and / or discrete components. In various embodiments, the system 100 is communicatively coupled to other systems, or to other electronic devices, via, for example, a communications bus or through dedicated input and / or output ports. In various embodiments, the system 100 is configured to implement one or more of the aspects described in this application.

[0029] The system 100 includes at least one processor 110 configured to execute instructions loaded therein for implementing, for example, the various aspects described in this application. Processor 110 may include embedded memory, input output interface, and various other circuitries as known in the art. The system 100 includes at least one memory 120 (e.g., a volatile memory device, and / or a non-volatile memory device). System 100 includes a storage device 140, which may include non-volatile memory and / or volatile memory, including, but not limited to, EEPROM, ROM, PROM, RAM, DRAM, SRAM, flash, magnetic disk drive, and / or optical disk drive. The storage device 140 may include an internal storage device, an attached storage device, and / or a network accessible storage device, as non-limiting examples.

[0030] System 100 includes an encoder / decoder module 130 configured, for example, to process data to provide an encoded video or decoded video, and the encoder / decoder module 130 may include its own processor and memory. The encoder / decoder module 130 represents module(s) that may be included in a device to perform the encoding and / or decoding functions. As is known, a device may include one or both of the encoding and decoding modules. Additionally, encoder / decoder module 130 may be implemented as a separate element of system 100 or may be incorporated within processor 110 as a combination of hardware and software as known to those skilled in the art.

[0031] Program code to be loaded onto processor 110 or encoder / decoder 130 to perform the various aspects described in this application may be stored in storage device 140 and subsequently loaded onto memory 120 for execution by processor 110. In accordance with various embodiments, one or more of processor 110, memory 120, storage device 140, and encoder / decoder module 130 may store one or more of various items during the performance of the processes described in this application. Such stored items may include, but are not limited to, the input video, the decoded video or portions of the decoded video, the bitstream, matrices, variables, and intermediate or final results from the processing of equations, formulas, operations, and operational logic.

[0032] In some embodiments, memory inside of the processor 110 and / or the encoder / decoder module 130 is used to store instructions and to provide working memory for processing that is needed during encoding or decoding. In other embodiments, however, a memory external to the processing device (for example, the processing device may be either the processor 110 or the encoder / decoder module 130) is used for one or more of these functions. The external memory may be the memory 120 and / or the storage device 140, for example, a dynamic volatile memory and / or a non-volatile flash memory. In several embodiments, an external non-volatile flash memory is used to store the operating system of a television. In at least one embodiment, a fast external dynamic volatile memory such as a RAM is used as working memory for video coding and decoding operations, such as for MPEG-2, (MPEG refers to the Moving Picture Experts Group, MPEG-2 is also referred to as ISO / IEC 13818, and 13818-1 is also known as H.222, and 13818-2 is also known as H.262), HEVC (HEVC refers to High Efficiency Video Coding, also known as H.265 and MPEG-H Part 2), or VVC (Versatile Video Coding, a new standard being developed by JVET, the Joint Video Experts Team).

[0033] The input to the elements of system 100 may be provided through various input devices as indicated in block 105. Such input devices include, but are not limited to, (i) a radio frequency (RF) portion that receives an RF signal transmitted, for example, over the air by a broadcaster, (ii) a Component (COMP) input terminal (or a set of COMP input terminals), (iii) a Universal Serial Bus (USB) input terminal, and / or (iv) a High Definition Multimedia Interface (HDMI) input terminal. Other examples, not shown in FIG. 1, include composite video.

[0034] In various embodiments, the input devices of block 105 have associated respective input processing elements as known in the art. For example, the RF portion may 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 may 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 portion of various embodiments includes one 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 may 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 portion 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 may include inserting elements in between existing elements, for example, inserting amplifiers and an analog-to-digital converter. In various embodiments, the RF portion includes an antenna.

[0035] Additionally, the USB and / or HDMI terminals may include respective interface processors for connecting system 100 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, may be implemented, for example, within a separate input processing IC or within processor 110 as necessary. Similarly, aspects of USB or HDMI interface processing may be implemented within separate interface ICs or within processor 110 as necessary. The demodulated, error corrected, and demultiplexed stream is provided to various processing elements, including, for example, processor 110, and encoder / decoder 130 operating in combination with the memory and storage elements to process the datastream as necessary for presentation on an output device.

[0036] Various elements of system 100 may be provided within an integrated housing, Within the integrated housing, the various elements may be interconnected and transmit data therebetween using suitable connection arrangement 115, for example, an internal bus as known in the art, including the I2C bus, wiring, and printed circuit boards.

[0037] The system 100 includes communication interface 150 that enables communication with other devices via communication channel 190. The communication interface 150 may include, but is not limited to, a transceiver configured to transmit and to receive data over communication channel 190. The communication interface 150 may include, but is not limited to, a modem or network card and the communication channel 190 may be implemented, for example, within a wired and / or a wireless medium.

[0038] Data is streamed to the system 100, in various embodiments, using a Wi-Fi network such as 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 190 and the communications interface 150 which are adapted for Wi-Fi communications. The communications channel 190 of these embodiments is typically connected to an access point or router that provides access to outside networks including the Internet for allowing streaming applications and other over-the-top communications. Other embodiments provide streamed data to the system 100 using a set-top box that delivers the data over the HDMI connection of the input block 105. Still other embodiments provide streamed data to the system 100 using the RF connection of the input block 105. 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.

[0039] The system 100 may provide an output signal to various output devices, including a display 165, speakers 175, and other peripheral devices 185. The display 165 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 165 can be for a television, a tablet, a laptop, a cell phone (mobile phone), or other device. The display 165 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 185 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 185 that provide a function based on the output of the system 100. For example, a disk player performs the function of playing the output of the system 100.

[0040] In various embodiments, control signals are communicated between the system 100 and the display 165, speakers 175, or other peripheral devices 185 using signaling such as AV. Link, CEC, or other communications protocols that enable device-to-device control with or without user intervention. The output devices may be communicatively coupled to system 100 via dedicated connections through respective interfaces 160, 170, and 180. Alternatively, the output devices may be connected to system 100 using the communications channel 190 via the communications interface 150. The display 165 and speakers 175 may be integrated in a single unit with the other components of system 100 in an electronic device, for example, a television. In various embodiments, the display interface 160 includes a display driver, for example, a timing controller (T Con) chip.

[0041] The display 165 and speaker 175 may alternatively be separate from one or more of the other components, for example, if the RF portion of input 105 is part of a separate set-top box. In various embodiments in which the display 165 and speakers 175 are external components, the output signal may be provided via dedicated output connections, including, for example, HDMI ports, USB ports, or COMP outputs.

[0042] The embodiments can be carried out by computer software implemented by the processor 110 or by hardware, or by a combination of hardware and software. As a non-limiting example, the embodiments can be implemented by one or more integrated circuits. The memory 120 can be of any type appropriate to the technical environment and can be implemented using any appropriate data storage technology, such as optical memory devices, magnetic memory devices, semiconductor-based memory devices, fixed memory, and removable memory, as non-limiting examples. The processor 110 can be of any type appropriate to the technical environment, and can encompass one or more of microprocessors, general purpose computers, special purpose computers, and processors based on a multi-core architecture, as non-limiting examples.

[0043] FIG. 2 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 an image, but INR can be used to represent signals of any dimension. INR parameterizes a signal (e.g., an image, a 3D scene) as a function (200), which takes coordinates (210), e.g., image coordinates, as input and outputs potentially approximated values (220) of a signal at these coordinates, e.g. luma and / or chroma values. INR has recently been applied to images, 2D videos or 3D objects among other applications. In the image case, the inputs (210) can be pixel coordinates (x, y) and the INR outputs (220) the color values (r, g, b) of the input pixels. In the video case, the output is similar, but the input can include the frame index t in addition to pixel coordinates. The INR can be used to reconstruct a signal by computing the signal values for every necessary coordinate inputs.

[0044] An INR network (200) is typically a neural network composed of multiple neural layers, such as fully connected layers. In FIG. 2, the network has four neural 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 this document, we may also refer to “neural layer” simply as “layer.” The shape (and other characteristics) of the tensor and the type of non-linear functions are called the architecture of the network. We will denote the values of the tensor and the bias by the term “weights”. The weights and, if applicable, the parameters of the non-linear functions, are called the parameters 6 of the network. The architecture and the parameters define a “model”. We will use fgto denote an INR function parameterized by 6.

[0045] FIG. 3 illustrates a typical process to encode a signal using INR. This is done by obtaining (310) (e.g., learning or optimizing) the parameters 6 (or a subset of them) of the INR network and optionally encoding (320) parameters to create the output bitstream. The parameters 6 may be used to reconstruct the signal. For an image I of size (M x Nf the parameters 0 or (the chosen subset) can for example be obtained (e.g., optimized) by minimizing the following loss function: where D is a distortion which quantifies the difference between the image predicted (e.g., reconstructed) by f and the original image / , R is the bitrate of the encoded parameters and A a trade-off parameter between D and R. D could be any differentiable distortion measure, such as mean squared error as Eq. (2). M and N are the width and height of the image I. Other metrics such as LPIPS (Learned Perceptual Image Patch Similarity) can also be used in this case. The optimization of the weights 6 may be performed by a machine learning approach such as a batch / stochastic gradient descent method. For each image I, there is one specific INR function fewhich is overfitted to the given image I. The quality of the reconstructed image by fedepends on the size of the neural network. As the weights are used as descriptors of the image, the larger the size of the neural network the higher the bitlength. On the other hand, constraining the number of weights will decrease the bitlength at the expense of the distortion. The weights 6 which are representative of the image may be encoded and transmitted to a receiver (e.g., a decoder) configured to reconstruct the image from the decoded weights 6.

[0046] To reconstruct (e.g., decompress) the signal, fgis evaluated at all relevant coordinates. These coordinates can be selected at decoding. A typical choice would be all pixel coordinates for an image or video. As an example, for a 256x256 pixel image, these coordinates could be all pairs (x, y) for all x G {0,1, ... ,255} and y G {0,1, ... ,255}. Other choices are possible, for example to upsample, downsample or extend the original image.

[0047] A signal or a part (a.k.a. partition) of a signal can be better encoded by approximating some parameters of the INR network using a dictionary approximation, e.g., a learned dictionary that has been known or trained beforehand. By doing so, the INR network can be encoded by the weights of the non-approximated parts and some additional information that describes the approximated parts. In an example, an INR may be divided into head and tail layers, as fe= t0. h6h. In an example, only the weights Otof the tail layers with some additional information about the head layers may be transmitted. This is an example of a decomposition into a composited representation, and other types of decompositions could be used without any loss of generality.

[0048] In an example, one INR is used to encode the entire image. In other examples, the input may be partitioned, and different INRs are used for different parts / partitions.

[0049] Sparse dictionary learning is a representation learning method which aims at finding a sparse representation of input data in the form of a linear combination of basic elements. These elements are called atoms and they compose a dictionary. A dictionary learning algorithm learns a set of atoms (a.k.a. basis functions) from some training signals in such a way that a signal can then be approximated as a linear combination of only a few atoms.

[0050] To mutualize the redundant information across images or to increase the capacity of the INR network, a dictionary D = [dx, d2, ... dK] with K atoms may be learned so that a head layer (e.g., each head layer) is approximated (represented) using a sparse linear combination Dy of the atoms of the dictionary. That is,

[0051] 0h= 0h« Dy (3)

[0052] The sparse coefficients y (a.k.a INR coefficients or approximation coefficients) used in the sparse linear combination are for example determined (e.g., approximated) by optimizing the following loss function, arg where 0hare the weights of the head layers, D is the learnt dictionary, and y is the sparse coefficients to be determined (e.g., to be optimized). To enforce the sparsity in the coefficient vector, the LI norm is used and a is the trade-off between the two terms in the equation.

[0053] Once the sparse coefficients are estimated, they may be transmitted to the decoder side. On the decoder side, the approximated head layers may be obtained (e.g., computed) from the dictionary D and the received sparse coefficients. It is noted that the dictionary may be known to both encoder and decoder. In this case, the size of the head layers can be large enough to increase the representation capacity of the INR, as the dictionary will not be included in the bitstream.

[0054] In another example, a signal or a part of a signal can be encoded by approximating some layers of the INR network using a dictionary approximation. This also allows encoding the INR network by the weights of the non-approximated parts and some additional information that describes the approximated parts. As in the previous example, the INR may be divided into head and tail layers, as fe = tet- heh. For the approximation, a dictionary D = [fd ’fd ’ - fdK] with K INR functions may be learned so that a head layer (e.g., each head layer) is approximated (represented) using a sparse linear combination of the INR functions of the dictionary. That is,

[0055] Such an approximation can for example be achieved by the optimization of the following cost: where B is the spatial support of the INR approximation (all image, block, superpixel, etc). This optimization problem may also be modified to optimize the dictionary D and / or the weights 6t. It may also include additional losses, such as or l2losses on some or all the optimized parameters.

[0056] The dictionary used to encode (e.g., by approximation of the INR parameters with the dictionary) part of a signal may not be optimal. This is typically the case when the dictionary is computed on another part of the signal or learned on a completely different data set than the current signal part to be encoded. This may lead to a suboptimal encoding of the current signal part. As an example, when the signal is a video, the dictionary may be learned on coding units (or another image segmentation) of a first frame of the video and reused for all subsequent frames. This dictionary may not be optimal to approximate parameters of INR representations encoding the coding units of the second or subsequent frames.

[0057] In contrast, an encoding method (decoding method respectively) is disclosed below wherein atoms (a.k.a. basis functions) of the dictionary D may be updated. In an example, an encoding method is thus disclosed that updates dictionary atoms (dictionary functions) used to approximate parameters of INRs, e.g., for parts of the signal. The updates may be encoded in the bitstream representative of the video and possibly transmitted. A corresponding decoding method is also disclosed that uses the decoded updates to reconstruct the video signal (e.g., an image, a video or a 3D scene).

[0058] FIG. 4 depicts a flowchart of an encoding method 400 according to an example.

[0059] At S420, a signal 410 to be encoded may be partitioned into parts (a.k.a. partitions) . The video data may be partitioned into parts (a.k.a. partitions) . e.g., into coding units. The partitioning of the video data may be of various type, e.g., quadtree, superpixels, binary -tree, ternary-tree partitioning or Multi-Type Tree. The partition is known to the decoder, e.g. it may be transmitted in the bitstream. This step is optional.

[0060] At S430, one INR is obtained (e.g., learned), i.e. the INR parameters (e.g., weights 0l) are obtained, e.g., for each partition if the signal was partitioned at S420.

[0061] At S440, a dictionary D (e.g., a dictionary of atoms) is obtained, e.g., from a memory or from a previously encoded signal, or from a previous frame of a video or a 3D scene.

[0062] At S445, the dictionary is updated based on the INR parameters learned at S430. To this aim, dictionary updates A may be computed. The updated dictionary D' is thus D + A. The updated dictionary Drmay then be used to approximate (e.g., represent) the INR parameters using a sparse linear combination of the atoms of the updated dictionary D'. This update can be done for example to yield interesting properties (e.g., small size) of the vectors (i.e., sparse coefficients) y' , for example by solving the following optimization problem:

[0063] A = arg

[0064] At S450, sparse coefficients ylare obtained from the updated dictionary based on the INR parameters learned at S430. For example, the following optimization problem can be solved to approximate each parameter vector 0lby D’: yl= arg minlle1— D'y|| + a Hxlli-

[0065] Y

[0066] At S460, the parameters of all INR (e.g., sparse coefficients ), the dictionary updates A and the partitions are encoded in a bitstream 470. Instead of directly encoding the INR weights determined at S430, sparse coefficients yfare encoded. Indeed, the INR weights determined at S430 are approximated by a sparse linear combination of the atoms of the dictionary, wherein the weights of the linear combination are the sparse coefficients y‘. These coefficients may also be quantized by a quantization function Q-. yl= Q(yl). This quantization may also be performed at the same time as the optimization in step S450.

[0067] FIG. 5 depicts a flowchart of a decoding method 500 according to an example.

[0068] At S520, the parameters included in the bitstream (e.g., the dictionary updates A , the coefficients yland possibly the partitions) are decoded. The signal partition may be decoded / recomputed if partition is used.

[0069] At S530, a dictionary D (e.g., a dictionary of atoms) is obtained, e.g., from a memory or from a previously encoded signal, or from a previous frame of a video or a 3D scene.

[0070] At S540, the dictionary is updated based on the updates decoded at S520. The updated dictionary D' is thus D + A.

[0071] At S550, one INR is obtained, i.e. the INR parameters (e.g., weights 0l) are obtained, e.g., for each partition if the signal was partitioned at S420. The INR parameters are obtained using a sparse linear combination of the atoms of the updated dictionary D'. The weights of the linear combination are the coefficients decoded at S520. The parameters 0lmay be determined (e.g., computed or reconstructed) as a linear combination of the atoms of the updated dictionary D’, e.g., as . 0l« D’Q-1^ ) in case the coefficients were quantized or 0l« D y1if the coefficients ylwere directly encoded in the bitstream.

[0072] At S560, the signal data (e.g. a video frame) may be reconstructed from the INR network using the parameters 0l. As an example, inference is performed using the INR network with all the coordinates in the corresponding partition.

[0073] In another example, the INR network femay be decomposed into at least two parts and the parameters of at least one part of the INR network is approximated using a multiscale dictionary approximation. By doing so, the INR network can be encoded by the weights of the nonapproximated parts and some additional information that describes the approximated parts. There are multiple possible approaches to decompose the INR network into parts. For example, a part may consist of the bias and / or the weights and / or the parameters of the non-linear functions and / or any subset of these elements. Such a subset may for example be defined as a subset of the layers, such as the last k layers, or the bias of the last k layers, or a subset of the neurons. In the following, we will take as an example an INR divided into head and tail layers, as fe = feg- fehwhere the head layers may be responsible for representing the global information and the tail layers for representing the local information. In an example, the decomposition into head and tail layers is up to the user. Exploiting the compositional property of the neural network, a function is decomposed into a combination / composition of head (global information) and tail (local) layers. Typically, the head would have a larger capacity to be general (e.g., from 6 to 10 layers) while the tail is an adaptation with limited layers (1 to 3 layers). The user chooses the setting, what is head and what is tail, that could depend on the complexity of the signal to be encoded.

[0074] The weights 0hof the head layers may be approximated through the dictionary D. The dictionary D defined as a collection of INR atoms (INR functions respectively) is known by the encoder and the decoder. These INR atoms (INR functions) may be chosen randomly, learned on a first frame of a video sequence, or learned using a large collection of data (e.g., a database of images). These INR atoms (INR functions respectively) may be included earlier in the bitstream and thus transmitted to the decoder. In another example, these INR atoms (INR functions respectively) may be standardized in which case they may be known by both the encoder and the decoder without the need to transmit them.

[0075] FIG. 6 depicts a flowchart of an encoding method 600 according to an example. The method may be used to encode video data, e.g., an image, a video or a 3D scene. The video data may be partitioned into parts (a.k.a. partitions) . e.g., into coding units. The partitioning of the video data may be of various type, e.g., quadtree, superpixels, binary-tree, ternary-tree partitioning or Multi-Type Tree. The partition is known to the decoder, e.g. it may be transmitted in the bitstream. At S602, INR parameters (e.g., weights 0) are obtained from the video data, e.g., from the image, to be coded. Indeed, for an image I, there is one specific INR function fewhich is overfitted to the given image I. In an example, an INR function feis overfitted over the signal part Ci to be coded. In an example, the INR function feis composed of head and tail layers as fg= tgt.hgh. To this aim, the INR parameters may be obtained (e.g., the INR may be trained) for a part of the signal (e.g., for each part of the signal) thus producing parameter vectors 0{((corresponding to the head layers) and 0J (corresponding to the tail layers) for the part .

[0076] At S604, updates A of the dictionary D are computed, wherein the dictionary D may be used to represent (e.g., approximate) the parameters (a.k.a. parameters vectors) 0{(. Updating the dictionary makes it possible to better encode the parameter vectors 0{(. For example, an update A of one atom (e.g., of each atom) of the dictionary D is computed. The updated dictionary D' is thus D + A. The updated dictionary Drmay then be used to approximate (e.g., represent) a head layer (e.g., the parameters 0{(of the head layer) using a sparse linear combination of the atoms of the updated dictionary D'. This update can be done for example to yield interesting properties (e.g., small size) of the vectors (i.e., sparse coefficients) yl, for example by solving the following optimization problem:

[0077] A = arg

[0078] Other approaches to update the dictionary are possible as well. In another example, one may want to optimize the updates to minimize the size of the updates, by solving for example the following optimization problem (e.g., rate-distortion optimization problem):

[0079] A = arg where / r is an hyperparameter controlling the importance of the encoding size R (A) of the updates.

[0080] The solution to such problems can for example be found using alternative minimization, e.g., by fixing one variable and optimizing another alternatively. More specifically, given the dictionary D and the updates A, the sparse coefficient ylmay be optimized using any sparse solvers, such as Lasso. In a next step, the sparse coefficient coefficients ylare fixed, and the dictionary updates A are optimized using (e.g., stochastic) gradient descent or co-ordinate descent method. These alternative steps are continued (e.g., repeated) until convergence or certain number of iterations. Other algorithms may be used as well, for example genetic algorithms, random sampling or simulated annealing.

[0081] In the above examples, the optimization problem does not take into account the tail layers. In another example, the dictionary updates A may also be computed by considering that the parameters 0J of the tail layers may be optimized later. The optimization problem to be solved may then be the following:

[0082] The procedures above mostly describe a sequential approach to updating the dictionary, computing other parameters and the encoding. There are many possible variants of this procedure in addition to those listed above. For example, several elements could be optimized at the same time. The dictionary updates A, the parameters y' and / or the parameters 0J could be optimized together using any optimization algorithm such as greedy search, gradient descent of a specific loss, genetic algorithms, the use of machine learning algorithms etc. This could be achieved by solving any previously mentioned optimization problem and also extracting the optimal values of these parameters.

[0083] At S606, the (e.g., sparse) INR coefficients (y's) are obtained, wherein y are coefficients of a linear combination of atoms of the updated dictionary approximating the parameters 0{(. The sparse coefficients (y's) may be directly obtained from S604. Indeed, the sparse coefficients (y's) may be determined together with the updates and stored at S604 in which case they do not need to be computed at S606. As explained above, several elements could be optimized at the same time. The dictionary updates A, the parameters y' and / or the parameters 0J could be optimized together using any optimization algorithm.

[0084] In another example, the sparse INR coefficients (y's) are computed at S606 to approximate parameters of head layers from the updated dictionary D' . Said otherwise, the parameter vectors 0{(are approximated based on the updated dictionary Dr= D + A. This approximation can be computed with any off-the-shelf approach, including approaches that can be used to compute the approximation with the original dictionary D. For example, the following optimization problem can be solved to approximate each parameter vector 0{(by D’: = arg min^ - D'y|| + a Urik

[0085] Y At S608, the dictionary updates A, the parameters y' and the parameters 0J are encoded to create a bitstream, e.g., for transmission or for later use. This may involve the use of entropy coders and / or quantization. The dictionary updates A, the parameters y' and the parameters 0f of the tail layers may be encoded using any off-the-shelf method. In particular, as they are parameters of neural networks, they may be encoded using existing codec specialized to encode such parameters such as MPEG-NNC. The dictionary updates A may be encoded using special features designed to encode updates in such codec, for example incremental neural network update data in MPEG-NNC. The parameters ylmay be directly entropy coded or may be quantized (e.g., using fixed bit quantization) then encoded in the bit-stream, for example as follows: o a maximal value is found: am= max Y;. i o the values are normalized based on the maximal value as: y” = Yi / amo fixed bit quantization using 2qbits is performed to obtain the symbols to be transmitted y; = Q(y ) = round(y * {(2}q— 1))

[0086] The encoding techniques of these parameters (i.e., dictionary updates A, the parameters yland the parameters 0J ) may be standardized and known both to the encoder and decoder. The encoder may also be allowed to choose the encoding technique. In that latter case, the chosen technique may be included in the bitstream and potentially entropy coded. The resulting bitstream may thus contain the dictionary updates A , the coefficients yfand the other parameters 0f

[0087] FIG. 7 depicts a flowchart of a decoding method 700 according to an example.

[0088] At S702, the parameters included in the bitstream (e.g., the dictionary updates A, the INR coefficients yland the other parameters 0f for all parts) are decoded. The signal partition may be decoded / recomputed if partition is used.

[0089] The following steps may be applied successively on each part of a signal to reconstruct the whole signal.

[0090] At S704, the head layers are obtained (e.g., approximated or computed) from the updated dictionary D’ and the INR coefficients yl. More precisely, the parameters 0{(of the head layers are obtained (e.g., computed) from the updated dictionary D’ and the INR coefficients yl. The parameters 0{(may be determined (e.g., computed or reconstructed) as a linear combination of the atoms of the updated dictionary D’, e.g., as . 0{(~ D'Q (l) in case the coefficients were quantized or 0l« D'y1if the y' were directly encoded in the bitstream. The updated dictionary D’ is obtained from the original dictionary D which is known by the decoder and the decoded updates A.

[0091] At S706, the video data may be reconstructed from the INR network composed of the head and tail layers parameterized by the parameters 0j(and 0f respectively. As an example, inference is performed using the INR network with all the coordinates in the corresponding partition.

[0092] In another example, the dictionary may consist of K INR functions, so that a head layer (e.g., each head layer) is approximated (represented) using a sparse linear combination of the INR functions of the dictionary. The updates modify the parameters of the functions of the dictionary:

[0093] The encoding process is similar to FIG.6. However, computing the dictionary updates at S604 and obtaining the coefficients of the approximation at S606 are different in the optimized cost functions and so is the reconstruction of the signal. The differences are due to the different use of the dictionary. In S604, such an update can for example be achieved by the optimization of the following cost:

[0094] A = arg

[0095] The objective may also involve a term that aims at minimizing the size of the bitstream necessary to encode the updates:

[0096] A = arg

[0097] An optimization of the tail parameters may also be taken into account:

[0098] A = arg In S606, when the dictionary update has been computed, the approximation coefficients ylcan for example be computed for each part of the signal by optimizing the following cost:

[0099] These coefficients may also have been computed in step S604 or use another loss adapted from any of the losses used in step S604.

[0100] FIG. 8 depicts a flowchart of a decoding method 800 according to an example.

[0101] At S802, the parameters included in the bitstream (e.g., the dictionary updates A , the coefficients y' and the other parameters 0J for all parts) are decoded. The signal partition may be decoded / recomputed if partition is used.

[0102] The following steps may be applied successively on each part of a signal to reconstruct the whole signal.

[0103] At S804, the head layers are obtained (e.g., approximated or computed) from the updated dictionary D' = ar|d the INR coefficients yl. The head layers may be approximated as a linear combination of the updated basis functions, e.g., as . h6h= ^j=i Yjfdj+8j ■ The updated basis functions fdj+8j are obtained from the original basis functions of the original dictionary D which is known by the decoder and from the decoded updates A = 82, ... , 8K. Said otherwise, the parameters dj + 8j of the updated basis functions are obtained (e.g., computed) from the dictionary D and the updates A.

[0104] At S806, the video data may be reconstructed from the INR network composed of the approximated heads and tail layers parameterized by the parameters 0J , where the approximated heads h6h= ^j i Yjfdj+8jareparameterized by the updated dictionary D’ and the decoded parameters yl. As an example, inference is performed using the INR network with all the coordinates in the corresponding partition.

[0105] Moreover, the present aspects are not limited to ECM, VVC or HEVC, and can be applied, for example, to other standards and recommendations, and extensions of any such standards and recommendations. Unless indicated otherwise, or technically precluded, the aspects described in this application can be used individually or in combination.

[0106] Various numeric values are used in the present application. The specific values are for example purposes and the aspects described are not limited to these specific values.

[0107] Note that syntax elements as used herein, such as terms in equations and algorithms, signal labels / names, etc., such as updates A, the parameters y' and so on, are descriptive terms. As such, they do not preclude the use of other syntax element names.

[0108] 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 sequence in order to produce a final output suitable for display. In various embodiments, such processes include one or more of the processes typically performed by a decoder, for example, entropy decoding, inverse quantization, inverse transformation, and differential decoding. In various embodiments, such processes also, or alternatively, include processes performed by a decoder of various implementations described in this application, for example, decode dictionary updates and reconstruct a video signal from the dictionary updates.

[0109] As further examples, in one embodiment “decoding” refers only to entropy decoding, in another embodiment “decoding” refers only to differential decoding, and in another embodiment “decoding” refers to a combination of entropy decoding and differential decoding, and in another embodiment “decoding” refers to the whole reconstructing picture process including entropy decoding. Whether the phrase “decoding process” is intended to refer specifically to a subset of operations or generally to the broader decoding process will be clear based on the context of the specific descriptions and is believed to be well understood by those skilled in the art.

[0110] 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 bitstream. In various embodiments, such processes include one or more of the processes typically performed by an encoder, for example, partitioning, differential encoding, transformation, quantization, and entropy encoding. In various embodiments, such processes also, or alternatively, include processes performed by an encoder of various implementations described in this application, for example, determining dictionary updates and encode a video signal from the dictionary updates.

[0111] As further examples, in one embodiment “encoding” refers only to entropy encoding, in another embodiment “encoding” refers only to differential encoding, and in another embodiment “encoding” refers to a combination of differential encoding and entropy encoding. Whether the phrase “encoding process” is intended to refer specifically to a subset of operations or generally to the broader encoding process will be clear based on the context of the specific descriptions and is believed to be well understood by those skilled in the art.

[0112] This disclosure has described various pieces of information, such as for example syntax, that can be transmitted or stored, for example. This information can be packaged or arranged in a variety of manners, including for example manners common in video standards such as putting the information into an SPS, a PPS, a NAL unit, a header (for example, a NAL unit header, or a slice header), or an SEI message. Other manners are also available, including for example manners common for system level or application level standards such as putting the information into one or more of the following: a. SDP (session description protocol), a format for describing multimedia communication sessions for the purposes of session announcement and session invitation, for example as described in RFCs and used in conjunction with RTP (Real-time Transport Protocol) transmission. b. DASH MPD (Media Presentation Description) Descriptors, for example as used in DASH and transmitted over HTTP, a Descriptor is associated with a Representation or collection of Representations to provide additional characteristic to the content Representation. c. RTP header extensions, for example as used during RTP streaming. d. ISO Base Media File Format, for example as used in OMAF and using boxes which are object-oriented building blocks defined by a unique type identifier and length also known as 'atoms' in some specifications. e. HLS (HTTP live Streaming) manifest transmitted over HTTP. A manifest can be associated, for example, to a version or collection of versions of a content to provide characteristics of the version or collection of versions.

[0113] When a figure is presented as a flow diagram, it should be understood that it 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.

[0114] Some embodiments refer to rate distortion optimization. In particular, during the encoding process, the balance or trade-off between the rate and distortion is usually considered, often given the constraints of computational complexity. The rate distortion optimization is usually formulated as minimizing a rate distortion function, which is a weighted sum of the rate and of the distortion. There are different approaches to solve the rate distortion optimization problem. For example, the approaches may be based on an extensive testing of all options, with a complete evaluation of their coding cost and related distortion of the reconstructed signal after coding and decoding. Faster approaches may also be used, to save encoding complexity, in particular with computation of an approximated distortion. Mix of these two approaches can also be used. Other approaches only evaluate a subset of the possible options. More generally, many approaches employ any of a variety of techniques to perform the optimization, but the optimization is not necessarily a complete evaluation of both the coding cost and related distortion.

[0115] 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 in, for example, 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.

[0116] 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.

[0117] 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, or retrieving the information from memory.

[0118] 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.

[0119] 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.

[0120] It is to be appreciated that the use of any of the following “and / or”, and “at least one of’, for example, in the cases of “A / B”, “A and / or B” and “at least one 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”, 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.

[0121] 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 particular one of dictionary update. In this way, in an embodiment the same parameter is 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 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.

[0122] 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 bitstream of a described embodiment. 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 a data stream and modulating a carrier with the encoded data 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.

[0123] Many examples are described herein. Features of examples may be provided alone or in any combination, across various claim categories and types. Further, examples may include one or more of the features, devices, or aspects described herein, alone or in any combination, across various claim categories and types. For example, features described herein may be implemented in a bitstream or signal that includes information generated as described herein. The information may allow a decoder to decode a bitstream, the encoder, bitstream, and / or decoder according to any of the embodiments described. For example, features described herein may be implemented by creating and / or transmitting and / or receiving and / or decoding a bitstream or signal. For example, features described herein may be implemented a method, process, apparatus, medium storing instructions, medium storing data, or signal. For example, features described herein may be implemented by a TV, set-top box, cell phone, tablet, or other electronic device that performs decoding. The TV, set-top box, cell phone, tablet, or other electronic device may display (e.g. using a monitor, screen, or other type of display) a resulting image (e.g., an image from residual reconstruction of the video bitstream). The TV, set-top box, cell phone, tablet, or other electronic device may receive a signal including an encoded image and perform decoding.

[0124] A number of embodiments has been described above. Features of these embodiments can be provided alone or in any combination, across various claim categories and types.

Claims

CLAIMS1. A decoding method comprising: decoding coefficients, dictionary updates and parameters of a second set of layers of an INR (Implicit Neural Representation) network decomposed into a first set of layers and a second set of layers; obtaining said first set of layers based on a linear combination of basis functions weighted by the coefficients, the basis functions being basis functions of a dictionary updated by the dictionary updates; and reconstructing an image or 3D scene based on said INR network using said first set of layers and said second set of layers.

2. The method of claim 1, wherein obtaining said first set of layers based on a linear combination of basis functions weighted by the coefficients comprises obtaining parameters of said first set of layers as a linear combination of atoms weighted by the coefficients, the atoms being atoms of the dictionary updated by the dictionary updates.

3. The method of claim 1 or 2, wherein said image or 3D scene includes a plurality of partitions, and wherein said decoding coefficients, dictionary updates and parameters of the second set of layers, said obtaining said first set of layers and said reconstructing the image or 3D scene are performed for each of said plurality of partitions.

4. The method of any one of claims 1-3, wherein said first set of layers corresponds to global information of said image or 3D scene and said second set of layers corresponds to local information of said image or 3D scene.

5. A method for encoding video data representative of an image, or a 3D scene, comprising: obtaining parameters of an INR (Implicit Neural Representation) network decomposed into a first set of layers and a second set of layers based on said video data ; computing updates of a dictionary of basis functions; obtaining coefficients of a linear combination of basis functions of the dictionary updated by the updates approximating said parameters for said first set of layers ; and encoding said coefficients, the updates and the parameters of said second set of layers.

6. The method of claim 5, wherein obtaining coefficients of a linear combination of basisfunctions of the dictionary updated by the updates comprises obtaining coefficients of a linear combination of atoms of the dictionary updated by the updates approximating said parameters for said first set of layers.

7. The method of claim 5 or 6, wherein said image or 3D scene includes a plurality of partitions, and wherein said obtaining parameters of the INR network, said obtaining coefficients of a linear combination of atoms and said encoding the coefficients, the updates and the parameters of said second set of layers are performed for each of said plurality of partitions.

8. The method of any one of claims 4-5, wherein said first set of layers corresponds to global information of said image or 3D scene and said second set of layers corresponds to local information of said image or 3D scene.

9. A decoding apparatus comprising one or more processors and at least one memory coupled to said one or more processors, wherein said one or more processors are configured to perform : decoding coefficients, dictionary updates and parameters of a second set of layers of an INR (Implicit Neural Representation) network decomposed into a first set of layers and a second set of layers; obtaining said first set of layers based on a linear combination of basis functions weighted by the coefficients, the basis functions being basis functions of a dictionary updated by the dictionary updates; and reconstructing an image or 3D scene based on said INR network using said first set of layers and said second set of layers.

10. The decoding apparatus of claim 9, wherein obtaining said first set of layers based on a linear combination of basis functions weighted by the coefficients comprises obtaining parameters of said first set of layers as a linear combination of atoms weighted by the coefficients, the atoms being atoms of the dictionary updated by the dictionary updates.

11. The decoding apparatus of claim 9 or 10, wherein said image or 3D scene includes a plurality of partitions, and wherein said decoding coefficients, dictionary updates and parameters of a second set of layers, said obtaining said first set of layers and said reconstructing the image or 3D scene are performed for each of said plurality of partitions.

12. The decoding apparatus of claim 9-11, wherein said first set of layers corresponds to global information of said image or 3D scene and said second set of layers corresponds to local information of said image or 3D scene.

13. An encoding apparatus for encoding video data representative of an image, or a 3D scene, comprising one or more processors and at least one memory coupled to said one or more processors, wherein said one or more processors are configured to perform : obtaining parameters of an INR (Implicit Neural Representation) network decomposed into a first set of layers and a second set of layers based on said video data ; computing updates of a dictionary of basis functions; obtaining coefficients of a linear combination of basis functions of the dictionary updated by the updates approximating said parameters for said first set of layers ; and encoding said coefficients, the updates and the parameters of said second set of layers.

14. The encoding apparatus of claim 13, wherein obtaining coefficients of a linear combination of basis functions of the dictionary updated by the updates comprises obtaining coefficients of a linear combination of atoms of the dictionary updated by the updates approximating said parameters for said first set of layers.

15. The encoding apparatus of claim 13 or 14, wherein said image or 3D scene includes a plurality of partitions, and wherein said obtaining parameters of the INR network, said obtaining coefficients of a linear combination of atoms and said encoding the coefficients, the updates and the parameters of said second set of layers are performed for each of said plurality of partitions.

16. The encoding apparatus of any one of claims 13-15, wherein said first set of layers corresponds to global information of said image or 3D scene and said second set of layers corresponds to local information of said image or 3D scene.

17. A signal comprising video data representative of an image or a 3D scene, formed by performing the method of any one of claims 5-8.

18. A computer program comprising program code instructions for implementing the method according to any one of claims 1-8 when executed by a processor.

19. A computer readable storage medium having stored thereon instructions for implementing the method of any one of claims 1-8.

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