Multiscale dictionary learning and training of INR network

Abstract

A decoding method is disclosed. Coefficients for a first set of layers of an (Implicit Neural Representation) network decomposed into a first set of layers and a second set of layers and parameters of the second set of layers are decoded. Parameters of the first set of layers are 5 determined as a linear combination of basis functions weighted by the coefficients, the basis functions being basis functions of a multiscale dictionary. An image or 3D scene is reconstructed based on the INR network using the parameters of the first set of layers and of the second set of layers.

Description

[0001] MULTISCALE DICTIONARY LEARNING AND TRAINING OF INR NETWORK

[0002] CROSS REFERENCE TO RELATED APPLICATIONS

[0003] This application claims the benefit of European Application No. 24305213. 1 , filed on February 09, 2024 which is incorporated herein by reference in its entirety.

[0004] TECHNICAL FIELD

[0005] The present embodiments generally relate to a method and an apparatus for neural compression.

[0006] BACKGROUND

[0007] 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.

[0008] SUMMARY

[0009] 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 are approximated through a dictionary basis, and this dictionary may be learned from a large collection of the data and known to both encoder and decoder. The dictionary may be learned at different scales (e.g., resolution, patch size). In an example, the INR parameters of the head layer may be approximated with the multiscale dictionary. Thus, only the weights of the tail layers are transmitted with and some extra information about the head layers. BRIEF DESCRIPTION OF THE DRAWINGS

[0010] FIG. 1 illustrates a block diagram of a system within which aspects of the present embodiments may be implemented;

[0011] FIG. 2 illustrates a simple neural network used for Implicit Neural Representation (INR);

[0012] FIG. 3 illustrates a typical process to encode a signal using INR;

[0013] FIG.4 depicts a flowchart of encoding method according to an example ; and

[0014] FIG. 5 depicts a flowchart of decoding method according to an example.

[0015] DETAILED DESCRIPTION

[0016] 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.

[0017] 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.

[0018] 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. Usually, but not necessarily, the term “reconstructed” is used at the encoder side while “decoded” is used at the decoder side.

[0019] 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.

[0020] 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.

[0021] 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.

[0022] 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.

[0023] 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.

[0024] 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.

[0025] 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. 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).

[0026] 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.

[0027] 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.

[0028] 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.

[0029] 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.

[0030] 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.

[0031] 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.

[0032] 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.

[0033] 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.

[0034] 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.

[0035] 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.

[0036] 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.

[0037] 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 9 of the network. The architecture and the parameters define a “model”. We will use fgto denote an INR function parameterized by 0.

[0038] 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 0 (or a subset of them) of the INR network and optionally encoding (320) parameters to create the output bitstream. The parameters 0 may be used to reconstruct the signal. For an image I of size (M x N), 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 fgand 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 0 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 fgwhich is overfitted to the given image I. The quality of the reconstructed image by fgdepends 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 0 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 0.

[0039] 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.

[0040] 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.

[0041] 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.

[0042] 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.

[0043] To mutualize the redundant information across images or to increase the capacity of the INR network, a dictionary D = [d1(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,

[0044] 0h= 0h« Dy (3)

[0045] 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 leamt 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.

[0046] 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. io 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 fo = tot- heh. For the approximation, a dictionary D = [fd fd2’ - 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,

[0047] Such an approximation can for example be achieved by the optimization of the following cost: arcmin 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.

[0048] 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 (e.g., learned) at a single scale. Indeed, such a dictionary may be unable to represent (e.g., approximate) signals at scales (e.g., different resolution, different sizes of patches, etc) different from the one used in the dictionary learning stage. This may lead to a suboptimal encoding of the current signal part.

[0049] As an example, when the signal is a video, the dictionary may be learned on the coding units (or another image partition) of the first frame of the video and reused for all subsequent frames. If the CTU has uniform patch size, then one dictionary is sufficient to approximate the patch of the signal. However, if the CTU has different patch size’s according to the complexity of the signal, then one dictionary might not be enough.

[0050] In contrast, an encoding method (decoding method respectively) is disclosed below wherein a dictionary D (called multiscale dictionary) learned at various scales is used to represent INR parameters (e.g., INR functions). The multiscale dictionary may comprise sub-dictionaries, and each sub-dictionary comprises the dictionary atoms of a particular scale. In an example, the INR networkemay 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 remaining of the disclosure, we will take as an example an INR divided into head and tail layers, as fe= feg-feh, and we transmit only the weights of the tail layers with some additional information about the head layers. This is an example of a decomposition into a composited representation, and other types of decompositions could be used without any loss of generality. 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.

[0051] The multiscale dictionary may be learned Dmon a large scale dataset, in which case the dictionary may be standardized and thus known by the both encoder and decoder without any transmission. In another example, the dictionary Dmmay be learned on a first frame of a video and then transmitted to the decoder side where it can be applied to all the subsequent frames. In this latter case, the transmission cost is negligible because the dictionary is applied to a large number of frames.

[0052] Let us consider the dataset which contains the signals of different resolutions, in this case a dictionary atom specific to each resolution is learned. The dictionaries are then concatenated to form a multiscale dictionary. Let 0h= {0S1ft, 0S2h, ■■■ , 0Snh}, be the collection of head layers corresponding to different scales. 0S1hcontains the head layers for the signals at the scale s1?and 0S2hand so on. The learning of multiscale dictionary is formulated as follows: arg r, where Dm= [piDsi, p2DS2, ... / 3nDs-] is the multiscale dictionary, where DS1corresponds to the dictionary atoms for scale , and DS2for scale s2and so on. T is the sparse coefficient matrix, ||. Ill is the LI norm to enforce the sparsity in the coefficient matrix T and a is the trade-off parameter to control the level of the sparsity: the higher the value, the greater the level of sparsity. The / ?i’s are the weight at the scale i. Each multiscale dictionary can have its own weights Pi's. These weights can be similar (same, e.g: = 0.5) for all the dictionaries or these weights can be optimized when encoding. When these weights are optimized while encoding they may be inserted into the bitstream to be transmitted to the decoder side.

[0053] The solution to the problem can be found using alternative minimization by fixing one variable and optimizing another alternatively. More specifically, given the dictionary Dm, the sparse coefficient matrix T may be optimized using any sparse solvers, such as Lasso. In the next step, the sparse coefficient matrix T may be fixed, and optimized for the dictionary Dmusing (stochastic) gradient descent or co-ordinate descent method. These alternative steps may be continued until convergence or certain number of iterations.

[0054] Further, group sparsity regularizer (e.g., group Lasso) may be used to introduce sparsity within each scale of the dictionary atoms. Group Lasso is similar to Lasso method. However, it forces the sparsity for the entire group. For example, in the multiscale dictionary, group sparsity can be used to force the coefficients of the dictionary (e.g., all the) atoms of a particular scale to zero.

[0055] In another variant, the multiscale dictionary learning can be used in the dictionary driven training of INR representation, and we call this as “multiscale dictionary driven training of INR representation”, where the leamt dictionary atoms (see Equation (6)) are further fine- tuned / optimized with respect to the reconstruction error together with the tail network and sparse-coefficients. In this case dictionary atoms are not only optimized to approximate the head functions but also to maximize the reconstruction quality of the signal

[0056] In the case of learning the multiscale dictionary on the first frame of the video, the frame may be partitioned into parts or coding units (CTU). The coding units can be different sizes depending on the complexity of the signal. Let’s say there are coding units of ‘n’ different sizes. In this case, we leam a multiscale dictionary for n different scales or a fixed number of scales. During encoding each coding units may be approximated with the leamt multiscale dictionary. The values of the in (6) can be predefined or can also be optimized, in this case one more term may be added in (6) to minimize the || P Hi also. This allows us to interpolated dictionaries to different scales with respect to the values of

[0057] FIG. 4 depicts a flowchart of an encoding method 400 according to an example.

[0058] Once the dictionary Dmis leamt, it is accessible for both encoder and decoder. The encoding of a given image or video may be performed as follows.

[0059] At S402, parameters of an INR (e.g., composed of first and second sets of layers such as head and tail layers) network are obtained. In an example, one specific INR function feis overfitted for the underlying image.

[0060] At S404, sparse coefficients (y's) are computed to approximate head layers from the off-the- shelf multiscale dictionary Dm. e.g., using sparse coding by solving equation (3).

[0061] At S406, the coefficients ( 's) of the head layers, the weights 0tof the tail layers and optionally the multiscale weights are encoded in a bitstream.

[0062] In an example, the sparse coefficients (y's) are entropy coded directly. In a variant, they are quantized using fixed bit quantization and 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 by the maximal value as: y = y; / amo fixed bit quantization using 2qbits may be performed to obtain the symbols to be transmitted yf= Q(yp) = round(yp * {(2}q— 1))

[0063] If the multiscale weights are not same and optimized, they may also be included in the bitstream with entropy coding or writing directly in the bitstream with fixed bits.

[0064] The weights of the tail layers may be quantized (fixed bit quantization) and encoded in the bitstream using any entropy coder or codec, for example NNC.

[0065] The bitstream may thus comprise the quantization bit q unless it is pre-defined (known to both side), the maximum values am, the list of symbols yj, the list of symbols / ?; and the weights of the tail layers. The encoding techniques of these parameters may be standardized and known both to the encoder and decoder. The encoder may also be allowed to choose the encoding technique. In that case, the chosen technique is indicated in the bitstream and potentially entropy coded. FIG. 5 depicts a flowchart of a decoding method 500 according to an example. From the bitstream, decoding is performed.

[0066] At S502, the coefficients ( 's) of the head layers, the weights 0tof the tail layers and optionally the multiscale weights are decoded from the bitstream.

[0067] For example, the quantization value q is decoded. The maximum value amand the list of symbols are decoded. The sparse coefficients are dequantized: <21(Yt ) = *am- The multiscale weights / ft may decoded from the bit-stream. The weights 0J of the tail layers are decoded from the bit-stream.

[0068] Once all the required information is decoded from the bitstream. The reconstruction of the image or video may be performed as follows. The signal partition may be decoded / recomputed if partition is used.

[0069] At S504, an INR is obtained (e.g., reconstructed), e.g. for each partition (if partition is used). To this aim, the decoded sparse coefficients of the partition are obtained (e.g., selected). The head layers weights are determined (e.g., computed) using the sparse linear combination of multiscale dictionary atoms as 0h~ They are used in the head layers of the INR network. The decoded tail layers weights are used in the tail layers of the INR network.

[0070] At S506, the video data may be reconstructed from the INR network composed of the head and tail layers. As an example, inference is performed using the INR network with all the coordinates in the corresponding partition.

[0071] FIGs 4 and 5 are described for an INR decomposed into head and tail layers. However, these same principles may be more generally applied to an INR decomposed into a first set of layers and a second set of layers.

[0072] 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.

[0073] 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.

[0074] Note that syntax elements as used herein, such as terms in equations and algorithms, signal labels / names, etc., such as the multiscale dictionary, the sparse coefficients and so on, are descriptive terms. As such, they do not preclude the use of other syntax element names. 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, determine a multiscale dictionary and decode a video signal from the multiscale dictionary.

[0075] 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.

[0076] 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, determine a multiscale dictionary and encode a video signal from the multiscale dictionary.

[0077] 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. 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.

[0078] 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.

[0079] 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.

[0080] 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.

[0081] 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.

[0082] 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.

[0083] 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.

[0084] 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.

[0085] 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.

[0086] 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.

[0087] 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.

[0088] 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.

[0089] 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 for a first set of layers of an INR (Implicit Neural Representation) network decomposed into a first set of layers and a second set of layers and parameters of the second set of layers ; determining parameters of the first set of layers as a linear combination of basis functions weighted by the coefficients, the basis functions being basis functions of a multiscale dictionary; and reconstructing an image or 3D scene based on the INR network using the parameters of the first set of layers and of the second set of layers.

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

3. The method of any one of claims 1-2, wherein the first set of layers corresponds to global information of the image or 3D scene and the second set of layers corresponds to local information of the image or 3D scene.

4. 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 the video data ; obtaining coefficients of a linear combination of basis functions of a multiscale dictionary approximating the parameters for the first set of layers ; and encoding the coefficients for the first set of layers and the parameters of the second set of layers.

5. The method of claim 4, wherein the image or 3D scene includes a plurality of partitions, and wherein obtaining parameters of the INR network, obtaining coefficients of a linear combination of basis functions and encoding the coefficients for the first set of layers and the parameters of the second set of layers are performed for each of the plurality of partitions.

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

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

8. The decoding apparatus of claim 7, wherein the image or 3D scene includes a plurality of partitions, and wherein decoding coefficients for the first set of layers and parameters of the second set of layers, determining parameters of the first set of layers and reconstructing the image or 3D scene are performed for each of the plurality of partitions.

9. The decoding apparatus of claim 7-8, wherein the first set of layers corresponds to global information of the image or 3D scene and the second set of layers corresponds to local information of the image or 3D scene.

10. An encoding apparatus video data representative of an image, or a 3D scene, comprising one or more processors and at least one memory coupled to the one or more processors, wherein the 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 the video data ; obtaining coefficients of a linear combination of basis functions of a multiscale dictionary approximating the parameters for the first set of layers ; and encoding the coefficients for the first set of layers and the parameters of the second set of layers.

11. The encoding apparatus of claim 10, wherein the image or 3D scene includes a plurality ofpartitions, and wherein obtaining parameters of the INR network, obtaining coefficients of a linear combination of basis functions and encoding the coefficients for the first set of layers and the parameters of the second set of layers are performed for each of the plurality of partitions.

12. The encoding apparatus of any one of claims 10-11, wherein the first set of layers corresponds to global information of the image or 3D scene and the second set of layers corresponds to local information of the image or 3D scene.

13. A signal comprising video data representative of an image or a 3D scene, formed by performing the method of any one of claims 4-6.

14. A computer program comprising program code instructions for implementing the method according to any one of claims 1-6 when executed by a processor.

15. A computer readable storage medium having stored thereon instructions for implementing the method of any one of claims 1-6.