JP2018033131A - Decoder, encoder and method for decoding encoded value - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide an encoding and decoding method that is feasible even in an environment in which an encoder is computationally restricted.SOLUTION: A decoder includes a memory for storing a map of the space of encoded values. The map encloses a plurality of cells dividing the space, and each cell encloses a cluster of encoded values, and quantizes the cluster into quantized encoded values. Each cell is identified by a label, the plurality of cells are identified by the same label, and the cells are labeled such that pairs of cells identified by the same label do not share a common boundary. The decoder includes: a receiver for receiving labels of cells that enclose encoded values on the map; and a processor for estimating encoded values by using side information, generating estimates of the encoded values, selecting cells being the closest to the estimates of the encoded values, identified by labels on the map, and determining the estimates as quantized encoded values of the selected cells.SELECTED DRAWING: Figure 7

Description

  The present invention relates generally to signal processing, and more particularly to coding of uncompressed signals, where coding includes at least one of encoding and decoding.

  Lossy compression is widely used in signal processing and signal transmission. There are several applications of lossy signal compression, such as compression of camera images, multispectral images, hyperspectral images, and synthetic aperture radar (SAR) data, to name a few. In such applications, the goal is to encode the signal using an encoder and represent the signal using a small number of bits, thereby allowing the signal to be transmitted at a lower bit rate, In exchange for this, there is some distortion of the signal, i.e. there is some loss of information during compression and the compression becomes irreversible.

  FIG. 1A is a block diagram of a conventional coding method and system. The system includes an encoder 110 and a decoder 120. The encoder takes an uncompressed signal 101 as input and generates a compressed signal 111. Lossless transmission 115 is used to send the compressed signal to the decoder. As a result, a decompressed signal 121 that is an estimated value of the uncompressed signal is obtained.

  The goal of an encoder, ie, a system or method that performs compression, is to generate a bitstream, ie, a bit sequence, that represents a signal with as little distortion as possible for a given bit rate. Alternatively, the encoder may generate a bitstream with as few bits as possible given the distortion that can be tolerated by the application.

  A decoder, ie, a system or method for decompressing a signal, uses the bit sequence generated by the decoder to recover the original signal with as little distortion as possible for a given bit rate.

  The most commonly used encoding method uses two techniques: prediction and subsequent transformation. Prediction attempts to predict a portion of the signal to be encoded, eg, a block of an image, using other portions of the signal or information from other signals. Thus, the encoder includes the prediction parameters in the bitstream, i.e. how the prediction was performed, e.g. which part of the signal was used and which prediction method was used, so that the decoder Allow the same prediction step to be performed.

  Since the prediction is usually incomplete, there is a prediction residual, and this prediction residual is also encoded. Since the encoding of the residual is expected to be easy, the rate used to transmit the prediction parameters and the rate used to code the residual are more than just encoding the signal without prediction. Low.

  To encode the residual, the encoder first uses a transform that maps the signal to a different region that is simpler to encode. The goal of the transformation is to expose the structure of the signal so that encoding requires only a few bits. For example, image and video compression may transform the residue using a discrete cosine transform (DCT). This is because it is easier to encode the residual DCT coefficient than the residual itself, even though the residual DCT coefficient and the residual itself represent the same information. The reason is that the DCT concentrates a small number of significant coefficient information to be encoded.

  These two techniques typically perform encoder performance by, for example, choosing how many bits of the bitstream to use for each part of the signal so that the trade-off between rate and distortion is optimally traded across the signal. Combined with other techniques to elaborate.

  Unfortunately, these encoding techniques produce very complex encoders and usually require a very simple decoder. This is acceptable in many applications such as image and video coding. In these applications, the encoder has a large resource available, but the decoder in the playback device has limited resources. However, in applications where the encoder must be computationally limited, this is a problem.

  For example, the computational resources available for satellite image or radar signal compression are very limited due to processor and power constraints that can withstand spatial movement conditions. Similarly, in applications such as hyperspectral or multispectral image compression, the amount of data that needs to be used for prediction and conversion requires very large memory storage for state-of-the-art portable devices. Even modern video compression on mobile devices, such as cell phones and other handheld devices, uses a separate processor to minimize the load on the main processor and reduce power consumption. For many such applications, the computational resources and power available to the decoder are essentially unlimited. For example, a satellite data decoder may be part of a large data center with large storage available for decoding and several processing nodes. For this reason, it makes sense to reduce the complexity of the encoder at the expense of more complex decoders.

  An alternative approach is distributed compression, also known in the art as compression using side information. This type of method does not perform a prediction step at the encoder. Rather than the encoder predicting the signal and encoding the residual, the encoder assumes that the decoder can perform some prediction on the signal from the side information available at the decoder. Since the prediction is based on side information, it may be incomplete and thus decoding can cause significant distortion. Thus, the role of the encoder is to transmit a bitstream at the decoder that can be used with prediction to reduce the distortion of the decoded signal.

  In practice, all practical coding methods using side information attempt to correct the bitstream. In particular, the prediction method at the decoder attempts to predict a prediction bitstream that can produce a decompressed signal when it is further decoded later. The encoder attempts to generate a transmission bitstream that can correct errors in the predicted bitstream and generate an error-free bitstream. The error free bit stream is then used for reconstruction.

  To encode the transmitted bitstream, the encoder still performs a conversion step, but then encodes the information using an error correction code (ECC). Since the bitstream is available at the decoder through prediction, it is only necessary to transmit a small amount of error correction information generated by ECC, known as syndrome. Since the prediction step is performed at the decoder, the complexity of the encoder is greatly reduced. On the other hand, decoder complexity is greatly increased, and compression using side information becomes applicable when the decoder can be a more powerful system than an encoder.

  FIG. 1B shows a coding method and system using syndrome and side information. The system includes an encoder 210 that takes an uncompressed signal 201 as input and generates a compressed signal 211 or syndrome. The compressed signal 211 or the syndrome is transmitted losslessly to the decoder 220 (115), and the decoder 220 generates a decompressed signal 221.

  Compression using side information reduces the load on the encoder, but still requires a transform step in addition to the encoding step, which can be computationally complex in some cases.

  Furthermore, since all actual compression methods use error correction and decode the bitstream separately, these methods ensure that the bitstream can be corrected accurately. If these methods fail to transmit sufficient error correction information, decoding may fail and recover signals that are not related to the original signal. In many cases, a failure in error correction can be the result of a failure to decode the bitstream.

  For this reason, most practical methods send more numbers of syndrome bits than necessary to ensure that the correction works, thereby wasting bandwidth. Furthermore, the extra bits do not improve the distortion characteristics of the compression method. Alternatively, a feedback-based rate control system may be implemented on top of the compression system, which attempts to decode and requires more syndrome bits if unsuccessful. This requires both real-time decoding and two-way communication between the encoder and decoder, which is not possible in many applications.

  One embodiment is a memory that stores a map of a space of encoded values, the map including a plurality of cells that divide the space, whereby each cell contains a cluster of encoded values. Enclosing and quantizing the cluster of encoded values into quantized encoded values, wherein each cell is identified by a label selected from a finite alphabet, whereby the plurality of cells in the map have the same label The cells are labeled such that pairs of cells identified by the same label do not share a common boundary, and from memory and an encoder, the encoded values on the map in multidimensional space A receiver that receives a label of an enclosing cell, and estimates the encoded value using side information, generates an estimate of the encoded value, and on the map of the space Selecting a cell closest to the estimate of the encoded value, identified by a received label, and determining the encoded value as the quantized encoded value of the selected cell; A decoder comprising:

  Another embodiment is to estimate a transmitted encoded value and generate an estimated value, wherein the estimation uses side information and said multi-dimensional space map of encoded values Locating an estimate, wherein the map includes a plurality of cells that divide the multi-dimensional space, whereby each cell surrounds a cluster of encoded values, and Quantizing the cluster into quantized encoded values, each cell is identified by a label selected from a finite alphabet, whereby the plurality of cells in the map are identified by the same label, and the cells are The cell pairs identified by the same label are labeled such that they do not share a common boundary; receiving a cell label transmitted over a communication channel; and In the above, selecting a cell closest to the estimated position value from the cells having the transmitted label, and using the quantized value of the second cell as a decoded value of the signal Selecting the method. The steps of the method are performed by a decoder processor.

  Another embodiment is a processor that determines encoded values and a memory that stores a map of a multidimensional space of encoded values, the map including a plurality of cells that divide the multidimensional space; Thereby, each cell surrounds a cluster of coded values, the cluster of coded values is quantized into a quantized coded value, and each cell is identified by a label selected from a finite alphabet, A plurality of cells in the map are identified by the same label, and the cells are labeled such that pairs of cells identified by the same label do not share a common boundary; And a transmitter for transmitting a label of the cell surrounding the encoded value on the map of the multidimensional space.

FIG. 2 is a schematic block diagram (high level block diagram) of a conventional compression method and system. It is a schematic block diagram of the conventional compression method and system using side information. 1 is a schematic block diagram of a compression method and system according to an embodiment of the present invention. It is the schematic of operation | movement of the universal encoder using the encoding matrix by embodiment of this invention. It is the schematic of the scalar quantization by embodiment of this invention. It is the schematic of the scalar quantization by embodiment of this invention. FIG. 5 is a schematic diagram of an alternative interpretation of the operation of a universal encoder according to an embodiment of the invention. It is a schematic diagram of restoration of missing information from prediction in a decoder according to an embodiment of the present invention. It is a schematic diagram of restoration of missing information from prediction in a decoder according to an embodiment of the present invention. 3 is a flow diagram of compression synthetic aperture radar (SAR) data using an embodiment of the present invention. 4 is a flowchart of compression of a multispectral or hyperspectral image using an embodiment of the present invention. FIG. 6 is a schematic diagram of a map of encoded value spaces used by encoders and decoders, according to some embodiments. FIG. 2 is a block diagram of an encoder that communicates with a decoder to perform encoding and / or decoding in accordance with the principles of some embodiments. FIG. 3 is a block diagram of a method for encoding a value, according to some embodiments. FIG. 3 is a block diagram of a method for decoding encoded values, according to some embodiments. FIG. 3 is a block diagram of an encoding method and a decoding method for performing data compression, according to one embodiment.

Non-monotonic quantization compression method and system for compression using side information FIG. 1C illustrates a method and system for compression according to some embodiments of the present invention. The system includes an encoder 310 that takes an uncompressed signal 301 as input and generates a quantized measurement 321 that can be losslessly transmitted to a decoder 320 (315). The decoder decodes the quantized measurement value using the side information y319 and generates the decompressed signal 321a.

Overview Encoder The role of the universal encoder is to encode the signal x 301 into a bit stream that is a compressed signal 321. In the encoder, the decoder uses the side information y319,

Suppose that we can form a prediction of x represented by This can include some distortion.

  To encode uncompressed x, encoder 310 takes a linear measurement of x, and a dither w360 is added to this linear measurement, which is then quantized using non-monotonic quantization, Quantized data q321, that is, a compressed signal is generated. As described below, non-monotonic quantization can be viewed as removing extra information, eg, one or more most significant bits, from the quantized measurements that can be recovered by the decoder 320.

Decoder Decoder is an estimate of x using side information 319

Form. Next, the decoder

Is obtained, and a dither w is added. This result is quantized by a non-monotonic quantizer, which generates a prediction of missing information from q, which is the encoding of x. Missing information is added to q and a set of quantized measurements

Is generated. These measurements are predictions of x

, And any other prior knowledge about x,

Is reconstructed.

Is

It is an estimated value of x with much less distortion.

Encoding FIG. 2A schematically illustrates encoding. The uncompressed signal x301 has N dimensions that can be real or complex. One embodiment uses an encoding matrix A350 having dimension M × N to obtain M linear measurements Ax of signal x. The matrix A can be a real matrix or a complex matrix. In a preferred embodiment, the real signal is measured using a real matrix and the complex value signal is measured using a complex value matrix. However, in some embodiments, the real signal can be measured using a complex-valued matrix and vice versa.

  The matrix can be generated in several ways. In the preferred embodiment, the matrix is randomly generated. For example, the entries in matrix A can be realizations of random variables taken from a uniform distribution of independent identical distributions, a Rademachel distribution, a Gaussian distribution or a sub-Gaussian distribution. Alternatively, the rows of matrix A can be sampled uniformly from an N-dimensional unit sphere.

  In another embodiment, the matrix A is a discrete Fourier transform (DFT) matrix, or a Hadamard transform matrix, or a discrete sine or cosine transform (DCT or DST) matrix, or a column is reordered and some of the rows Can be any of the above matrices from which has been removed. In another embodiment, the matrix may be a low density parity check code (LDPC) matrix or an expander graph matrix. The advantage of using structured matrices (DFT, DCT, DST, Hadamard) or sparse matrices (LDPC, expander graph) is that these matrices require less memory and processing, thus reducing encoder complexity It is to be.

A dither w360 is then added to the linear measurement as Ax + w and the result is quantized using a non-monotonic B-bit scalar quantizer with a quantization parameter Δ. In a preferred embodiment, the dither is randomly generated from a uniform distribution with support Δ or 2 ^B Δ. Note that since this is a scalar quantizer and the input is a vector, the quantizer function is applied element by element to each of the vector elements.

2B and 2C show B-bit scalar quantizers for B = 1 and B = 2, respectively. In particular, the scalar quantization function is periodic with period 2 ^B and has 2 ^B distinct output levels. This can be represented using B bits. The input space is divided into intervals of length Δ, each interval being mapped to one of 2 ^B output levels. Multiple intervals are mapped to the same level.

  As shown in FIG. 2D, the non-monotonic quantizer Q (•) can also be regarded as a uniform scalar quantizer Q ′ (•) with a quantization interval Δ, after which different quantization levels are set to 1. The operation that maps to The uniform scalar quantizer Q '(.) Generates a multi-bit representation q'240 in which one or more of the most significant bits (MSBs) are discarded (250). For this reason, all quantization levels with the same least significant bit (LSB) held (251) have the same output. The output of the encoder is q321, which is used by the decoder 320 to estimate the input signal x301.

Decoding Decoder 320 estimates with some distortion of signal x

Has access to side information y319 that enables

The predictor for the estimate of is a function f (·), and the prediction is obtained by applying this function.

  Signals can be predicted using multiple methods, and side information can be obtained at the decoder using multiple methods. Some of them are described below.

  The decoder measures the prediction signal and adds a dither w in the same manner as the encoder.

  When quantized using a uniform scalar quantizer Q ′ (•) with a quantization interval Δ, the predicted quantized value is

It becomes. However, the predicted measurement

, When combined with encoding q, is a decoded quantization measure.

The signal can be decompressed based on this decoded quantization measurement, which contains more information than can be generated. To extract this information, the decoder selects a level from the set of possible output levels used by the uniform quantizer Q '(.). In particular, each coefficient

Are selected from all levels that match the corresponding encoding q _i . Predictive coefficients from all these levels

The level closest to is selected.

This selection is demonstrated by the example shown in FIGS. 3A-3B. Given an encoding level q _i = 1, there are multiple possible matching regions, two of which are shown in FIG. 3A. The corresponding uniform quantizer shown in FIG. 3B has two different quantization levels corresponding to the coding q _i = 1, which are represented by circles in the figure,

as well as

Corresponding to Prediction from side information

Is the closest to level-2.5, so this is the decoded quantization measurement

Whereas level 1.5 is discarded, as indicated by the circle with a cross in the figure. Note that the levels of non-monotonic and uniform quantizers do not necessarily match.

  Ideally, decoding measurements

Should be equal to the corresponding measurement of the signal compressed using the scalar quantizer, ie the measurement should be equal to Q '(Ax + w). In practice, however, there may be some decoding error. In some embodiments, these errors can be ignored because subsequent reconstructions can compensate for the errors, as described below.

  In some embodiments, the encoder can use other information that enables correction of these errors at the decoder. For example, if the encoder has access or can determine a predictive measure, the encoder can determine a coefficient in case an error occurs. The encoder can then send a separate bitstream indicating the location of these errors, so that the decoder can discard these coefficients. Alternatively, the encoder can send corrections for these errors so that the coefficients are not discarded.

  Decryption measurement

Given that, the decoder uses any prior information about x such as side information, prediction, and general model to estimate the signal

Reconfigure.

Reconstruction The goal of the decoder is a signal that agrees with the decoding measurements and follows prior knowledge about the model of x

Is to estimate. For example, conventional models have sparsity or a low total variation norm at some criterion.

  For sparsity models, the reconstruction for the estimate is

Take the form of optimization. Where 0 ≦ p ≦ 1, || · || _p represents the l _p norm, B represents a reference or dictionary in which the signal is assumed to be sparse,

Represents a sparse coefficient containing the signal in reference B.

  Similarly, for the low total variation model, the reconstruction takes the following form.

Where || · || _TV represents the appropriate total variation norm for the signal model.

  In many cases, the optimization can use side information that generates weights for the norm.

Where || · || _{p, v} and || · || _{TV, v} are respectively the weighted l _p and the total variation norm known in the art. The weight v can be derived from the side information or prediction of x. For example, if the prediction is sparse in criterion B, the weight is set so that the sparsity pattern of the reconstructed signal is similar to the sparsity of the criterion using methods well known in the art. Can do.

  If the side information is a similar signal, for example, the recovered signal

Predicted

This similar signal can also be used as a further soft or hard constraint in the above optimization by requiring that it be similar to. This can be done, for example, in the cost function of optimization using methods well known in the art.

Additional penalty factors (soft constraints) such as

Can be enforced using constraints such as (hard constraints).

  In the above optimization, constraints

Is convex,

Can be expressed as or equivalently

Can be expressed as Alternatively, for example, for p> 1,

Or

By imposing penalties on them, they can be relaxed and imposed as soft constraints.

  Other optimizations that can be used include greedy algorithms or convex optimizations.

  In some embodiments, the reconstructed signal

Can be regarded as a new and improved prediction of x, and thus a new and improved prediction of x, resulting in a new and improved decoding measurement, eg, with fewer errors. This time, a new reconstruction with less distortion

Is obtained. This process can be repeated until an end condition is reached, for example, there is no improvement or the improvement is below a predetermined threshold.

  In addition, the reconstructed signal

Once is available, it can be used in conjunction with side information and prediction to further improve the prediction. For example, the dictionary is a reconstructed signal

And prediction signal

And can be used to generate a new prediction of the signal given the side information using methods well known in the art. Here again, an improved prediction is provided that can be used in the same manner as described above to improve the reconstruction. This process can be repeated until there is no improvement or the improvement is below a predetermined threshold.

Generation of side information The side information used in the decoder can come from multiple sources as well as separate bitstreams from the encoder itself. For example, the side information can be a compressed version of the same signal with higher distortion and lower rate, or a compressed version of a different signal that is very similar to the signal being compressed. The side information can also include an amount that improves the prediction of the compressed signal from the signal in the side information, such as the average value of both signals, their variance and their cross correlation. This information can also be determined at the encoder and stored or transmitted along with the universal encoding of the signal.

Compression Method and System FIG. 4 shows details of a system according to one embodiment of the present invention. The encoder 310 acquires the linear measurement value Ax of the input signal 301 and adds the dither w as Ax + w410. Non-monotonic quantization 412 is applied to the universal measurement. Universal measurements can be sent to the decoder 320. This embodiment in FIG. 4 can be used, for example, to compress synthetic aperture radar (SAR) signals, or other radar or light and radar (LIDAR) data. Such data is often used to reconstruct an image through a transformation known as image formation or image reconstruction.

  In this particular embodiment, the encoder may also separately encode the information necessary to generate side information 450. To do this, the encoder can perform non-uniform subsampling 455 and coarse quantization 456. Side information y 319 can also be sent to the decoder for image formation 470, which generates a coarse image prediction that serves as side information 319. The decoder can predict the measurement value Ax + w 410 by applying the data prediction 440 to the side information.

  From the measurements, the decoder recovers the most significant bit (MSB) of quantization 420, thereby recovering the data necessary to perform image formation 430. Image formation can also use prediction data 440.

  FIG. 5 shows details of a system according to another embodiment of the invention. This embodiment can be used to compress signals similar to reference signals such as multispectral images and hyperspectral images. Although this embodiment has been described assuming that the signal is a multi-band image, such as a multi-spectral or hyper-spectral image, other examples are the same obtained by various cameras, among others. It can be a video sequence or image of a scene.

  Here, the encoder generates a reference band and side information 520 that is used by the image prediction 540 and is further described below.

Applications and Protocols Synthetic Aperture Radar (SAR) is a radar system that is often mounted on a satellite or aircraft and is typically used to image large areas with very high resolution. The SAR system operates by emitting a pulse and receiving and recording its reflection. These records are raw SAR data that is later processed to generate a SAR image. This process, known as imaging, requires large computational power and memory that is not available on satellites or aircraft, and is therefore typically performed by powerful computers at ground stations.

  SAR raw data is particularly difficult to compress. This is because at first glance, these appear to lack structure. However, the SAR image has a structure (because it is an image), which can in principle be used for compression. Conventional compression methods or compression methods using side information require that image formation be performed in the encoding stage. This may exceed the computational capability of the encoder in the satellite.

  However, using one embodiment of the present invention, data can be compressed without performing image formation. This is performed during the prediction and reconstruction step at the decoder, usually a powerful ground station. Note that the subsequent description uses the word “transmit” to represent the use of the encoded bitstream. This is because, in typical modern applications, such data is immediately transmitted to the server for decoding and processing at the ground station. Data can also be stored in memory or persistent storage, such as disk or tape, for subsequent retrieval and processing.

  The encoder encodes and transmits data using the protocol described above. Note that the data received by the SAR system is already an image measurement, and the encoding matrix implemented for the encoder can be an identity matrix or a sub-sampling matrix that selects a subset of the data. . On the other hand, an effective coding matrix A is a matrix decomposition implemented using a matrix that describes a linear system from SAR images to SAR data.

  In many SAR systems, the decoder may not have side information from another source. For this reason, the SAR system also generates and transmits side information. In one embodiment, the SAR data is subsampled or measured using a linear system and then quantized using a conventional coarse or uniform quantizer with very few bits. These quantized measurement values are transmitted as side information.

  The decoder uses sparse reconstruction, reconstruction with low total variation, or reconstruction using a dictionary learned from previous SAR data, and an optimization-based reconstruction method to produce a coarse image from the side information. Reconfigure. This coarse image uniformly serves as a prediction for the encoded signal. Thus, the image is used to generate a prediction of the data and follow the decoding protocol described above.

  The SAR data can include data of different polarizations or data collected by different satellites. The present invention can be used to compress this data as well. In some embodiments, data from one polarization or one satellite, or these linear measurements, serve as side information for decoding data from another polarization or another satellite. Can be fulfilled.

Multispectral data and hyperspectral data Similar problems appear in multispectral data or hyperspectral data. This data includes multiple images obtained from the same target, e.g., scene, ground swath or object, each image having a relatively wide range in the case of multispectral and relatively in the case of hyperspectral. Only the reflectivity of the target in a specific spectral band range, which is a narrow range, is recorded. Such systems are often portable and are typically mounted on satellites, aircraft, autonomous airplanes, or ground vehicles that do not have access to large computational resources.

  The main difference between multispectral and hyperspectral data with SAR and other radar data is that multispectral and hyperspectral images are usually acquired directly and no imaging step is required to generate the image. . In other words, the data to be compressed is the image itself.

  Also, conventional compression methods require that prediction and conversion steps be performed at the encoder. When such a system is used in computationally constrained applications, image prediction and transformation can be very complex. Note that in the discussion that follows, the word “transmit” is used to represent the use of the encoded bitstream. This is because in typical modern applications, such data is immediately sent to the server for decoding and processing. However, the data may also be stored in memory or permanent storage, which is a hard drive or tape for later retrieval and processing.

  Again, embodiments of the present invention can be used to efficiently compress such images. The universal encoder protocol operates as described above. For efficiency, the measurement matrix A is for the entire set of images, for a small subset of images, separately for each spectral band, or for each block of images, or a combination thereof. Can act against.

  Side information is also transmitted by the encoder system. In some embodiments, the side information includes a single reference band, which is a single image or a full color image that includes the sum of all images on a satellite, or some other combination of images. can do. This reference band is encoded using an embodiment of the invention or using a separate encoding system such as Joint Photographic Expert Group (JPEG) (ISO / IEC 10918) or JPEG 2000. Since multispectral and hyperspectral images are very similar between bands, the reference band can be used as a prediction of the encoded data.

  On the other hand, in many cases, prediction can be improved using a linear prediction scheme. If y is the criterion and x is predicted, the linear minimum mean square error (MMSE) predictor of x is

Where μ _x and μ _y are the average of x and y, respectively

as well as

Is their variance and σ _xy is their covariance. In the art, methods for extending this prediction to prediction using multiple criteria are simple and well known.

  Since the encoder has access to the reference band, it is easy to determine and transmit the relevant means as side information, variance and covariance for all spectral bands, thereby improving the prediction at the receiver can do. If this is transmitted as side information, the receiver uses the side information to improve the prediction of each spectral band from the reference band. In some embodiments, these quantities can be determined, transmitted, and used in a portion of an image, such as a block, to further improve performance, so that local statistics of the image are more predictable. It is used well.

  Furthermore, as described above, the encoder in this case has a function of determining simple prediction of a signal using side information, and thus can detect when a decoding error occurs. is there. Thus, the encoder can send the position as separate side information and can be the magnitude of these errors, which can correct these errors at the decoder.

  Of course, as more side information is determined and transmitted, the rate consumed by the side information increases. Increasing the rate used for side information can improve prediction, which reduces the rate required for universal coding. On the other hand, there is a gradual return, that is, the gain decreases. For this reason, the amount and rate required for side information should be balanced with the rate required for universal coding.

  The decoder uses side information to predict one or more spectral bands, and then uses coding to reconstruct the image. If a subset of spectral bands has already been decoded, the subset can be used to improve the prediction of subsequently decoded spectral bands, which improves decoding performance. As explained above, reconstruction can be used to generate new side information as a new prediction, thereby repeating the process and further improving decoding performance. Dictionary learning techniques can also be used as described above.

Multispectral image compression using universal vector quantization Some embodiments are based on the realization that scalar quantization can be generalized to vector quantization. Thereby, the compression efficiency of scalar quantization can be further improved. To that end, in some embodiments, the encoding reuses quantization labels to label multiple quantization cells and uses side information to select the correct cells at the decoder. The image can be reconstructed using weighted total variation minimization, incorporating side information into the weights, while enforcing consistency with the restored quantized cells.

  Indeed, one embodiment uses the correlation between spectral bands to reduce the bit rate while maintaining low complexity at the encoder. Correlation is utilized at the decoder. The decoder is designed to extend and decode the bitstream using information from the previously decoded spectral band as side information. Decoding and restoring the image requires solving the sparse optimization problem. This can be regarded as a quantized compressed sensing (CS) problem.

  Some embodiments can be based on the recognition that lightweight encoders can be designed using CS, but the most significant bit (MSB) encodes redundant information and is therefore not rate efficient. Universal quantization removes redundancy by eliminating the MSB. However, this makes the reconstruction problem non-convex, possibly with combinatorial complexity. Generalization to vector quantization further exacerbates the problem.

  As a workaround, some embodiments use side information to make the reconstruction convex and manageable without compromising rate efficiency. In particular, similar to the principle of distributed coding, in one embodiment, the encoder has information about how to refine the prediction from the side information, i.e. the relative location of the compression measurements of the signal relative to those predictions. Send only. For this reason, the decoder generates a convex quantized cell to which the measurement value belongs using prediction and decodes the signal using the measurement value in the cell using a sparse restoration algorithm. In addition, the decoder uses the side information to bias the decompression algorithm closer to the solution that is closer to the encoded signal.

FIG. 6 shows a schematic diagram of a map 610 of encoded value spaces used by encoder 620 and decoder 630, according to some embodiments. The map 610 includes a plurality of cells, for example, 611, 612, and 613, that divide the encoded value space. In this example, space is multi-dimensional, i.e., a two-dimensional over the value of x ₁ and x _2. The dimension of the space can vary for different embodiments. The space is divided so that each cell surrounds a cluster of coded values and the cluster of coded values is quantized into quantized coded values. For example, cell 613 surrounded, i.e., quantized, a subset of consecutive values. Each cell is identified by a label selected from a finite alphabet, so that multiple cells in the map are identified by the same label, and the cell has a common pair of cells identified by the same label Labeled so as not to share the boundaries of

  For example, in FIG. 6, cells are labeled with integers 1, 2, 3,... N, where N is a finite number. On the other hand, different embodiments may use different values. For example, one embodiment labels cells with letters of the alphabet “a, b, c, etc.”. The value of the number N is usually low and can depend on the space dimension D of the coded values. For example, N can be equal to D + 1, but other values are possible. A low value of N helps to improve the compression ratio. Due to the low value of N, different cells may have the same label. For example, cells 611 and 613 have the same label “2”. In order to disambiguate cells having the same label, one embodiment labels the cells such that pairs of cells identified by the same label do not share a common boundary.

  In different embodiments, the cells can have different shapes. For example, in the two-dimensional example of FIG. 6, the cell has a hexagonal shape that is more effective in dividing the two-dimensional space. In an alternative embodiment, the cell has a rectangular shape that is more easily used for partitioning.

  The encoder encodes the value 622 and locates the cell that surrounds the encoded value on the map 610. In this example, the encoder selects cell 624 having label “0” and transmits label “0” to decoder 630. The decoder 630 predicts an encoded value using the side information (632). Such a predicted value is different from the encoded value. The label of the cell 633 on the map 610 surrounding the predicted value 632 is “1”, which is different from the transmission value of the label “0”. For this purpose, the decoder selects the cell closest to the predicted value 632 having the transmission label “0”. This is cell 634 in this example. Cell 634 surrounds the subset of continuous values, i.e., quantizes the subset of continuous values into quantized values. Such a quantized value for cell 634 is the decoded value determined by decoder 630.

  FIG. 7 illustrates a block diagram of an encoder that communicates with a decoder to perform encoding and / or decoding in accordance with the principles of some embodiments. The encoder 720 includes a processor that determines an encoded value and a memory 724 that stores a map 710 of the multi-dimensional space of the encoded value. The map 610 includes a plurality of cells that divide the multidimensional space, and each cell surrounds a cluster of coded values, and the cluster of coded values is quantized into a quantized coded value. Here, each cell is identified by a label selected from a finite alphabet so that multiple cells in the map are identified by the same label, and the cells are bounded by a common pair of cells identified by the same label Will not be shared. The encoder determines a cell 750 that surrounds the encoded value on the map in the multidimensional space, and transmits the label 740 of the cell 750 to the decoder 730 using the transmitter 722.

  Similarly, the decoder 730 includes a receiver 732 for receiving the label 740 from the encoder 720 and a memory 734 for storing the map 710. The decoder also includes a processor 736 that estimates the encoded value using the side information, generates an estimate of the encoded value, and is identified by a label received on the map in the multidimensional space. The cell closest to the estimated value of the quantized value is selected, and the encoded value is determined as the quantized encoded value of the selected cell.

  As used herein, the term processor refers to a single core microprocessor, multi-core microprocessor, computing cluster, field programmable gate array (FPGA), application specific integrated circuit (ASIC), or a combination thereof. It is understood to encompass any number of other configurations including. The memory may include random access memory (RAM), read only memory (ROM), flash memory or any other suitable memory (including storage) system, and be a non-transitory computer-readable storage medium Can do. As used herein, the term “non-transitory computer readable storage medium” includes volatile memory (eg, DRAM and SRAM) and non-volatile memory (eg, flash memory, magnetic memory and optical memory). It is understood to exclude transient signals.

  FIG. 8A shows a block diagram of a method for encoding a value according to some embodiments. The steps of the method are performed by the processor of the encoder. The encoder encodes the value (810), generates an encoded value 815, and selects a cell 750 on the map 710 that surrounds the encoded value 815 (820). The encoder selects a cell label 740 (830) and transmits the selected label (840).

  FIG. 8B shows a block diagram of a method for decoding encoded values, according to some embodiments. The steps of the method are performed by the processor of the decoder. The decoder estimates the transmitted encoded value (850) and generates an estimated value 845. The estimation is performed using side information 847 such as a statistical similarity measure of the signal reconstructed by the decoder. The decoder receives the transmitted label 740 (860) and selects, on the map 710, the cell 875 that is closest to the estimated value 845 among the cells having the label 740 (870). The decoder selects the quantized value of the cell 875 as the decoded value.

For example, some embodiments use a D ₃ lattice and the quantization level of the vector y is

Is calculated using Where D ₃ (•) is a D ₃ lattice quantizer that performs operations on the triples in its argument, Δ is a scaling factor, and w is an optional extracted uniformly across the canonical quantization cell. Dither, mod is taken separately along each of the three coordinates. D ₃ Voronoi region of the lattice quantizer is dodecahedron, to form a space filling packing in 3D. mod function is reused quantization labels, it centers with the same label, to ensure that it has an offset equal to an integer multiple of Delta] 2 ^B along each coordinate.

  In various embodiments, the decoder can have access to side information, eliminate ambiguity resulting from label reuse, and solve the quantized compressed sensing (CS) problem. CS problem is a sparse signal

To consider. The signal is measured using a random projection y = Ax and the detection matrix

By

Is obtained. For natural images, the slope is sparse, ie low total variation (TV) is usually the preferred signal model. Restoration forces the model through TV minimization.

Here, X is a two-dimensional image, x is a vectorized version of the image X, and isotropic TV is defined as follows.

  Using an appropriate detection matrix compared to n required when the signal is not known to be sparse, only m = O (k log n) << n may be used for signal reconstruction. . Here, k measures model sparsity. For this reason, CS acquisition performs implicit compression of the signal being acquired. Multiple matrix configurations can be used, including a fully randomized matrix configuration and a more structured matrix configuration utilizing fast transforms. Fast conversion is attractive for lightweight compression because it significantly reduces memory and computational requirements.

  Although CS is a very effective acquisition technique, it does not function well as a compression method when implemented in a simple manner. In particular, CS-based compression methods suffer from poor rate-distortion performance compared to transform coding, despite large undersampling factors. The reason is basically that CS-based measurements oversample the signal once the sparse pattern is taken into account. To that end, some embodiments combine CS with vector quantization to increase the compression rate of transmission.

  FIG. 9 shows a block diagram of an encoding and decoding architecture that performs compression, according to one embodiment. In this embodiment, the encoding reuses quantization labels to label multiple quantization cells and uses side information to select the correct cell at the decoder. The image is reconstructed using weighted total variation minimization, incorporating side information into the weights while enforcing consistency with the restored quantized cells.

Encoding In some embodiments, the encoder 910 transmits one of the bands 925 of the image 905 as side information 923. Side information 923 can be encoded or compressed using various techniques. This side information can also be combined with further statistics sent by the encoder to predict other bands of the image.

The remaining bandwidth is divided into blocks of all distinct size n _x × n _y. A few random projections

For example, each block using the partial Hadamard matrix A915

I.e., obtained by randomly subsampling the Hadamard transform rows and dither w. According to equation (10), with D ₃ grating having a scaling delta, measured values are quantized by the three in one set (920). When the universal vector quantizer uses a D ₃ lattice, each block of three measurements can be mapped to one of 2 ^3B-1 points. Therefore, every measurement

A bit is needed. Taking into account the subsampling factor, the actual rate is

Bit per pixel (bpp).

Side information 923 is used to predict the original quantized cell at the decoder, thereby eliminating ambiguity arising from mod operations and making consistent reconstruction a convex problem. On the other hand, the prediction may cause an error depending on its quality. A group is affected by a primary error when the error vector has a norm equal to Δ2 ^B , ie when only one of the error vector entries contains any of ± Δ2 ^B. The decoder itself can be robust against some sparse errors, but low quality predictions can cause more errors than the decoder can correct.

  Conveniently, the encoder also has access to other bands and can calculate, encode and transmit (927) additional side information indicating where such errors occur. Thus, the trade-off in designing Δ and B to yield more or less errors now appears as the additional rate required to encode the side information using the error location. . As Δ increases and B increases, the prediction error decreases, so that these reduce the rate for error coding, respectively, in exchange for a larger reconstruction error and a higher universal quantization rate. I need. Correspondingly, the smaller Δ and B are, the lower the reconstruction distortion and the universal quantization rate, respectively, but the higher the rate at which side information about errors is encoded.

  The compromise used by some embodiments is achieved by explicitly encoding the primary error. This is because correction of those errors in the reconstruction program is not very effective due to their small norm. For example, this is done in the following manner. Each group is 0

It has the label which takes the range. The labels of groups exhibiting primary errors are sorted in ascending order and differentially encoded using a universal exponent Golomb code. Since only six types of errors can exist, a code that requires at least log ₂ (6) bits per group is sufficient to distinguish the correct error. For higher order errors, the group label is again the only information coded using the difference exponent Golomb code.

Decoding Decoder 930 has universally quantized CS measurements y _{q available} and p that is their real value prediction 950 obtained from side information 923. For example, prediction 950 can be obtained by first predicting signal x _pred and then measuring (940) using a measurement matrix, ie, p = Ax _pred + w.

  Similarly, in the case of a scalar, the prediction is used to determine the correct Voronoi cell to which the measurement value to be universally quantized belongs before the universal quantization (935). There are several ways to select the closest Voronoi cell that matches the received label and is closest to the predicted measurement. In a preferred embodiment, the prediction p is the closest grid point

Quantized to universal, then universally quantized,

Is obtained. Next, to determine the search area for consistent labels,

Is subtracted from p _q . As shown in FIG. 6 for a 2D lattice, the goal is to select the region that matches the universal quantized measurement and is closest to the prediction. For D ₃ grid 27 near point of which is generated as follows exist.

Here, _{s i} is the element ^{0, 2} B in the three-dimensional vectors are all the possible combinations of -2 ^B.
Finally, the estimated reconstruction point is

And where

It is.

  Depending on the quality of the prediction and the selected values of B and Δ, the frequency of prediction errors may increase or decrease. For this reason, the restored quantized measurement can be modeled as follows.

Here, v is a quantization error, and e is a vector having elements derived from a finite alphabet that is an integral multiple of Δ2 ^B that captures a decoding error.

  Given a good prediction of Δ and an appropriate value, e tends to be group sparse. In addition, the encoder can include information about e that can be used to correct some or all of the errors and reset the corresponding coefficients of e˜0. here,

Represents a set of labels of a group containing known errors that are not corrected, usually of order 2 or higher.

Consistency with the quantized lattice is enforced in the reconstruction problem. On the other hand, the Voronoi region of the D ₃ lattice is a dodecahedron, and decoding can be very complicated. An approximation is therefore used and the dodecahedron is replaced by a sphere of radius Δ.

  To reconstruct the image 960 (970), the decoder uses the reconstructed measurements with the aid of image prediction. In particular, restoration solves weighted TV minimization with consistent reconstruction.

Where WTV (•) is a weighted isotropic total variation,

And f (•) penalizes the decoding error with a penalty having a mixed l ₁ / l ₂ norm due to the group sparsity of the error,

And W _{i, j} is a weight that determines how the gradient at each pixel of the image should be penalized;

Is a set containing the labels of the groups that contain known errors that have not been corrected.

In addition to resolving quantization ambiguity, predictions obtained from side information are also used to derive weights W _{i, j} . A low weight is used when the magnitude of the prediction gradient is greater than a predetermined threshold, and a high weight is used when the gradient is lower and is a setting similar to the weighted l ₁ minimization. The resulting model penalizes more of the edges that are not in the prediction than the edges that are in the prediction. Since predictions are derived from other spectral bands, the model enhances the correlation between spectral bands, especially between edges.

  The function f (•) is

Promote data consistency for portions of data within it, i.e., those portions suspected of having decoding errors. Second order penalties are a more general data consistency penalty, but similar penalties for universal scalar quantizers have allowed some decoding errors to be recovered due to their sparsity. For example, in one embodiment, the penalty is a generalization to a block sparse vector because it is a type of decoding error resulting from vector universal quantization.

  The above-described embodiments of the present invention can be implemented in any of a number of ways. For example, the embodiments can be implemented using hardware, software, or a combination thereof. When implemented in software, the software code may be executed on any suitable processor or collection of processors, whether provided on a single computer or distributed among multiple computers. Such a processor can be implemented as an integrated circuit having one or more processors in an integrated circuit component. However, the processor can be implemented using circuitry in any suitable format.

  For example, one embodiment is implemented using a non-transitory computer readable storage medium embodying a program executable by a processor for performing the method. This method estimates the transmitted encoded value and generates an estimated value. The estimation uses side information and surrounds the estimated value on a map of the encoded value in a multidimensional space. Wherein the map includes a plurality of cells that divide the multi-dimensional space so that each cell surrounds a cluster of encoded values and the cluster of encoded values Is quantized into a quantized encoded value, each cell is identified by a label selected from a finite alphabet, whereby multiple cells in the map are identified by the same label, and the cells are identified by the same label Cell pairs are labeled so that they do not share a common boundary, receive cell labels transmitted over the communication channel, and have transmitted labels on the map. Among that cell, comprising selecting a closest second cell to the first cell, the quantized value of the second cell, and selecting as the decoded value of the signal.

  Also, the embodiments of the invention can be implemented as methods provided with examples. The operations performed as part of this method can be ordered in any suitable manner. Thus, embodiments can be constructed in which the operations are performed in a different order than shown, which includes several operations despite being shown as a series of operations in the exemplary embodiment. Can be included at the same time.

Claims (20)

A memory for storing a map of a space of encoded values, wherein the map includes a plurality of cells that divide the space, whereby each cell surrounds a cluster of encoded values, and the encoded values And each cell is identified by a label selected from a finite alphabet, whereby the plurality of cells in the map are identified by the same label, A memory labeled so that pairs of cells identified by the same label do not share a common boundary;
A receiver for receiving, from an encoder, a label of a cell surrounding an encoded value on the map in a multidimensional space;
Estimate the encoded value using side information, generate an estimate of the encoded value, and identify the estimated value of the encoded value identified by the received label on the map of the space. A processor that selects a near cell and determines the encoded value as the quantized encoded value of the selected cell;
A decoder.   The decoder of claim 1, wherein the space is a multidimensional space.   The decoder of claim 1, wherein the cells are arranged along a regular grid.   The decoder according to claim 1, wherein the space is a two-dimensional space, and each cell in the map has a hexagonal shape.   The decoder according to claim 1, wherein the space is a three-dimensional space, and the cells are arranged along a regular three-dimensional lattice.   The decoder of claim 1, wherein the side information includes a statistical similarity measure of a signal.   The decoder of claim 1, wherein the side information includes corrections for errors generated by determining one or more missing upper bits.   The decoder of claim 7, wherein the correction is determined at an encoder.   The decoder of claim 1, wherein the signal is a multispectral image.   The decoder of claim 1, wherein the signal is acquired by a radar system.   The decoder of claim 10, wherein the radar system is a synthetic aperture radar (SAR) system.   The decoder of claim 1, wherein the encoded value is generated by measuring a signal using a measurement matrix.   The decoder according to claim 12, wherein the encoded value is generated by adding a dither to the measured value of the signal.   The decoder according to claim 12, wherein the signal is reconstructed using the determined encoded value.   The decoder of claim 14, wherein the reconstruction is performed using one or a combination of convex optimization and a greedy algorithm. A method for decoding an encoded value, comprising:
Estimating a transmitted encoded value to generate an estimated value, wherein the estimation uses side information;
Locating the estimated value on a map of a multi-dimensional space of encoded values, wherein the map includes a plurality of cells that divide the multi-dimensional space, whereby each cell is encoded Enclosing a cluster of values, quantizing the cluster of encoded values into a quantized encoded value, wherein each cell is identified by a label selected from a finite alphabet, whereby the plurality of Cells are identified by the same label, and the cells are labeled such that pairs of cells identified by the same label do not share a common boundary;
Receiving a label of a cell transmitted over a communication channel;
Selecting, on the map, a cell closest to the estimated value from among cells having the transmitted label;
Selecting the quantized value of the cell as a decoded value;
Wherein each step of the method is performed by a processor of a decoder.   The method of claim 16, wherein the multi-dimensional space is a two-dimensional space and each cell in the map is a hexagonal shape.   The method of claim 16, wherein the multi-dimensional space is a three-dimensional space, and the cells are arranged along a regular three-dimensional lattice. Reconstructing a signal using the decoded value to promote sparsity of the reconstructed signal, wherein the sparsity is weighted based on the side information;
The method of claim 16, further comprising: A processor for determining an encoded value;
A memory for storing a map of a multidimensional space of encoded values, the map including a plurality of cells dividing the multidimensional space, whereby each cell encloses a cluster of encoded values; Quantizing the cluster of encoded values into quantized encoded values, wherein each cell is identified by a label selected from a finite alphabet, whereby multiple cells in the map are identified by the same label; The memory is labeled such that pairs of cells identified by the same label do not share a common boundary; and
A transmitter for transmitting a label of the cell enclosing the encoded value on the map of the multidimensional space to a decoder;
An encoder.

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