Abstract:
This invention relates to a method of increasing spatial/temporal resolution including the steps of (a) providing a current video having an initial temporal/spatial resolution; (b) repeatedly reducing the temporal/spatial resolution of the current video to produce a lowest temporal/spatial resolution current video; (c) increasing the spatial/temporal resolution of the lowest temporal/spatial resolution current video; (d) increasing the spatial/temporal resolution of the next higher temporal/spatial resolution current video; and (e) repeating step (d) up to the initial temporal/spatial resolution.

Description:
CROSS-REFERENCE TO RELATED PATENT APPLICATIONS 
       [0001]    This patent application claims priority from and is related to U.S. Provisional Patent Application Ser. No. 61/838,892, filed on Jun. 25, 2013, this U.S. Provisional patent application incorporated by reference in its entirety herein. 
     
    
     TECHNOLOGY FIELD 
       [0002]    The present invention is in the field of image and video processing. 
       BACKGROUND 
       [0003]    Raw video files are huge. For example, an Ultra High Definition (UHD) movie with 120 frames per second (fps), 3840×2160 pixels per frame, 3 colors per pixel, and 16 bits per color, requires bandwidth of:
       3840*2160*120*3*16=47,775,744,000 Bits per sec≈50 Giga bits per sec,
 
equivalent to about 500 high speed (100 Mbps) fiber channels.
       
 
         [0005]    If the movie last for two hours, as usual, it requires storage of:
       47,775,744,000*7,200≈343,985 Giga bits≈45 Tera bytes,
 
equivalent to about 5,000 regular (5 Gbytes) DVD disks.
       
 
         [0007]    Video compression,
       “The art of reducing the video size without affecting its visual quality”, is therefore a necessary tool for any applications that deals with video.       
 
         [0009]    In general, a video consists of several components, such as in the RGB color space or in the YUV color space. However, without loss of generality we consider here only one such component. The generalization to a whole video is discussed in Pat [1]. 
         [0010]    The lattice of integers, Z n , is the set of n tuples of integers in the real Euclidean space of R n . A frame can be viewed as a rectangular grid on the lattice Z 2 , and a video as a cubic grid on Z 3 . A subset of a lattice, which is itself a lattice, is called a sub-lattice, see Ref [1]. Examples of sub-lattices of Z 2  are given in  FIG. 1 . The two Quincunx sub-lattices are given in unit  110 . The white circled points constitute the even sub-lattice and the dark circled points the odd sub-lattice. The four Dyadic sub-lattices are similarly given in unit  120 . A dilation matrix is associated with the sub-lattices, see unit  115  for the Quincunx case and unit  125  for the Dyadic case. Note further that the number of possible sub-lattices is determined by the determinant of the corresponding dilation matrix. 
         [0011]    Down-sampling refers to the process of extracting a sub-lattice from a given lattice. For example, we show Dyadic down sampling in  FIG. 2 . The input signal is shown in unit  210 . A temporal down sampling is shown in unit  220 , and a spatial down sampling in unit  230 . A combined temporal and spatial down sampling is shown in unit  240 . 
         [0012]    A Generic Video Codec, as depicted in  FIG. 3 , consists of the following:
       1. The Encoder:
           The input video is denoted by Y, and the output encoded video by Y′.   
           2. The Bit Stream:
           The Bit Stream is the encoded video Y′.   Depending on the application, it is either transmitted or stored on disk.   
           3. The Decoder:
           The input to the Decoder is the Bit Stream, and the output decoded video is denoted by Ŷ.   
               
 
         [0020]    See Pat [1] for more details. 
       SUMMARY 
       [0021]    According to a first aspect of the present invention there is provided a method of increasing spatial resolution, comprising: a. providing a current video having an initial temporal resolution; b. repeatedly reducing the temporal resolution of the current video to produce a lowest temporal resolution current video; c. increasing the spatial resolution of said lowest temporal resolution current video; d. increasing the spatial resolution of the next higher temporal resolution current video; and e. repeating step (d) up to the initial temporal resolution. 
         [0022]    The current video in step (a) may comprise a spatially reduced video of an original video; step (b) may be performed on both said current video and said original video; and steps (c) and (d) may further comprise calculating enhancement data and using said enhancement data to enhance the increased spatial resolution of the current video, said calculating may comprise using the respective reduced temporal resolution original video. 
         [0023]    The method may comprise a method of video compression, wherein the current video may comprise an already decoded spatially reduced video of the original video; wherein said operations on the original video may be performed in an encoder; said calculating enhancement data may be performed in the encoder; said enhancement data may be provided from said encoder to a decoder; and said using the enhancement data may be performed in both the encoder and the decoder. 
         [0024]    The enhancement data may be provided in a compressed mode. 
         [0025]    Calculating enhancement data may comprise comparing the increased spatial resolution current video with the respective reduced temporal resolution original video. The method may further comprise, before reducing in step (b), temporally blurring the current video. 
         [0026]    Step (d) may further comprise temporally deblurring said current video. 
         [0027]    The deblurring may be performed after increasing the spatial resolution of the next higher temporal resolution current video. 
         [0028]    According to a second aspect of the present invention there is provided a method of increasing temporal resolution, comprising: a. providing a current video having an initial spatial resolution; b. repeatedly reducing the spatial resolution of the current video to produce a lowest spatial resolution current video: c. increasing the temporal resolution of said lowest spatial resolution current video; d. increasing the temporal resolution of the next higher spatial resolution current video; and e. repeating step (d) up to the initial spatial resolution. 
         [0029]    The current video in step (a) may comprise a temporally reduced video of an original video; step (b) may be performed on both said current video and said original video; and steps (c) and (d) may further comprise calculating enhancement data and using said enhancement data to enhance the increased temporal resolution of the current video, calculating may comprise using the respective reduced spatial resolution original video. The method may comprise a method of video compression, wherein said current video may comprise an already decoded temporally reduced video of the original video; wherein said operations on the original video may be performed in an encoder; said calculating enhancement data may be performed in the encoder; said enhancement data may be provided from said encoder to a decoder; and said using the enhancement data may be performed in both the encoder and the decoder. 
         [0030]    The enhancement data may be provided in a compressed mode. 
         [0031]    Calculating enhancement data may comprise comparing the increased temporal resolution current video with the respective reduced spatial resolution original video. The method may further comprise, before reducing in step (b), spatially blurring the current video. 
         [0032]    Step (d) may further comprise spatially deblurring said current video. 
         [0033]    The deblurring may be performed after increasing the temporal resolution of the next higher spatial resolution current video. 
         [0034]    According to a third aspect of the present invention there is provided a method of image compression comprising: a. providing an original image having an initial spatial resolution; b. repeatedly reducing the spatial resolution of said original image to produce a lowest spatial resolution original image; c. providing a lowest spatial resolution current image from said lowest spatial resolution original image; d. increasing the spatial resolution of the current image to the next higher spatial resolution of the original image; and e. repeating step (d) up to the initial spatial resolution of the original image; wherein said step (d) may further comprise calculating enhancement data and using said enhancement data to enhance the increased spatial resolution of the current image, said calculating may comprise using the respective reduced spatial resolution original image, wherein said operations on the original image may be performed in an encoder; said lowest spatial resolution current image may be provided from said encoder to a decoder; said calculating enhancement data may be performed in the encoder; said enhancement data may be provided from said encoder to a decoder; and said using the enhancement data may be performed in both the encoder and the decoder. 
         [0035]    The lowest spatial resolution current image may be provided in a compressed mode. The enhancement data may be provided in a compressed mode. 
         [0036]    Calculating enhancement data may comprise comparing the increased spatial resolution current image with the respective reduced spatial resolution original image. The method may further comprise, before reducing in step (b), spatially blurring the original image. 
         [0037]    Step (d) may further comprise spatially deblurring said current image. 
         [0038]    The deblurring may be performed after increasing the spatial resolution of the current image. 
         [0039]    According to a fourth aspect of the present invention there is provided a method of no latency video compression. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0040]      FIG. 1  depicts Quincunx and Dyadic sub-lattices and dilation matrices; 
           [0041]      FIG. 2  depicts Dyadic down samplings; 
           [0042]      FIG. 3  is a diagram of a Generic Video Codec; 
           [0043]      FIG. 4S  is a diagram of the spatial resolution increase of the video; 
           [0044]      FIG. 4T  is a diagram of the temporal resolution increase of the video; 
           [0045]      FIG. 5  is a diagram of the Single Image Encoder Raise Algorithm; 
           [0046]      FIG. 6  is a diagram of the Single Image Decoder Raise Algorithm; 
           [0047]      FIG. 7  is a diagram of a Specific Single Image Encoder Raise Algorithm; 
           [0048]      FIG. 8  is a diagram of a Specific Single Image Decoder Raise Algorithm; 
           [0049]      FIG. 9  is a diagram of the No Latency Video Encoder; 
           [0050]      FIG. 10  is a diagram of the No Latency Video Decoder; 
           [0051]      FIG. 11  is a diagram of the No Latency Encoder Raise Algorithm; 
           [0052]      FIG. 12  is a diagram of the No Latency Decoder Raise Algorithm; 
           [0053]      FIG. 13  is a diagram of a Specific No Latency Encoder Raise Algorithm; 
           [0054]      FIG. 14  is a diagram of a Specific No Latency Decoder Raise Algorithm; 
           [0055]      FIG. 15  is a diagram of the Multi Frame Video Codec; 
           [0056]      FIG. 16  is a diagram of the Multi Frame Encoder Raise Algorithm; 
           [0057]      FIG. 17  is a diagram of the Multi Frame Decoder Raise Algorithm; 
           [0058]      FIG. 18  is a diagram of a Specific Temporal Multi Frame Encoder Raise Algorithm; 
           [0059]      FIG. 19  is a diagram of a Specific Temporal Multi Frame Decoder Raise Algorithm. 
           [0060]      FIG. 20  is a diagram of a Specific Spatial Multi Frame Encoder Raise Algorithm; and 
           [0061]      FIG. 21  is a diagram of a Specific Spatial Multi Frame Decoder Raise Algorithm. 
       
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
       [0062]    The present invention provides a new algorithm for the Raise operation as described in Pat [1], namely, the respective one stage of the spatial-temporal resolution increase of the video. The Raise operation is performed at both the Encoder and Decoder. The Encoder simulates the Raise operation of the Decoder and sends additional details if needed. 
         [0063]    The new Raise algorithm gives rise to new image and video compression codecs with many fundamental advantages over the current state of the art image and video codecs. Namely:
       1. The Decoder performs the Oracle operation of the Raise algorithm without the need for supplementary information such as motion vectors.   2. Because there is no need to receive supplementary information from the Encoder, the compression factors improve significantly.   3. The Codec can work on the pixel level, so as to achieve the best compression results. In contrast, mpeg is forced to use varying block size.   4. Because we work on the pixel level, we do not get the annoying blocking artifacts that are common to the mpeg standard.   5. The Decoder can use more advanced methods such as optical flows to detect complex motions such as zoom and rotation. In contrast, mpeg uses block matching algorithm that only detect translations.   6. The Decoder can also use more advanced spatial prediction methods, such as edge detection methods. This is not possible with mpeg.   7. The Codec can use SIMD (single instruction multiple data) processing hardware such as GPUs to accelerate the computation as opposed to mpeg where SIMD is nearly impossible.   8. Because we can use SIMD hardware we can design better compression algorithms, trading processing power for compression factors. This is not possible with mpeg, where the need to send supplementary information rules out any real improvement in compression.       
 
         [0072]      FIG. 4S  is a flowchart of the Raise algorithm for the spatial resolution increase of the video. In step  410 , the initial temporal resolution of the video is repeatedly decreased, until we reach some given lowest temporal resolution video. In step  420 , the spatial resolution of this given lowest temporal resolution video is then increased using an Oracle algorithm. In the Oracle algorithm we first analyze the lowest temporal resolution video both temporally and spatially. In terms of the temporal analysis we compute the temporal motion field of the would-be increased spatial resolution video. Similarly, in terms of the spatial analysis, we compute the spatial geometrical structure of the would-be increased spatial resolution video. Finally, we predict the increased spatial resolution video using that spatial and/or temporal information. We stress that the Oracle algorithm reconstructs the higher spatial resolution video of the given lowest temporal resolution video, without receiving any supplementary information from the Encoder. Once this is done, the Encoder may decide that some additional details should be sent to the Decoder in order to enhance the quality of the predicted increased spatial resolution video. In step  430 , these missing details are then added to the reconstructed video. In step  440 , the opposite operation to step  410  is performed. Namely, the temporal resolution of the video is repeatedly increased. This is done using the following sub-steps:
       In sub-step  441  the spatial resolution of the next higher temporal resolution video is increased using an Oracle algorithm as discussed in Step  420 . Here, we stress again that the Oracle algorithm prediction is performed without receiving any supplementary information from the Encoder.   Once this is done, the Encoder may decide that some additional details should be sent to the Decoder in order to enhance the quality of that predicted increased spatial resolution video. In sub-step  442 , these missing details are then added to the reconstructed higher spatial resolution video.       
 
         [0075]    The above two sub-steps are repeatedly performed until we reach the initial temporal resolution of step  410 . Note, however, that by this time, the spatial resolution of the whole video has been increased. 
         [0076]    The Raise algorithm for the temporal resolution increase is very similar. We only have to interchange the terms spatial and temporal in  FIG. 4S  to get  FIG. 4T . Here, in step  460 , the initial spatial resolution of the video is repeatedly decreased, until we reach some given lowest spatial resolution video. In step  470 , the temporal resolution of the given lowest spatial resolution video is increased. As above, in the Oracle algorithm we first analyze the lowest spatial resolution video both temporally and spatially. In terms of the temporal analysis we compute the temporal motion field of the would-be increased temporal resolution video. Similarly, in terms of the spatial analysis, we compute the spatial geometrical structure of the would-be increased temporal resolution video. 
         [0077]    Finally, we predict the increased temporal resolution video using that temporal and/or spatial information. We stress again that that prediction is done without receiving any supplementary information from the Encoder. The Encoder may then decide that some additional details should be sent to the Decoder in order to enhance the quality of the predicted increased temporal resolution video. In step  480 , these missing details are then added to the reconstructed video. In step  490 , the opposite operation to step  460  is performed. Namely, the spatial resolution of the video is repeatedly increased, using the following sub-steps:
       In sub-step  491 , the temporal resolution of the next higher spatial resolution video, is increased using an Oracle algorithm as discussed in Step  470 . Here, we stress again that the Oracle algorithm prediction is performed without receiving any supplementary information from the Encoder.   Once this is done, the Encoder may decide that some additional details should be sent to the Decoder in order to enhance the quality of that predicted increased temporal resolution video. In sub-step  492 , these missing details are then added to the reconstructed higher temporal resolution video.       
 
         [0080]    The above two sub-steps are repeatedly performed until we reach the initial spatial resolution of step  460 . As above, by this time, the temporal resolution of the whole video has been increased. 
         [0081]    The present invention is also useful in many other image and video applications such as super-resolution, image matting and compositing, hole filling, image stitching, 3D reconstruction, in-painting, recognition, and more, see Ref [4]. For example, if we omit step  430  and sub-step  442  from  FIG. 4S , we get an algorithm for the spatial super resolution increase of videos. Similarly, if we omit step  480  and sub-step  492  from  FIG. 4T , we get an algorithm for the temporal super resolution increase of videos. 
         [0082]    In what follows, we proceed to describe the new Raise algorithm in terms of the following use cases: single image compression, no latency video compression, and multi frame video compression. 
       Use Case 
     The Single Image Codec 
       [0083]    The present invention also applies to the compression of single images, where the Raise algorithm may be viewed as the temporal resolution increase of a video with no frames. The Raise algorithm is depicted in  FIG. 5  and  FIG. 6 . After reviewing the main stages we proceed to describe a specific Raise implementation. 
       The Single Image Encoder Raise Algorithm 
     FIG.  5   
     Stage I 
       [0084]    Step 1: Let Y be the input image. Then apply a two dimensional blur filter to Y and denote the resulting blurred image as B. 
         [0085]    Step 2: Down sample B, and denote the resulting down sampled sub-image as C. For example, down sample by the Quincunx method as depicted in  FIG. 1 , unit  110 . 
         [0086]    Step 3: Recursively encode C into C′ using the current Single Image Encoder Raise algorithm applied to the blurred and down sampled sub-image C. At the lowest level, we reach a sub-image X of lowest resolution. We then encode X using existing image compression methods such as the ones described in Ref [2]. The lowest level by which we end the recursion can be determined in advance or dynamically using rate distortion techniques such as described in Ref [3]. 
         [0087]    Step 4: Put the encoded data C on the Bit Stream. 
       Stage II 
       [0088]    Step 1: Recursively decode C′ into Ĉ, see Step 3 of Stage I above. 
         [0089]    Step 2: Predict the original image Y from Ĉ, using an Oracle method, and denote the result as  Y . For the Oracle method see the detailed description of the invention above. 
         [0090]    Step 3: Decide on the additional details D needed for recovering a good presentation of the original image. For example, the details can be the difference between the original image Y and the predicted one  Y . 
         [0091]    Step 4: Encode the details D using  Y , and denote the result as D′. Here again we use existing two-dimensional compression methods, see Ref [2], Pat [2], and Pat [3]. 
       Stage III 
       [0092]    Step 1: Put the encoded details D′ on the Bit Stream. 
         [0093]    Step 2: Decode {circumflex over (D)} from D′ using  Y , see Step 4, Stage II above. 
         [0094]    Step 3: Reconstruct Ŷ from  Y , and {circumflex over (D)}. For example, if the details were the difference as in Step 3 of Stage II above, then we reconstruct by adding {circumflex over (D)} to  Y . 
       The Single Image Bit Stream 
       [0095]    The Bit Stream consists of the encoded sub-image C′, and the details D′. Since C′ is recursively computed, C′ itself consists of a very low resolution encoded sub-image and the sequence of the corresponding details. 
       The Single Image Decoder Raise Algorithm 
     FIG.  6   
     Stage I 
       [0096]    Step 1: Get C′ from the Bit Stream. 
       Stage II 
       [0097]    Step 1: Recursively decode C′ into Ĉ, see Step 1 of Stage II of the Encoder above. 
         [0098]    Step 2: Predict the original image Y from Ĉ, using an Oracle method, and denote the result as  Y . Note that this is the same Oracle method as in Step 2 of Stage II of the Encoder above. 
       Stage III 
       [0099]    Step 1: Get D′ from the Bit Stream. 
         [0100]    Step 2: Decode {circumflex over (D)} from D′ using  Y . 
         [0101]    Step 3: Reconstruct the decoded image Ŷ from  Y , and {circumflex over (D)}. 
       Example 1 
     A Specific Single Image Raise Algorithm 
     FIGS.  7 ,  8   
       [0102]    In this section we describe one possible implementation of the single image Raise algorithm above. Note however, that many other Encoder/Decoder implementations are possible. In our example, the Oracle predicts an image  B  which is the completion of the sub-image Ĉ to the spatial resolution of the whole image B. More precisely, the pixels in  B  that correspond to the down sampled sub-image Ĉ, are exactly those of Ĉ. Then, the other pixels in  B  are predicted from those of Ĉ. For example, consider the case of the Quincunx down sampling method, where we assume that Ĉ corresponds to the even sub-lattice. Then, the even sub-lattice of  B  is determined by Ĉ, and the odd sub-lattice is predicted from this. Many image processing tools, such as edge detection methods can be used for this purpose, see for example Ref [4] and Ref [5]. 
         [0103]    To complete the description of the algorithm, we note that we determine the details D from B and  B , and reconstruct {circumflex over (B)} from {circumflex over (D)} and  B . We finally recover the original image Ŷ by de-blurring the decoded blurred image {circumflex over (B)}. 
       Use Case 
     The No Latency Video Codec 
       [0104]    In the no latency video codec, the video frames are processed one after the other. Namely, at each step we compress the next coming frame given the already compressed video frames. The Raise algorithm in this case amounts to the temporal resolution increase of a video with an additional last frame. The no latency video codec is essential for time-critical applications such as video conferencing and videophone where latency is the most crucial aspect of the system. 
         [0105]    The no latency video compression algorithm consists of the following steps:
       1. We denote the input video frames as: Y=[Y 0 , . . . , Y N ].   2. We start by Encoding/Decoding the first frame Y 0 , using for example the image compression algorithm of the previous section.   3. We denote the decoded first frame by Ŷ 0 .       
 
         [0109]    We now assume by induction that we have already compressed the first k≧1 frames.
       4. Let us denote the first k already decoded frames as:       
 
         [0000]      Ŷ 0   k-1 =[Ŷ 0 , . . . ,Ŷ k-1 ], k=1, . . . , N.
       5. Then, we proceed to Encode/Decode Y k  using Ŷ 0   k-1 , namely, the previously decoded frames.   6. We denote the resulting new decoded frame as Ŷ k .       
 
         [0113]    We apply steps 4-6 above, iteratively, N times, for k=1, . . . , N. 
         [0114]    The No Latency Video Encoder is depicted in  FIG. 9  and the corresponding No Latency Video Decoder is depicted in  FIG. 10 . 
         [0115]    Next, we review the main stages of the no latency Raise algorithm, and proceed to describe a specific no latency Raise implementation. 
       The No Latency Encoder Raise Algorithm 
     Iteration k=1, . . . , N 
     FIG.  11   
     Stage I 
       [0116]    Step 1: Let Y k  denote the input frame, and let Ŷ 0   k-1  denote the first k so far decoded frames. Then, apply two dimensional blur filters to frame Y k , and to frames in Ŷ 0   k-1 . Denote the respective resulting blurred frames by B k , and {circumflex over (B)} 0   k-1 . 
         [0117]    Step 2: Down sample B k  and denote the resulting down sampled frame as C k . Similarly, down sample each frame in {circumflex over (B)} 0   k-1  and denote the resulting down sampled frames as Ĉ 0   k-1 . For example, see the Quincunx method of  FIG. 1 , unit  110 . 
         [0118]    Step 3: We apply the current No Latency Encoder Raise algorithm recursively to the blurred and down sampled sub-frame C k  using the blurred and down sampled decoded sub-frames Ĉ 0   k-1 , and denote the result as C′ k . At the lowest level, we reach a sub-frame X k  and decoded sub-frames {circumflex over (X)} 0   k-1  of lowest resolution. We then encode X k  using existing image compression methods such as described in Ref [2]. Alternatively, we can apply the following algorithm:
       Predict X k  from {circumflex over (X)} 0   k-1  and denote the predicted frame by  X   k . This can be done using known frame extrapolation methods, see for example Ref [4].   Determine the additional details {tilde over (X)} k  needed to recover X k . For example this could be the difference {tilde over (X)} k =X k − X   k .   Encode {tilde over (X)} k  using existing two dimensional methods, see Ref [2] and Pat [3]. We denote the resulting encoded data by {tilde over (X)}′ k .       
 
         [0122]    The lowest level by which we end the recursion can be determined in advance or dynamically using rate distortion techniques such as described in Ref [3]. 
         [0123]    Step 4: Put the encoded C′ k  on the Bit Stream. 
       Stage II 
       [0124]    Step 1: Recursively decode C′ k  into Ĉ k  using Ĉ 0   k-1 , see Step 3 of Stage I above. 
         [0125]    Step 2: Predict the original frame Y k  from Ĉ k  and Ŷ 0   k-1 , using an Oracle method, and denote the resulting frame as  Y   k . For the Oracle method, see the detailed description of the invention above. 
         [0126]    Step 3: Decide on the additional details D k  needed for recovering a good presentation of the original frame from Y k  and  Y   k  using Ŷ 0   k-1 . For example, the details can be the difference between the original frame and the predicted one  Y   k . 
         [0127]    Step 4: Encode the details D k  using Ŷ 0   k-1  and  Y   k  and denote the result by D′ k . Here again we use existing two dimensional compression methods, see Ref [2], Pat [2], and Pat [3]. 
       Stage III 
       [0128]    Step 1: Put the encoded data D′ k  on the Bit Stream. 
         [0129]    Step 2: Decode {circumflex over (D)} k  from D′ k  using Ŷ 0   k-1  and  Y   k , see Step 4, Stage II above. 
         [0130]    Step 3: Reconstruct Ŷ k  from  Y   k , and {circumflex over (D)} k  using Ŷ 0   k-1 . For example, if the details were the difference as in Step 3 of Stage II above, then we reconstruct by adding {circumflex over (D)} k  to  Y   k . 
       The No Latency Video Bit Stream 
     Iteration k=1, . . . , N 
       [0131]    The Bit Stream consists of the encoded sub-frame C′ k , and the details D′ k . Since C′ k  is recursively computed, C′ k  itself consists of a very low resolution encoded sub-frame and the sequence of the corresponding details. 
       The No Latency Decoder Raise Algorithm 
     Iteration k=1, . . . , N 
     FIG.  12   
     Stage I 
       [0132]    Step 1: Apply the same two dimensional blur filters, as in Step 1 of Stage I of the Encoder to the frames in Ŷ 0   k-1 . Denote the resulting blurred frames as {circumflex over (B)} 0   k-1 . 
         [0133]    Step 2: Down sample each frame in {circumflex over (B)} 0   k-1 , as in Step 2 of Stage I of the Encoder. Denote the resulting down sampled frames as Ĉ 0   k-1 . 
         [0134]    Step 3: Get the encoded data C′ k  from the Bit Stream. 
       Stage II 
       [0135]    Step 1: Recursively decode C′ k  into Ĉ k  using Ĉ 0   k-1 . 
         [0136]    Step 2: Predict the original frame Y k  from Ĉ k  and Ŷ 0   k-1 , using an Oracle method, and denote the resulting frame as Ŷ k . Note that this is the same Oracle method as in Step 2 of Stage II of the Encoder above. 
       Stage III 
       [0137]    Step 1: Get the encoded details D′ k  from the Bit Stream. 
         [0138]    Step 2: Decode {circumflex over (D)} k  from D′ k , using Ŷ 0   k-1  and  Y   k . 
         [0139]    Step 3: Reconstruct the decoded frame Ŷ k  from  Y   k , and {circumflex over (D)} k  and using Ŷ 0   k-1 . 
       Example 2 
     A Specific No Latency Raise Algorithm 
     FIGS.  13 ,  14   
       [0140]    In this section we describe one possible implementation of the No Latency Raise algorithm above. Note however, that many other implementations are possible. 
         [0141]    In our example, the Oracle method predicts the frame  B   k  which is the completion of the sub-frame Ĉ k  to the spatial resolution of the whole frame B k . More precisely, the pixels in  B   k  that correspond to the down sampled sub-frame Ĉ k , are exactly those of Ĉ k . Then, the other pixels in  B   k  are predicted from those of Ĉ k , and the previously decoded blurred frames {circumflex over (B)} 0   k-1 . We call the missing pixels the new pixels. In our example, we further assume for simplicity, that Ĉ k  correspond to the even-quincunx sub-lattice as in Example 1 above. 
       Spatial Prediction 
       [0142]    In spatial prediction, we predict the new pixels in  B   k  using the pixels in Ĉ k . This can be done using the methods described in Example 1 above. We denote this completed whole frame by  B   k   s , with pixels values denoted as  b   i,j,k   s  Note that the pixel values corresponding to the sub-lattice Ĉ k  remain unchanged. 
       Temporal Prediction 
       [0143]    In temporal prediction, we predict the new pixels in  B   k  using the previously decoded frames {circumflex over (B)} 0   k-1 . In what follows we describe a simple block matching algorithm for that purpose. Note however, that many other implementations are possible. 
       Block Construction 
       [0144]    Given a new pixel  b   i,j,k  meaning a new pixel at row i and column j of  B   k , construct a block  B   i,j,k  consisting of the surrounding nearest neighboring known pixels. For the example above, a block can consists of just the top, right, bottom, and left nearest neighbors of the new pixel. To complete the construction we subtract the average a i,j,k  of the block&#39;s pixels from each pixel in the block. We consider similarly, blocks {circumflex over (B)} m,n,l , in the previously decoded blurred frames {circumflex over (B)} 0   k-1 . Here {circumflex over (B)} m,n,l  denote the block at row m and column n of frame {circumflex over (B)} l  which is the l=0, . . . , k−1 frame in {circumflex over (B)} 0   k-1 . Note that as above, we also subtract the average of this block&#39;s pixels from each pixel in this block. 
       Block Matching 
       [0145]    Given a block  B   i,j,k  find the closest block in the previous frames {circumflex over (B)} l  for l=0, . . . , k−1. For example, we can find the closest {circumflex over (B)} m,n,l  block in the sense of the sum of max absolute difference, see Ref [4]. 
       Prediction 
       [0146]    Let {circumflex over (B)} m,n,l  denote the corresponding matched block of  B   i,j,k . 
         [0147]    Let {circumflex over (b)} m,n,l  be the pixel in {circumflex over (B)} m,n,l  corresponding to pixel {circumflex over (b)} i,j,k  in  B   i,j,k . 
         [0148]    Then  b   i,j,k ={circumflex over (b)} m,n,l +a i,j,k , where a i,j,k  is the respective average computed above, is the temporal prediction of the new pixel at row i and column j of  B   k . 
       The Low Latency Oracle Prediction Method 
       [0149]    For each new pixel at row i and column j of  B   k , we consider both the corresponding spatial prediction value  b   i,j,k   s  and the corresponding temporal prediction value  b   i,j,k   t . We then choose the best one of them, namely, the temporal prediction if the corresponding blocks&#39; difference is below some threshold, or the spatial prediction otherwise. 
         [0150]    To complete the description of the algorithm, we note that we determine the details D k  from B k  and  B   k  using {circumflex over (B)} 0   k-1 . Then, we reconstruct {circumflex over (B)} k  from {circumflex over (D)} k  and  B   k  using {circumflex over (B)} 0   k-1 . Finally we recover the original image Ŷ k  by de-blurring the decoded blurred frame {circumflex over (B)} k . 
       Use Case 
     The Multi Frame Video Codec 
       [0151]    In the multi frame video codec the video frames are processed in blocks, for example, blocks corresponding to the respective cuts of the video, see Pat [1]. We then process each such block of frames independently and in parallel. In this section, we therefore consider the video to be simply that corresponding block of frames. The multi frame video codec is useful for applications that do not require real-time interaction such as Video On Demand (VOD) and DVD. 
         [0152]    The multi frame video codec, see  FIG. 15 , consists of the following stages: 
       Stage I 
     The Shrink Operation 
       [0153]    Let us denote by Y the input video, and choose an axis, space or time. Then we blur Y along the corresponding axis direction and denote the blurred video as P. We then accordingly down sample P to get Q. For example, if the axis is temporal, down sampling may be the act of removing every other frame of the video, see  FIG. 2 . Similarly, if the axis is spatial, down sampling may be the act of removing the odd Quincunx sub-lattice from every frame, see  FIG. 1 . 
       Stage II 
     The Encode/Decode Operation 
       [0154]    We recursively encode Q to get Q′, and then recursively decode Q′ into {circumflex over (Q)}. See Pat. 1 for more details. 
       Stage II 
     The Raise Operation 
       [0155]    The Raise algorithm is the multi level resolution increase of {circumflex over (Q)} to the resolution of the input video Y. 
         [0156]    In this section, we describe the Raise algorithm for the multi frame video codec. After reviewing the main stages of the Raise Algorithm, we proceed to describe some specific Raise implementations. 
       The Multi Frame Encoder Raise Algorithm 
     FIG.  16   
     Stage I 
       [0157]    Step 1: Set the axis direction to be the complement to the respective Shrink axis direction. Namely, if the respective Shrink axis was Space, then axis is Time and vice versa. 
         [0158]    Step 2: Let R denotes the complement of Q in P, see  FIG. 15 . For example, if down sampling was the act of removing every other frame of the video, then R is that every other removed frame from P. Similarly, if down sampling was the act of removing the odd Quincunx sub-lattice from every frame, then R is that odd Quincunx sub-lattice of each and every frame. 
         [0159]    Step 3: We accordingly apply blur filters to Q to get B Q , to R to get B R , and to {circumflex over (Q)} to get B {circumflex over (Q)} . Note that if the axis is space we apply two dimensional blur filters to each frame, and if the axis is time we apply one dimensional blur filters along the frames&#39; direction. 
         [0160]    Step 4 We accordingly down sample B Q  to get C Q , to B R  to get C R , and to B {circumflex over (Q)}  to get C {circumflex over (Q)} . Note that if the axis is space we spatially down sample each frame, for example, removing the odd Quincunx sub-lattice in each frame, see  FIG. 1 . unit  110 . Similarly, if the axis is time we temporally down sample the frames, for example by removing every other frame, see  FIG. 2 . 
       Stage II 
       [0161]    Step 1: We apply the current multi frame Encoder Raise algorithm recursively to the blurred and down sampled sub-video C R  using C Q , and C {circumflex over (Q)} . and denote the result as C′ R . At the lowest level, we reach sub-videos X R , X Q  and X {circumflex over (Q)}  of lowest respective resolution. We then encode X R  directly using existing video compression method as described in Ref [2]. Alternatively, we can apply the following algorithm:
       Predict X R  from X {circumflex over (Q)}  and denote the predicted video by  X   R . This can be done using known frame interpolation methods, see for example Ref [4].   Determine the additional details {tilde over (X)} R  needed to recover X R . For example this could be the difference {tilde over (X)} R =X R − X   R .   Encode {tilde over (X)} R  using existing video compression methods, see Ref [2] and Pat [3]. We denote the resulting encoded details by {tilde over (X)}′ R .       
 
         [0165]    The lowest level by which we end the recursion can be determined in advance or dynamically using rate distortion techniques such as described in Ref [3]. 
         [0166]    Step 2: Put the encoded video C′ R  on the Bit Stream. 
         [0167]    Step 3: Recursively decode C′ R  into Ĉ R , using C {circumflex over (Q)} , see Step 1 above. 
       Stage III 
       [0168]    Step 1: Predict the original Y from Ĉ R  and {circumflex over (Q)} using an Oracle method, and denote the resulting video as  Y . For the Oracle method see the detailed description of the invention above. 
         [0169]    Step 2: Determine the additional details D needed for recovering a good presentation of the original video from Y and  Y . For example, the details can be the difference between the original video Y and the predicted one  Y . 
         [0170]    Step 3: Encode the details D using  Y  and denote the result by D′. Here, we use existing video compression methods, see Ref [2]. Pat [2], and Pat [3]. 
       Stage IV 
       [0171]    Step 1: Put the encoded data D′ on the Bit Stream. 
         [0172]    Step 2: Decode {circumflex over (D)} from D′ using  Y , see Step 4 of Stage III above. 
         [0173]    Step 3: Reconstruct Ŷ from  Y , and {circumflex over (D)}. For example, if the details were the difference as in Step 3 of Stage III above, then we reconstruct by adding {circumflex over (D)} to  Y . 
       The Multi Frame Video Bit Stream 
       [0174]    The Bit Stream consists of the encoded sub-video C′ R , and the details D′. Since C′ R  is recursively computed, C′ R  itself consists of a very low resolution encoded sub-video and the sequence of the corresponding details. 
       The Multi Frame Decoder Raise Algorithm 
     FIG.  17   
     Stage I 
       [0175]    Step 1: Set the axis direction accordingly, see Step 1 of Stage I of the Encoder. 
         [0176]    Step 2: Accordingly, see Step 3 of Stage I of the Encoder, we apply blur filters to {circumflex over (Q)} to get B {circumflex over (Q)} . 
         [0177]    Step 3: Accordingly, see Step 4 of Stage I of the Encoder, we down sample B {circumflex over (Q)}  to get C {circumflex over (Q)} . 
       Stage II 
       [0178]    Step 1: Get the encoded data C′ R , on the Bit Stream. 
         [0179]    Step 2: Recursively decode C′ R  into Ĉ R , using C {circumflex over (Q)} , see the corresponding step 3 of Stage II of the Encoder. 
       Stage III 
       [0180]    Step 1: Predict the original video Y from Ĉ R  and {circumflex over (Q)} using an Oracle method, and denote the resulting video as  Y . Note that this is the same Oracle method as in Step 1 of Stage III of the Encoder above. 
       Stage IV 
       [0181]    Step 1: Get the encoded data D′ from the Bit Stream. 
         [0182]    Step 2: Decode {circumflex over (D)} from D′ using  Y , see Step 2 of Stage IV of the Encoder above. 
         [0183]    Step 3: Reconstruct Ŷ from  Y , and {circumflex over (D)}, see Step 3 of Stage IV of the Encoder above. 
       Example 3 
     A Specific Temporal Multi Frame Raise Algorithm 
     FIGS.  18 ,  19   
       [0184]    In this section we describe one possible implementation of the temporal multi frame Raise algorithm above. Note however, that many other implementations are possible. 
         [0185]    In our example, the Oracle method predicts the sub-video  B   R  which is the completion of the sub-video Ĉ R , to the spatial resolution of the whole video B R . More precisely, the pixels in  B   R  that correspond to the down sampled sub-video Ĉ R , are exactly those of Ĉ R . Then, the other pixels in  B   R  are predicted from those of Ĉ R , and the previously decoded blurred frames {circumflex over (Q)}. We call the missing pixels the new pixels. In our example, we further assume for simplicity that Ĉ R  correspond to the even-quincunx sub-lattices as in Example 2 above. 
       Spatial Prediction 
       [0186]    In spatial prediction, we predict the new pixels in a given frame of  B   R  using the pixels in the respective sub-frame of Ĉ R . This can be done using the methods described in Example 2 above. 
       Temporal Prediction 
       [0187]    In temporal prediction, we predict the new pixels in a given frame of  B   R  using the previously decoded frames of {circumflex over (Q)}. This is similar to what was done in Example 2 above. However, now we obtain better prediction, since in {circumflex over (Q)} we have both past and future (in time) frames with respect to the predicted frame of B R . 
       The Multi-Frame Oracle Method 
       [0188]    As in Example 2 above, the Oracle prediction is the best prediction among the spatial and temporal predictions. To complete the description of the algorithm, we note that we determine the details D R  from B R  and  B   R  using {circumflex over (Q)}. Then, we reconstruct {circumflex over (B)} R  from {circumflex over (D)} k  and  B   R , using {circumflex over (Q)}. Finally we recover the original image Ŷ by de-blurring the decoded blurred frame {circumflex over (B)} R . 
       Example 4 
     A Specific Spatial Multi Frame Raise Algorithm 
     FIGS.  20 ,  21   
       [0189]    In this section we describe one possible implementation of the spatial multi frame Raise algorithm above. This is very similar to Example 3, only that now the roles of spatial and temporal operations get interchanged. Note however, that many other implementations are possible. 
         [0190]    In our example, the Oracle method predicts the sub-video  B   R  which is the completion of the sub-video Ĉ R , to the temporal resolution of the whole video B R . More precisely, the pixels in  B   R  that correspond to the down sampled sub-video Ĉ R , are exactly those of Ĉ R . Then, the other pixels in  B   R  are predicted from those of Ĉ R , and the previously decoded blurred frames {circumflex over (Q)}. We call the missing pixels the new pixels. In our example, we further assume for simplicity that, Ĉ R  correspond to the every other frame in the video. 
       Spatial Prediction 
       [0191]    This is the same as in Example 3 above. 
       Temporal Prediction 
       [0192]    This is the same as in Example 3 above. 
       The Multi-Frame Oracle Method 
       [0193]    As in Example 3 above, the Oracle prediction is the best prediction among the spatial and temporal predictions. To complete the description of the algorithm, we note that we determine the details D R  from B R  and  B   R  using {circumflex over (Q)}. Then, we reconstruct {circumflex over (B)} R  from {circumflex over (D)} k  and  B   R  using {circumflex over (Q)}. Finally we recover the original image Ŷ by de-blurring the decoded blurred frame {circumflex over (B)} R . 
         [0194]    The following documents are referenced in the application and are all incorporated by reference herein: 
       PATENTS 
       [0000]    
       
         Pat [1] Ilan Bar-On and Oleg Kostenko, A New Algorithm for Video Compression, Pub. No. WO/2014/053982. 
         Pat [2] Ilan Bar-On, Method and Apparatus for a Multidimensional Discrete Multiwavelet Transform, U.S. Pat. No. 8,331,708 B2, Dec. 11, 2012. 
         Pat [3] Ilan Bar-On and Oleg Kostenko, A Method and a System for Wavelet Based Processing, Pub. No. WO/2008/081459. 
       
     
       REFERENCES 
       [0000]    
       
         Ref [1 ]“Multiwavelets in R   n    with an Arbitrary Dilation Matrix ”, C. Cabrelli, C. Heil, and U. Molter, in L. Debnath, Wavelets and Signal Processing, 2002 
         Ref [2 ]“Introduction to Data Compression ” Khalid Sayood, Second Edition, 2000 
         Ref [3 ]“Rate - distortion optimization ”, http://en.wikipedia.org/wiki/Rate-distortion_optimization 
         Ref [4 ]“Computer Vision: Algorithms and Applications ”, Richard Szeliski, 2010. 
         Ref [5 ]“Computer Vision: A Modern Approach ”, David A. Forsyth, Jean Ponce, 2011.