 Karthik Gurumoorthy  Ajit Rajwade  Arunava Banerjee  Anand Rangarajan Department of CISE University of Florida 1

 A new approach to lossy image compression based on machine learning.  Key idea: Learning of Matrix Ortho-normal Bases from training data to efficiently code images.  Applied to compression of well-known face databases like ORL, Yale.  Competitive with JPEG. 2

Vector Conventional learning methods in vision like PCA, ICA, etc. Image 3

Our approach following Rangarajan [EMMCVPR-2001] & Ye [JMLR-2004] Treated as a Image Matrix 4

Image of size divided into N patches of size each treated as a Matrix. Image 5

6 = PUSV U and V: Ortho-normal matrices S: Diagonal Matrix of singular values

7 useful for compression (e.g.: SSVD [Ranade et al- IVC 2007]).

8  Consider a set of N image patches:  SVD of each patch gives:  Costly in terms of storage as we need to store N ortho-normal basis pairs.

 Produce ortho-normal basis-pairs, common for all N patches.  Since storing the basis pairs is not expensive. 9

10 Non-diagonal Non-sparse

 What sparse matrix will optimally reconstruct from ?  Optimally = least error:  Sparse = matrix has at most some non-zero elements. 11

 We have a simple, provably optimal greedy method to compute such a 1. Compute the matrix. 2. In matrix, nullify all except the largest elements to produce. 12

 A set of N image patches.  Learning K << N ortho-normal basis pairs 13 Memberships Projection Matrices

 Input: N image patches of size.  Output: K pairs of ortho-normal bases called as dictionary. 14

 Divide each test image into patches of size  Fix per-pixel average error (say e), similar to the “quality” user-parameter in JPEG. 15

RPP = number of bits per pixel 17

bits 0.92 bits1.36 bits 1.78 bits3.023 bits

 Size of original database is 3.46 MB.  Size of dictionary of 50 ortho-normal basis pairs is 56 KB=0.05MB.  Size of database after compression and coding with our method with e = is 1.3 MB.  Total compression rate achieved is 61%. 19

RPP = number of bits per pixel 20

 New lossy image compression method using machine learning.  Key idea 1: matrix based image representation.  Key idea2: Learning small set of matrix ortho- normal basis pairs tuned to a database.  Results competitive with JPEG standard.  Future extensions: video compression. 21

 A. Rangarajan, Learning matrix space image representations, Energy Minimizing Methods in Computer Vision and Pattern Recognition,  J. Ye, Generalized low rank approximation of matrices, Journal of Machine Learning Research,2004.  M. Aharon, M. Elad and A. Bruckstein, The K-SVD: An algorithm for designing of overcomplete dictionaries for sparse representation. IEEE Transactions on Signal Processing,  A. Ranade, S. Mahabalarao and S. Kale. A variation on SVD based image compression. Image and Vision Computing,

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