CODEWITHSUNDEEP
tensorflowconvolutioncomplex-numbers
notmyname
notmyname

Reputation: 181

Complex convolution in tensorflow

I'm trying to run a simple convolution but with complex numbers:

r = np.random.random([1,10,10,10])
i = np.random.random([1,10,10,10])
x = tf.complex(r,i)

conv_layer = tf.layers.conv2d(
            inputs=x,
            filters=10,
            kernel_size=[3,3],
            kernel_initializer=utils.truncated_normal_complex(),
            activation=tf.nn.sigmoid)

However I get this error:

TypeError: Value passed to parameter 'input' has DataType complex128 not in list of allowed values: float16, float32

Does anyone know how to implement such a convolution in Tensorflow?

Will I need to implement a custom op, or is there some better option here?

Frustratingly, complex matrix multiplication is possible, e.g. the following runs fine: 

def r():
    return np.random.random([10,10])
A = tf.complex(r(),r())
B = tf.complex(r(),r())
C = tf.multiply(A,B)
sess.run(C)

So there's no real reason convolution shouldn't work, I would think (as convolution is essentially just matrix multiplication).

Thanks

Upvotes: 5

Views: 2865

Answers (3)

user3433489
user3433489

Reputation: 989

You can perform complex convolution by breaking up your tensors into real and imaginary parts. If x=a+bi and y=c+di then xy = ac-bd + i*(bc+ad). Similarly, you can break up your tensors into real and imaginary parts and convolve each part separately. Pseudo code:

A_real = tf.math.real(A)
A_imag = tf.math.imag(A)

B_real = tf.math.real(B)
B_imag = tf.math.imag(B)

AB_conv_real = convolve(A_real, B_real) - convolve(A_imag, B_imag) 
AB_conv_imag = convolve(A_real, B_imag) + convolve(A_imag, B_real)

Upvotes: 0

tdMJN6B2JtUe
tdMJN6B2JtUe

Reputation: 428

All complex-valued features are split into either Cartesian (real, imaginary) or polar (modulus, angle) representations. Nobody is really trying to use a single feature that is purely complex; I would love to be proven wrong!

Upvotes: 0

Hossein
Hossein

Reputation: 1

Probably too late but for anyone who still is interested: applying convolutions to complex valued data is not as straightforward as your usual data types, like float32. There are studies that investigat different network structures for this purpose (for example see this link for "Deep Complex U-Net"). There are implementations of these structures in pytorch and tensorflow.

Upvotes: 0

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