As you noticed, phase is discontinuous function. One can convert this to the continuous function, for example, by using cosine and sine functions, for which interpolation works.
%% generate original phase image
x = -1:0.1:1; % original x-coordinate
y = -1:0.1:1; % original y-coordinate
[X, Y] = meshgrid(x,y);
phase = angle(complex(X,Y)) * 180 / pi;
imagesc(phase);
colormap hsv;
% not-correct
figure,imagesc(imresize(phase, [100,100])),colormap hsv;
% phase is converted by cos and sin.
X = cos(phase/180*pi);
Y = sin(phase/180*pi);
% interpolation
X_interp = imresize(X, [100, 100]);
Y_interp = imresize(Y, [100, 100]);
% re-convert to phase
phase_interp = angle(complex(X_interp,Y_interp)) * 180 / pi;
figure, imagesc(phase_interp), colormap hsv;
hope this helps.
